ALBERT

Beschreibung: 〈p〉Publication date: Available online 1 November 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Complexity〈/p〉 〈p〉Author(s): Robert J. Kunsch, Erich Novak, Daniel Rudolf〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We compute the integral of a function or the expectation of a random variable with minimal cost and use, for our new algorithm and for upper bounds of the complexity, i.i.d. samples. Under certain assumptions it is possible to select a sample size based on a variance estimation, or – more generally – based on an estimation of a (central absolute) 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈mi〉p〈/mi〉〈/math〉-moment. That way one can guarantee a small absolute error with high probability, the problem is thus called solvable. The expected cost of the method depends on the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈mi〉p〈/mi〉〈/math〉-moment of the random variable, which can be arbitrarily large. In order to prove the optimality of our algorithm we also provide lower bounds. These bounds apply not only to methods based on i.i.d. samples but also to general randomized algorithms. They show that – up to constants – the cost of the algorithm is optimal in terms of accuracy, confidence level, and norm of the particular input random variable. Since the considered classes of random variables or integrands are very large, the worst case cost would be infinite. Nevertheless one can define adaptive stopping rules such that for each input the expected cost is finite. We contrast these positive results with examples of integration problems that are not solvable.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Sustainable Cities and Society, Volume 44〈/p〉 〈p〉Author(s): Hye Soo Suh, Daeung Danny Kim〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The study demonstrated a systematic approach to achieve the nearly zero energy community building through the assessment of energy performance of the combined passive and active design solutions and renewable energy systems. Among 16 community buildings, four buildings were selected and the parameters that had an impact on energy consumption were identified through the analysis of electricity and gas consumption. After the validation with the measured data of electricity and gas, the energy simulation was used to model the newly constructed community building. A combined passive and active design strategy was applied to improve the energy performance. To offset the energy use for the domestic hot water, possible renewable energy systems such as the PV system, the solar thermal system, and the geothermal heat pump system were reviewed and their efficiency was analyzed. As a result, the combination of the PV system with additional PV modules and the geothermal system was chosen for the achievement of the nearly zero energy target.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Sustainable Cities and Society, Volume 44〈/p〉 〈p〉Author(s): Zhiqiang John Zhai, Jacob Michael Helman〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Climate change is a widely acknowledged major environmental problem whose impacts on building energy use however are not fully understood. Various climate models have been developed and used to project climate changes; however most of existing studies on climate change impacts only use few model outcomes, providing narrow predictions on the influences. This study analyzed a large number (i.e., 56) of models and scenarios. The obtained future climate data showed a wider range of potential changes and thus impacts on building energy. Four reference climate models were identified to cover the full range of the 56 models for three time periods and seven climate zones. The accuracy of model projections was validated using historical data. The study predicted the potential energy implications of climate changes to a campus building stock. Influences of these changes on utility and economics were analyzed. The study further explored the potential impacts of climate change to the current climate zones that directly relate to building energy consumption.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Sustainable Cities and Society, Volume 44〈/p〉 〈p〉Author(s): Jorge Navarro-Rubio, Paloma Pineda, Antonio García-Martínez〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Eco-efficiency and building optimization potential of prefabricated structures to be used in new buildings are studied, focusing on the analysis of a novel dry precast beam-column connection under different durability and re-using scenarios. The analyses include structural response (via numerical models), optimization potential (material take off, building schedule and economic cost) and environmental impact (via Life Cycle Assessment, LCA). The connection is applied to a case study which is representative of common buildings: a seven-story concrete structure with frames and deck slabs. The structural response of the connection accomplishes the Eurocode safety prescriptions. Man-hours and task duration decrease around 80%, and the global schedule undergoes 60% diminution. Focusing on economic issues, when the prefabricated structural elements are reused the accumulated economic cost significantly decreases. LCA shows that durability, in terms of service life, is directly related to the environmental impact. However, other design options, such us re-using, have less repercussion in the impact categories (i.e. Global Warming Potential and Embodied Energy), and in the global cost. Results from this research could contribute to the implementation of prefabricated elements in the building stock promoting eco-efficiency.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Technological Forecasting and Social Change, Volume 138〈/p〉 〈p〉Author(s): Jae-Woong Min, Nicholas S. Vonortas, YoungJun Kim〈/p〉 〈div xml:lang="en"〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This study explores the factors that contribute to the commercialization of technologies transferred from universities and public research institutes (U&PRIs) to companies. We take a step further than the established literature focusing on technology transfer to examine factors that also affect the chances of the successful commercialization of the transferred technologies through an empirical analysis of 669 technology transfer cases in Korea. The study shows that the intensity of market competition is a key factor in moderating the effects of partnership and absorptive capacity on the successful commercialization of transferred technologies. While collaboration with U&PRIs exerts a positive effect on commercialization success, this effect is weakened by the intensity of market competition. The intensity of market competition boosts the importance of company absorptive capacity for the commercialization success of the transferred technology. We conclude that strategic management of the absorptive capacities of companies and their partnership with U&PRIs are necessary ingredients of the success of technology transfer in concordance with the intensity of competition that the company faces in the market.〈/p〉〈/div〉 〈/div〉

Beschreibung: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers in Industry, Volume 104〈/p〉 〈p〉Author(s): Jacques Bahi, Wiem Elghazel, Christophe Guyeux, Mourad Hakem, Kamal Medjaher, Noureddine Zerhouni〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Monitoring activities in industry may require the use of wireless sensor networks, for instance due to difficult access or hostile environment. But it is well known that this type of networks has various limitations like the amount of disposable energy. Indeed, once a sensor node exhausts its resources, it will be dropped from the network, stopping so to forward information about maybe relevant features towards the sink. This will result in broken links and data loss which impacts the diagnostic accuracy at the sink level. It is therefore important to keep the network's monitoring service as long as possible by preserving the energy held by the nodes. As packet transfer consumes the highest amount of energy comparing to other activities in the network, various topologies are usually implemented in wireless sensor networks to increase the network lifetime. In this paper, we emphasize that it is more difficult to perform a good diagnostic when data are gathered by a wireless sensor network instead of a wired one, due to broken links and data loss on the one hand, and deployed network topologies on the other hand. Three strategies are considered to reduce packet transfers: (1) sensor nodes send directly their data to the sink, (2) nodes are divided by clusters, and the cluster heads send the average of their clusters directly to the sink, and (3) averaged data are sent from cluster heads to cluster heads in a hop-by-hop mode, leading to an avalanche of averages. Their impact on the diagnostic accuracy is then evaluated. We show that the use of random forests is relevant for diagnostics when data are aggregated through the network and when sensors stop to transmit their values when their batteries are emptied. This relevance is discussed qualitatively and evaluated numerically by comparing the random forests performance to state-of-the-art PHM approaches, namely: basic bagging of decision trees, support vector machine, multinomial naive Bayes, AdaBoost, and Gradient Boosting. Finally, a way to couple the two best methods, namely the random forests and the gradient boosting, is proposed by finding the best hyperparameters of the former by using the latter.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: Available online 30 October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Technological Forecasting and Social Change〈/p〉 〈p〉Author(s): Sonal Choudhary, Rakesh Nayak, Sushma Kumari, Homagni Choudhury〈/p〉 〈div xml:lang="en"〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Drawing on theories of acculturation and information diffusion, this paper examines whether social media usage, intergroup contacts and information dissemination influence the cultural adaptation of three ethnic groups, and its implications on sustainable consumption behaviour. Twenty-four semi-structured interviews containing multiple dimensions of social media uses, acculturation, food consumption behaviour, and information diffusion were administered to a sample of Indians (living in the home country), British Indians (living in the host country for more than 10 years) and White British (natives of Britain) users of social media. Our findings suggest that there is a clear link between the integrated strategy of acculturation and information diffusion on social media, which influences acculturation to sustainable food consumption behaviour among social media users. Managerial implications of this research finding are that intervention in information diffusion aids acculturation through the social media, which serves to infuse social media and sustainability strategist with knowledge to best influence the consumers in developing sustainable food consumption behaviour. This research also identifies opportunities to expand this academic research and contribute further to the theories of remote acculturation on which limited research has been done.〈/p〉〈/div〉 〈/div〉

Beschreibung: 〈p〉Publication date: 15 February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 379〈/p〉 〈p〉Author(s): Takashi Shiroto, Naofumi Ohnishi, Yasuhiko Sentoku〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉For more than half a century, most of the plasma scientists have encountered a violation of the conservation laws of charge, momentum, and energy whenever they have numerically solved the first-principle equations of kinetic plasmas, such as the relativistic Vlasov–Maxwell system. This fatal problem is brought by the fact that both the Vlasov and Maxwell equations are indirectly associated with the conservation laws by means of some mathematical manipulations. Here we propose a quadratic conservative scheme, which can strictly maintain the conservation laws by discretizing the relativistic Vlasov–Maxwell system. A discrete product rule and summation-by-parts are the key players in the construction of the quadratic conservative scheme. Numerical experiments of the relativistic two-stream instability and relativistic Weibel instability prove the validity of our computational theory, and the proposed strategy will open the doors to the first-principle studies of mesoscopic and macroscopic plasma physics.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Sustainable Cities and Society, Volume 44〈/p〉 〈p〉Author(s): Fabiana Silvero, Fernanda Rodrigues, Sergio Montelpare, Enrico Spacone, Humberto Varum〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Nowadays, energy efficiency (EE) is presented as a reliable strategy towards sustainable development, but its application has not been developed equitably worldwide, since most EE policies have been implemented in industrialised nations, and developing countries are still in the process of improving their EE levels. This paper provides a contextual framework to analyse the EE situation in countries of Latin American Southern Cone, such as Argentina, Brazil, Chile and Uruguay, with the objective of describing the policies and projects implemented, highlighting the results achieved and outlining the path followed towards EE. A focus was placed on the building sector, where thermal performance standards and the programs to achieve EE in this sector were briefly described. Furthermore, a comparison between these standards was developed, to identify the country with the most demanding standard. As a result, it was found that all the countries are implementing several EE programs and recognising the importance of this issue within their policies. Through this paper, energy policy implications of the region can be identified, which can be useful for energy policymakers of other countries, who are beginning to consider EE policies and can take as an example the path followed by the countries analysed.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers & Geosciences, Volume 122〈/p〉 〈p〉Author(s): Hassan Talebi, Ute Mueller, Raimon Tolosana-Delgado〈/p〉 〈div xml:lang="en"〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Ore deposits usually consist of ore materials with different discrete (e.g. rock and alteration types) and continuous (e.g. geochemical and mineral composition) features. Financial feasibility studies are highly dependent on the modelling of these features and their associated joint uncertainties. Few geostatistical techniques have been developed for the joint modelling of high-dimensional mixed data (continuous and categorical) or constrained data, such as compositional data. The compositional nature of the mineral and geochemical data induces several challenges for multivariate geostatistical techniques, because such data carry relative information and are known for spurious statistical and spatial correlation effects. This paper investigates the application of the direct sampling algorithm for joint modelling of compositional and categorical data. In some mining projects the amount of available data may be enormous in some parts of the deposit and if the density of measurements is sufficient, multivariate geospatial patterns can be derived from that data and be simulated (without model inference) at other undersampled areas of the deposit with similar characteristics. In this context, the direct sampling multiple-point simulation method can be implemented for this reconstruction process. The compositional nature of the data is addressed via implementing an isometric log-ratio transformation. The approach is illustrated through two case studies, one synthetic and one real. The accuracy of the results is checked against a set of validation data, revealing the potential of the proposed methodology for joint modelling of compositional and categorical information. The direct sampling technique can be considered as a smart move to assess the future risk and uncertainty of a resource by making use of all the information hidden within the early data.〈/p〉〈/div〉 〈/div〉

Beschreibung: 〈p〉Publication date: Available online 14 August 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics〈/p〉 〈p〉Author(s): Mehdi Samiee, Mohsen Zayernouri, Mark M. Meerschaert〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present the stability and error analysis of the unified Petrov–Galerkin spectral method, developed in [1], for linear fractional partial differential equations with two-sided derivatives and constant coefficients in any (〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mn〉1〈/mn〉〈mo〉+〈/mo〉〈mi〉d〈/mi〉〈/math〉)-dimensional space-time hypercube, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈mi〉d〈/mi〉〈mo〉=〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo〉,〈/mo〉〈mn〉3〈/mn〉〈mo〉,〈/mo〉〈mo〉⋯〈/mo〉〈/math〉, subject to homogeneous Dirichlet initial/boundary conditions. Specifically, we prove the existence and uniqueness of the weak form and perform the corresponding stability and error analysis of the proposed method. Finally, we perform several numerical simulations to compare the theoretical and computational rates of convergence.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Giovanni Soligo, Alessio Roccon, Alfredo Soldati〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this work, we propose and test the validity of a modified Phase Field Method (PFM), which is specifically developed for large scale simulations of turbulent flows with large and deformable surfactant-laden droplets. The time evolution of the phase field, 〈em〉ϕ〈/em〉, and of the surfactant concentration field, 〈em〉ψ〈/em〉, are obtained from two Cahn–Hilliard-like equations together with a two-order-parameter Time-Dependent Ginzburg–Landau (TDGL) free energy functional. The modifications introduced circumvent existing limitations of current approaches based on PFM and improve the well-posedness of the model. The effect of surfactant on surface tension is modeled via an Equation Of State (EOS), further improving the flexibility of the approach. This method can efficiently handle topological changes, i.e. breakup and coalescence, and describe adsorption/desorption of surfactant. The capabilities of the proposed approach are tested in this paper against previous experimental results on the effects of surfactant on the deformation of a single droplet and on the interactions between two droplets. Finally, to appreciate the performances of the model on a large scale complex simulation, a qualitative analysis of the behavior of surfactant-laden droplets in a turbulent channel flow is presented and discussed.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Sergii V. Siryk〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We provide a careful Fourier analysis of the Guermond–Pasquetti mass lumping correction technique (Guermond and Pasquetti, 2013 [11]) applied to pure transport and convection–diffusion problems. In particular, it is found that increasing the number of corrections reduces the accuracy for problems with diffusion; however all the corrected schemes are more accurate than the consistent Galerkin formulation in this case. For the pure transport problems the situation is the opposite. We also investigate the differences between two numerical solutions – the consistent solution and the corrected ones, and show that increasing the number of corrections makes solutions of the corrected schemes closer to the consistent solution in all cases.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): Adam S. Jermyn〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is actually set not by the rank but by the mutual information amongst the variables in question. Representations such as the tensor tree perform near-optimally when the tree decomposition is chosen to reflect the correlation structure in question, but making such a choice is non-trivial and good heuristics remain highly context-specific. In this work I present two new algorithms for choosing efficient tree decompositions, independent of the physical context of the tensor. The first is a brute-force algorithm which produces optimal decompositions up to truncation error but is generally impractical for high-rank tensors, as the number of possible choices grows exponentially in rank. The second is a greedy algorithm, and while it is not optimal it performs extremely well in numerical experiments while having runtime which makes it practical even for tensors of very high rank.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): Lam H. Nguyen, Dominik Schillinger〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We describe a local iterative corrector scheme that significantly improves the accuracy of the multiscale finite element method (MsFEM). Our technique is based on the definition of a local corrector problem for each multiscale basis function that is driven by the residual of the previous multiscale solution. Each corrector problem results in a local corrector solution that improves the accuracy of the corresponding multiscale basis function at element interfaces. We cast the strategy of residual-driven correction in an iterative scheme that is straightforward to implement and, due to the locality of corrector problems, well-suited for parallel computing. We show that the iterative scheme converges to the best possible fine-mesh solution. Finally, we illustrate the effectiveness of our approach with multiscale benchmarks characterized by missing scale separation, including the microCT-based stress analysis of a vertebra with trabecular microstructure.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): Brody Bassett, Brian Kiedrowski〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The meshless local Petrov–Galerkin (MLPG) method is applied to the steady-state and 〈em〉k〈/em〉-eigenvalue neutron transport equations, which are discretized in energy using the multigroup approximation and in angle using the discrete ordinates approximation. To prevent oscillations in the neutron flux, the MLPG transport equation is stabilized by the streamline upwind Petrov–Galerkin (SUPG) method. Global neutron conservation is enforced by using moving least squares basis and weight functions and appropriate SUPG parameters. The cross sections in the transport equation are approximated in accordance with global particle balance and without constraint on their spatial dependence or the location of the basis and weight functions. The equations for the strong-form meshless collocation approach are derived for comparison to the MLPG equations. The method of manufactured solutions is used to verify the resulting MLPG method in one, two and three dimensions. Results for realistic problems, including two-dimensional pincells, a reflected ellipsoid and a three-dimensional problem with voids, are verified by comparison to Monte Carlo simulations.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: Available online 28 May 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics〈/p〉 〈p〉Author(s): Frederic Gibou, David Hyde, Ron Fedkiw〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present a review on numerical methods for simulating multiphase and free surface flows. We focus in particular on numerical methods that seek to preserve the discontinuous nature of the solutions across the interface between phases. We provide a discussion on the Ghost-Fluid and Voronoi Interface methods, on the treatment of surface tension forces that avoid stringent time step restrictions, on adaptive grid refinement techniques for improved efficiency and on parallel computing approaches. We present the results of some simulations obtained with these treatments in two and three spatial dimensions. We also provide a discussion of Machine Learning and Deep Learning techniques in the context of multiphase flows and propose several future potential research thrusts for using deep learning to enhance the study and simulation of multiphase flows.〈/p〉〈/div〉 〈h5〉Graphical abstract〈/h5〉 〈div〉〈p〉〈/p〉〈/div〉 〈figure〉〈img src="https://ars.els-cdn.com/content/image/1-s2.0-S0021999118303371-gr001.jpg" width="500" alt="Graphical abstract for this article" title=""〉〈/figure〉

Beschreibung: 〈p〉Publication date: Available online 26 October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics〈/p〉 〈p〉Author(s): Xiaodong Liu, Jiguang Sun〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Inverse scattering has been an active research area for the past thirty years. While very successful in many cases, progress has lagged when only 〈em〉limited-aperture〈/em〉 measurement is available. In this paper, we perform some elementary study to recover data that can not be measured directly. In particular, we aim at recovering the 〈em〉full-aperture〈/em〉 far field data from 〈em〉limited-aperture〈/em〉 measurement. Due to the reciprocity relation, the multi-static response matrix (MSR) has a symmetric structure. Using the Green's formula and single layer potential, we propose two schemes to recover 〈em〉full-aperture〈/em〉 MSR. The recovered data is tested by a recently proposed direct sampling method and the factorization method. Numerical results show that it is possible to, at least, partially recover the missing data and consequently improve the reconstruction of the scatterer.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): D. Reiser, J. Romazanov, Ch. Linsmeier〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The problem of constructing Monte-Carlo solutions of drift-diffusion systems corresponding to Fokker–Planck equations with sources and sinks is revisited. Firstly, a compact formalism is introduced for the specific problem of stationary solutions. This leads to identification of the dwell time as the key quantity to characterize the system and to obtain a proper normalization for statistical analysis of numerical results. Secondly, the question of appropriate track length estimators for drift-diffusion systems is discussed for a 1D model system. It is found that a simple track length estimator can be given only for pure drift motion without diffusion. The stochastic nature of the diffusive part cannot be appropriately described by the path length of simulation particles. Further analysis of the usual situation with inhomogeneous drift and diffusion coefficients leads to an error estimate based on particle trajectories. The result for limits in grid cell size and time step used for the construction of Monte-Carlo trajectories resembles the Courant-Friedrichs-Lewy and von Neumann conditions for explicit methods.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Dinshaw S. Balsara, Roger Käppeli〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉The time-dependent equations of computational electrodynamics (CED) are evolved consistent with the divergence constraints on the electric displacement and magnetic induction vector fields. Respecting these constraints has proved to be very useful in the classic finite-difference time-domain (FDTD) schemes. As a result, there has been a recent effort to design finite volume time domain (FVTD) and discontinuous Galerkin time domain (DGTD) schemes that satisfy the same constraints and, nevertheless, draw on recent advances in higher order Godunov methods. This paper catalogues the first step in the design of globally constraint-preserving DGTD schemes. The algorithms presented here are based on a novel DG-like method that is applied to a Yee-type staggering of the electromagnetic field variables in the faces of the mesh. The other two novel building blocks of the method include constraint-preserving reconstruction of the electromagnetic fields and multidimensional Riemann solvers; both of which have been developed in recent years by the first author.〈/p〉 〈p〉The resulting DGTD scheme is linear, at least when limiters are not applied to the DG scheme. As a result, it is possible to carry out a von Neumann stability analysis of the entire suite of DGTD schemes for CED at orders of accuracy ranging from second to fourth. The analysis requires some simplifications in order to make it analytically tractable, however, it proves to be extremely instructive. A von Neumann stability analysis is a necessary precursor to the design of a full DGTD scheme for CED. It gives us the maximal CFL numbers that can be sustained by the DGTD schemes presented here at all orders. It also enables us to understand the wave propagation characteristics of the schemes in various directions on a Cartesian mesh. We find that constraint-preserving DGTD schemes permit CFL numbers that are competitive with conventional DG schemes. However, like conventional DG schemes, the CFL of DGTD schemes decreases with increasing order. To counteract that, we also present constraint-preserving PNPM schemes for CED. We find that the third and fourth order constraint-preserving DGTD and P1PM schemes have some extremely attractive properties when it comes to low-dispersion, low-dissipation propagation of electromagnetic waves in multidimensions. Numerical accuracy tests are also provided to support the von Neumann stability analysis. We expect these methods to play a role in those problems of engineering CED where exceptional precision must be achieved at any cost.〈/p〉 〈/div〉

Beschreibung: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): Yinghe Qi, Jiacai Lu, Ruben Scardovelli, Stéphane Zaleski, Grétar Tryggvason〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In spite of considerable progress, computing curvature in Volume of Fluid (VOF) methods continues to be a challenge. The goal is to develop a function or a subroutine that returns the curvature in computational cells containing an interface separating two immiscible fluids, given the volume fraction in the cell and the adjacent cells. Currently, the most accurate approach is to fit a curve (2D), or a surface (3D), matching the volume fractions and finding the curvature by differentiation. Here, a different approach is examined. A synthetic data set, relating curvature to volume fractions, is generated using well-defined shapes where the curvature and volume fractions are easily found and then machine learning is used to fit the data (training). The resulting function is used to find the curvature for shapes not used for the training and implemented into a code to track moving interfaces. The results suggest that using machine learning to generate the relationship is a viable approach that results in reasonably accurate predictions.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Mani Razi, Robert M. Kirby, Akil Narayan〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we introduce a novel approach for the construction of multi-fidelity surrogate models with “discrete” fidelity levels. The notion of a discrete level of fidelity is in contrast to a mathematical model, for which the notion of refinement towards a high-fidelity model is relevant to sending a discretization parameter toward zero in a continuous way. Our notion of discrete fidelity levels encompasses cases for which there is no notion of convergence in terms of a fidelity parameter that can be sent to zero or infinity. The particular choice of how levels of fidelity are defined in this framework paves the way for using models that may have no apparent physical or mathematical relationship to the target high-fidelity model. However, our approach requires that models can produce results with a common set of parameters in the target model. Hence, fidelity level in this work is not directly representative of the degree of similarity of a low-fidelity model to a target high-fidelity model. In particular, we show that our approach is applicable to competitive ecological systems with different numbers of species, discrete-state Markov chains with a different number of states, polymer networks with a different number of connections, and nano-particle plasmonic arrays with a different number of scatterers. The results of this study demonstrate that our procedure boasts computational efficiency and accuracy for a wide variety of models and engineering systems.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Hasan Almanasreh〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this work we will treat the spurious eigenvalues obstacle that appears in the computation of the radial Dirac eigenvalue problem using numerical methods. The treatment of the spurious solution is based on applying Petrov–Galerkin finite element method. The significance of this work is the employment of just continuous basis functions, thus the need of a continuous function which has a continuous first derivative as a basis, as in [2], [3], is no longer required. The Petrov–Galerkin finite element method for the Dirac eigenvalue problem strongly depends on a stability parameter, 〈em〉τ〈/em〉, that controls the size of the diffusion terms added to the finite element formulation for the problem. The mesh-dependent parameter 〈em〉τ〈/em〉 is derived based on the given problem with the particular basis functions.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): S.B. Adrian, F.P. Andriulli, T.F. Eibert〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present a Calderón preconditioner for the electric field integral equation (EFIE), which does not require a barycentric refinement of the mesh and which yields a Hermitian, positive definite (HPD) system matrix allowing for the usage of the conjugate gradient (CG) solver. The resulting discrete equation system is immune to the low-frequency and the dense-discretization breakdown and, in contrast to existing Calderón preconditioners, no second discretization of the EFIE operator with Buffa–Christiansen (BC) functions is necessary. This preconditioner is obtained by leveraging on spectral equivalences between (scalar) integral operators, namely the single layer and the hypersingular operator known from electrostatics, on the one hand, and the Laplace–Beltrami operator on the other hand. Since our approach incorporates Helmholtz projectors, there is no search for global loops necessary and thus our method remains stable on multiply connected geometries. The numerical results demonstrate the effectiveness of this approach for both canonical and realistic (multi-scale) problems.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: Available online 21 February 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics〈/p〉 〈p〉Author(s): Mehdi Samiee, Mohsen Zayernouri, Mark M. Meerschaert〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We develop a unified Petrov–Galerkin spectral method for a class of fractional partial differential equations with two-sided derivatives and constant coefficients of the form 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mmultiscripts〉〈mrow〉〈mi mathvariant="script"〉D〈/mi〉〈/mrow〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈none〉〈/none〉〈none〉〈/none〉〈mrow〉〈mn〉2〈/mn〉〈mi〉τ〈/mi〉〈/mrow〉〈mprescripts〉〈/mprescripts〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈none〉〈/none〉〈/mmultiscripts〉〈mi〉u〈/mi〉〈mo〉+〈/mo〉〈msubsup〉〈mrow〉〈mo〉∑〈/mo〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈mo〉=〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msubsup〉〈mo stretchy="false"〉[〈/mo〉〈msub〉〈mrow〉〈msub〉〈mrow〉〈mi〉c〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉l〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈msubsup〉〈mrow〉〈mi mathvariant="script"〉D〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈msub〉〈mrow〉〈mi〉μ〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msubsup〉〈mi〉u〈/mi〉〈mo〉+〈/mo〉〈msub〉〈mrow〉〈msub〉〈mrow〉〈mi〉c〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉r〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈msubsup〉〈mrow〉〈mi mathvariant="script"〉D〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉b〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈msub〉〈mrow〉〈mi〉μ〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msubsup〉〈mi〉u〈/mi〉〈mo stretchy="false"〉]〈/mo〉〈mo〉+〈/mo〉〈mi〉γ〈/mi〉〈mspace width="0.2em"〉〈/mspace〉〈mspace width="0.2em"〉〈/mspace〉〈mi〉u〈/mi〉〈mo〉=〈/mo〉〈msubsup〉〈mrow〉〈mo〉∑〈/mo〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈mo〉=〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msubsup〉〈mo stretchy="false"〉[〈/mo〉〈msub〉〈mrow〉〈msub〉〈mrow〉〈mi〉κ〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉l〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈msubsup〉〈mrow〉〈mi mathvariant="script"〉D〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈msub〉〈mrow〉〈mi〉ν〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msubsup〉〈mi〉u〈/mi〉〈mo〉+〈/mo〉〈msub〉〈mrow〉〈msub〉〈mrow〉〈mi〉κ〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉r〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉x〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈msubsup〉〈mrow〉〈mi mathvariant="script"〉D〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉b〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈msub〉〈mrow〉〈mi〉ν〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msubsup〉〈mi〉u〈/mi〉〈mo stretchy="false"〉]〈/mo〉〈mo〉+〈/mo〉〈mi〉f〈/mi〉〈/math〉, where 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈mn〉2〈/mn〉〈mi〉τ〈/mi〉〈mo〉∈〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈mn〉2〈/mn〉〈mi〉τ〈/mi〉〈mo〉≠〈/mo〉〈mn〉1〈/mn〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.gif" overflow="scroll"〉〈mn〉2〈/mn〉〈msub〉〈mrow〉〈mi〉μ〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈mo〉∈〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mn〉0〈/mn〉〈mo〉,〈/mo〉〈mn〉1〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si5.gif" overflow="scroll"〉〈mn〉2〈/mn〉〈msub〉〈mrow〉〈mi〉ν〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈mo〉∈〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, in a (〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si6.gif" overflow="scroll"〉〈mn〉1〈/mn〉〈mo〉+〈/mo〉〈mi〉d〈/mi〉〈/math〉)-dimensional 〈em〉space–time〈/em〉 hypercube, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.gif" overflow="scroll"〉〈mi〉d〈/mi〉〈mo〉=〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo〉,〈/mo〉〈mn〉3〈/mn〉〈mo〉,〈/mo〉〈mo〉⋯〈/mo〉〈/math〉, subject to homogeneous Dirichlet initial/boundary conditions. We employ the eigenfunctions of the fractional Sturm–Liouville eigen-problems of the first kind in [1], called 〈em〉Jacobi poly-fractonomial〈/em〉s, as temporal bases, and the eigen-functions of the boundary-value problem of the second kind as temporal test functions. Next, we construct our spatial basis/test functions using Legendre polynomials, yielding mass matrices being independent of the spatial fractional orders (〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si8.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉μ〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈msub〉〈mrow〉〈mi〉ν〈/mi〉〈/mrow〉〈mrow〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mi〉i〈/mi〉〈mo〉,〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mi〉j〈/mi〉〈mo〉=〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo〉,〈/mo〉〈mo〉⋯〈/mo〉〈mo〉,〈/mo〉〈mi〉d〈/mi〉〈/math〉). Furthermore, we formulate a novel unified fast linear solver for the resulting high-dimensional linear system based on the solution of generalized eigen-problem of spatial mass matrices with respect to the corresponding stiffness matrices, hence, making the complexity of the problem optimal, i.e., 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si9.gif" overflow="scroll"〉〈mi mathvariant="script"〉O〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈msup〉〈mrow〉〈mi〉N〈/mi〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈mo〉+〈/mo〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉)〈/mo〉〈/math〉. We carry out several numerical test cases to examine the CPU time and convergence rate of the method. The corresponding stability and error analysis of the Petrov–Galerkin method are carried out in [2].〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Ruilian Du, Yubin Yan, Zongqi Liang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A new high-order finite difference scheme to approximate the Caputo fractional derivative 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mfrac〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/mfrac〉〈mo stretchy="true" maxsize="2.4ex" minsize="2.4ex"〉(〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mmultiscripts〉〈mrow〉〈mi〉D〈/mi〉〈/mrow〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈mrow〉〈mi〉α〈/mi〉〈/mrow〉〈mprescripts〉〈/mprescripts〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈/mmultiscripts〉〈mi〉f〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈mo〉+〈/mo〉〈mspace width="0.2em"〉〈/mspace〉〈mmultiscripts〉〈mrow〉〈mi〉D〈/mi〉〈/mrow〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈mrow〉〈mi〉α〈/mi〉〈/mrow〉〈mprescripts〉〈/mprescripts〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈mrow〉〈mi〉C〈/mi〉〈/mrow〉〈/mmultiscripts〉〈mi〉f〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈mrow〉〈mi〉k〈/mi〉〈mo〉−〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈mo stretchy="true" maxsize="2.4ex" minsize="2.4ex"〉)〈/mo〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈mi〉k〈/mi〉〈mo〉=〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo〉,〈/mo〉〈mo〉…〈/mo〉〈mo〉,〈/mo〉〈mi〉N〈/mi〉〈/math〉, with the convergence order 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si160.gif" overflow="scroll"〉〈mi〉O〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="normal"〉Δ〈/mi〉〈msup〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈mrow〉〈mn〉4〈/mn〉〈mo〉−〈/mo〉〈mi〉α〈/mi〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.gif" overflow="scroll"〉〈mi〉α〈/mi〉〈mo〉∈〈/mo〉〈mo stretchy="false"〉(〈/mo〉〈mn〉1〈/mn〉〈mo〉,〈/mo〉〈mn〉2〈/mn〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is obtained when 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si123.gif" overflow="scroll"〉〈msup〉〈mrow〉〈mi〉f〈/mi〉〈/mrow〉〈mrow〉〈mo〉‴〈/mo〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉(〈/mo〉〈msub〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈mrow〉〈mn〉0〈/mn〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉)〈/mo〉〈mo〉=〈/mo〉〈mn〉0〈/mn〉〈/math〉, where Δ〈em〉t〈/em〉 denotes the time step size. Based on this scheme we introduce a finite difference method for solving fractional diffusion wave equation with the convergence order 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si6.gif" overflow="scroll"〉〈mi〉O〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="normal"〉Δ〈/mi〉〈msup〉〈mrow〉〈mi〉t〈/mi〉〈/mrow〉〈mrow〉〈mn〉4〈/mn〉〈mo〉−〈/mo〉〈mi〉α〈/mi〉〈/mrow〉〈/msup〉〈mo〉+〈/mo〉〈msup〉〈mrow〉〈mi〉h〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, where 〈em〉h〈/em〉 denotes the space step size. Numerical examples are given to show that the numerical results are consistent with the theoretical results.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): Jie Du, Yang Yang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Local discontinuous Galerkin (LDG) methods are popular for convection-diffusion equations. In LDG methods, we introduce an auxiliary variable 〈em〉p〈/em〉 to represent the derivative of the primary variable 〈em〉u〈/em〉, and solve them on the same mesh. It is well known that the maximum-principle-preserving (MPP) LDG method is only available up to second-order accuracy. Recently, we introduced a new algorithm, and solve 〈em〉u〈/em〉 and 〈em〉p〈/em〉 on different meshes, and obtained stability and optimal error estimates. In this paper, we will continue this approach and construct MPP third-order LDG methods for convection-diffusion equations on overlapping meshes. The new algorithm is more flexible and does not increase any computational cost. Numerical evidence will be given to demonstrate the accuracy and good performance of the third-order MPP LDG method.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Yunchang Seol, Yu-Hau Tseng, Yongsam Kim, Ming-Chih Lai〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, a two-dimensional immersed boundary method is developed to simulate the dynamics of Newtonian vesicle in viscoelastic Oldroyd-B fluid under shear flow. The viscoelasticity effect of extra stress is well incorporated into the immersed boundary formulation using the indicator function. Our numerical methodology is first validated in comparison with theoretical results in purely Newtonian fluid, and then a series of numerical experiments is conducted to study the effects of different dimensionless parameters on the vesicle motions. Although the tank-treading (TT) motion of Newtonian vesicle in Oldroyd-B fluid under shear flow can be observed just like in Newtonian fluid, it is surprising to find that the stationary inclination angle can be negative without the transition to tumbling (TB) motion. Moreover, the inertia effect plays a significant role that is able to turn the vesicle back to positive inclination angle through TT-TB-TT transition as the Reynolds number increases. To the best of our knowledge, this is the first numerical work for the detailed investigations of Newtonian vesicle dynamics suspended in viscoelastic Oldroyd-B fluid. We believe that our numerical results can be used to motivate further studies in theory and experiments for such coupling vesicle problems.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers & Geosciences, Volume 122〈/p〉 〈p〉Author(s): Seth Goodman, Ariel BenYishay, Zhonghui Lv, Daniel Runfola〈/p〉 〈div xml:lang="en"〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Interdisciplinary use of geospatial data requires the integration of data from a breadth of sources, and frequently involves the harmonization of different methods of sampling, measurement, and technical data types. These integrative efforts are often inhibited by fundamental geocomputational challenges, including a lack of memory efficient or parallel processing approaches to traditional methods such as zonal statistics. GeoQuery (〈a href="http://geoquery.org/" target="_blank"〉geoquery.org〈/a〉) is a dynamic web application which utilizes a High Performance Computing cluster and novel parallel geospatial data processing methods to overcome these challenges. Through an online interface, GeoQuery users can request geospatial data - which spans categories including geophysical, environmental and social measurements - to be aggregated to user-selected units of analysis (e.g., subnational administrative boundaries). Once a request has been processed, users are provided with permanent links to access their customized data and documentation. Datasets made available through GeoQuery are reviewed, prepared, and provisioned by geospatial data specialists, with processing routines tailored for each dataset. The code used and steps taken while preparing datasets and processing user requests are publicly available, ensuring transparency and replicability of all data and processes. By mediating the complexities of working with geospatial data, GeoQuery reduces the barriers to entry and the related costs of incorporating geospatial data into research across disciplines. This paper presents the technology and methods used by GeoQuery to process and manage geospatial data and user requests.〈/p〉〈/div〉 〈/div〉

Beschreibung: 〈p〉Publication date: February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers & Geosciences, Volume 123〈/p〉 〈p〉Author(s): Pouyan Pirnia, François Duhaime, Yannic Ethier, Jean-Sébastien Dubé〈/p〉 〈div xml:lang="en"〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The thermal, mechanical and hydrodynamic behaviour of porous media in geoscience applications is usually modelled through the finite-element (FEM) or finite-difference methods. These continuum models tend to perform poorly when modelling phenomena that are essentially dependent on behaviour at the particle scale or phenomena that are not accurately described by partial differential equations (PDE), such as internal erosion and filtration. The discrete nature of granular materials can be modelled through the discrete-element method (DEM). However, in some instances, DEM models would benefit from an interface with continuum models to solve coupled PDEs or to model phenomena that occur at a different scale. This paper introduces ICY, an interface between COMSOL Multiphysics, a commercial finite-element engine, and YADE, an open-source discrete-element code. The interface is centred on a JAVA class. It was verified using the simple example of a sphere falling in water according to Stokes’ law. For this example, the drag force was calculated in COMSOL and body forces (gravity, buoyancy and drag) on the sphere were summed in YADE. The paper also presents an application example for the interface based on the modelling of internal erosion tests.〈/p〉〈/div〉 〈/div〉 〈h5〉Graphical abstract〈/h5〉 〈div〉〈p〉〈figure〉〈img src="https://ars.els-cdn.com/content/image/1-s2.0-S0098300417313213-fx1.jpg" width="334" alt="Image 1" title="Image 1"〉〈/figure〉〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Sustainable Cities and Society, Volume 45〈/p〉 〈p〉Author(s): Jinsoo Park, Dong Ho Shin, Seung Joo Lee, Youhwan Shin, Sarng Woo Karng〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Thermal energy storage is an essential technology for using renewable energy to reduce building energy consumption. Among the various energy technologies, much attention has been paid to latent thermal energy storage system using phase change materials because of its large capacity of thermal energy. However, due to the low thermal conductivity of the phase change materials, the system has disadvantages at low charging and discharging rates. To address this issue, a new latent heat thermal energy storage system using a flexible and thin pouch is proposed. The effectively designed pouch arrangement and thin pouch shape provide better heat transfer performance. The real product is tested at various flow rates of heat transfer fluids and the thermal and fluid characteristics of the system are analyzed by the computational fluid dynamics model. As a result, the proposed system has 1.4 times larger amount of discharged energy than that of the water storage system. Moreover, the system can reduce charging, discharging, and total process times by 1.7, 2.5, and 2.2 times, respectively, compared with the conventional sphere capsule piling system.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Sustainable Cities and Society, Volume 44〈/p〉 〈p〉Author(s): Logaraj Ramakreshnan, Nasrin Aghamohammadi, Chng Saun Fong, Amirhosein Ghaffarianhoseini, Li Ping Wong, Nik Meriam Sulaiman〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A very few studies have evaluated and understood the temporal dynamics of UHI in many expanding tropical cities. Hence, this study investigated the temporal variations of canopy-level UHI in selected urban stations, namely Petaling Jaya (PJ) and Subang (SUB), of Greater Kuala Lumpur (GKL) using 2016’s hourly data set obtained from meteorological observatories. The association between meteorological factors and UHI Intensity (UHII) is evaluated using linear regression models and Pearson correlation analysis. The findings revealed positive thermal contrasts between urban and sub-urban stations with maximum UHII during dry, southwest monsoon season in PJ (June: 1.68 °C) and SUB (August: 1.29 °C) stations respectively. PJ station exhibited a distinct diurnal cycle with the maximum nocturnal UHII of 1.71 °C at about 8 p.m. after sunset under ideal meteorological conditions. The results also demonstrated that UHI events occurred more frequently at nights in urban stations in the magnitude range of 0–2 °C. Cooling at all urban sites starts around 2–3 p.m. with the highest rate of 0.73 °C/h and 0.96 °C/h in PJ and SUB stations. Meanwhile, relative humidity displayed a low positive correlation (r = 0.37, p ≥ 0.05) and a high negative correlation (r = −0.79, p 〈 0.05) with UHII in PJ and SUB stations respectively. The influence of wind speed on UHII is weak (r = −0.44, p 〈 0.05) in PJ station and strong (r = 0.83, p 〈 0.05) in SUB station. Overall, this study can be regarded as one of the comprehensive observational investigations of canopy-level UHI in a tropical city that provide vital inputs to enrich the tropical urban climate literacy.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Sustainable Cities and Society, Volume 44〈/p〉 〈p〉Author(s): Bao-Jie He, Zi-Qi Zhao, Li-Du Shen, Hong-Bo Wang, Li-Guang Li〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Numerous studies on urban heat island (UHI) effects have examined relationships between land use/land cover (LULC) and land surface temperature (LST), while impacts of environmental temperatures on these relationships have received little attention. This paper has investigated how background temperature affects performances of cool/hot sources in either enhancing or mitigating LST in Shenyang, China based on Landsat 8 image. In specific, according to the method of standard classification method with an interval of 1.0 standard deviation, LST was classified into seven temperature levels: highest, higher, high, medium, low, lower and lowest. Afterwards, the seven levels were merged into three temperature zones (TZ), namely cold TZ (CTZ, highest, higher and high), neutral TZ (NTZ, medium) and hot TZ (HTZ, low, lower and lowest), for investigating relationships between LST and LULC (including building (BU), road (RO), bare land (BA), green land (GR), agricultural land (AG) and water bodies (WA)). LST generally follows the order of BU 〉 RO 〉 BA 〉 AR 〉 GR 〉 WA, but temperature differences between cool/hot sources reduce as background temperature increases. LULC-LST relationships vary greatly with background temperature. Overall, BU and RO have significant positive relationships with LST, while negative relationships are found among GR, AR, WA and LST. However, in CTZ, RO is in negative relationships with LST, GR and WA are no longer significant in NTZ, and GR and BA play significant positive roles in aggravating LST in HTZ. Generally, this study can help orientate scientific decisions in urban environmental governance.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 378〈/p〉 〈p〉Author(s): Oscar P. Bruno, Martín Maas〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper introduces a fast algorithm, applicable throughout the electromagnetic spectrum, for the numerical solution of problems of scattering by periodic surfaces in two-dimensional space. The proposed algorithm remains highly accurate and efficient for challenging configurations including randomly rough surfaces, deep corrugations, large periods, near grazing incidences, and, importantly, Wood-anomaly resonant frequencies. The proposed approach is based on use of certain “shifted equivalent sources” which enable FFT acceleration of a Wood-anomaly-capable quasi-periodic Green function introduced recently (Bruno and Delourme (2014) [4]). The Green-function strategy additionally incorporates an exponentially convergent shifted version of the classical 〈em〉spectral〈/em〉 series for the Green function. While the computing-cost asymptotics depend on the asymptotic configuration assumed, the computing costs rise at most linearly with the size of the problem for a number of important rough-surface cases we consider. In practice, single-core runs in computing times ranging from a fraction of a second to a few seconds suffice for the proposed algorithm to produce highly-accurate solutions in some of the most challenging contexts arising in applications.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 15 February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 379〈/p〉 〈p〉Author(s): Denis S. Grebenkov, Sergey D. Traytak〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The generalized method of separation of variables (GMSV) is applied to solve boundary value problems for the Laplace operator in three-dimensional domains with disconnected spherical boundaries (e.g., an arbitrary configuration of non-overlapping partially reactive spherical sinks or obstacles). We consider both exterior and interior problems and all most common boundary conditions: Dirichlet, Neumann, Robin, and conjugate one. Using the translational addition theorems for solid harmonics to switch between the local spherical coordinates, we obtain a semi-analytical expression of the Green function as a linear combination of partial solutions whose coefficients are fixed by boundary conditions. Although the numerical computation of the coefficients involves series truncation and solution of a system of linear algebraic equations, the use of the solid harmonics as basis functions naturally adapted to the intrinsic symmetries of the problem makes the GMSV particularly efficient, especially for exterior problems. The obtained Green function is the key ingredient to solve boundary value problems and to determine various characteristics of stationary diffusion such as reaction rate, escape probability, harmonic measure, residence time, and mean first passage time, to name but a few. The relevant aspects of the numerical implementation and potential applications in chemical physics, heat transfer, electrostatics, and hydrodynamics are discussed.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): Samar Chehade, Audrey Kamta Djakou, Michel Darmon, Gilles Lebeau〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Non Destructive Examination (NDE) of industrial structures requires the modeling of specimen geometry echoes generated by the surfaces (entry, backwall …) of inspected blocks. For that purpose, the study of plane wave diffraction by a wedge is of great interest. The work presented here is preliminary research to model the case of an elastic wave diffracted by a wedge in the future, for which there exist various modeling approaches but the numerical aspects have only been developed for wedge angles lower than 〈em〉π〈/em〉. The spectral functions method has previously been introduced to solve the 2D diffraction problem of an immersed elastic wedge for angles lower than 〈em〉π〈/em〉. As a first step, the spectral functions method has been developed here for the diffraction on an acoustic wave by a stress-free wedge, in 2D and for any wedge angle, before studying the elastic wave diffraction from a wedge. In this method, the solution to the diffraction problem is expressed in terms of two unknown functions called the spectral functions. These functions are computed semi-analytically, meaning that they are the sum of two terms. One of them is determined exactly and the other is approached numerically, using a collocation method. A successful numerical validation of the method for all wedge angles is proposed, by comparison with the GTD (Geometrical Theory of Diffraction) solution derived from the exact Sommerfeld integral.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Sustainable Cities and Society, Volume 44〈/p〉 〈p〉Author(s): Xiaojun Liu, Wei Hu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Energy conservation and consumption reduction in the field of construction are the keys to achieving the target global temperature growth of the Paris Agreement. However, the current promotion of 〈strong〉green〈/strong〉 buildings is still stuck in the rut of government excessive intervention, market less participation. In order to explore the status of the Chinese public’s attention, changing trends, sentiment orientation, and focus toward 〈strong〉green〈/strong〉 buildings, this paper collected and analyzed information of Weibo users and posts and comments of popular posts related to 〈strong〉green〈/strong〉 buildings. We used the Sina Weibo platform with web crawler technology and a text mining method. The results showed that: the public’s attention toward 〈strong〉green〈/strong〉 buildings has enhanced significantly with the change of government governance ideas, but still needs to be improved. Although vertical greening houses possess good heat preservation and thermal insulation, 46.32% of the Chinese public has negative sentiments toward vertical greening houses mainly due to worries about the increase in snakes, and mosquitoes and other insects caused by the increased vegetation cover. Price is not the main reason why the public has negative sentiments toward vertical greening houses.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Sustainable Cities and Society, Volume 44〈/p〉 〈p〉Author(s): Charles Peprah, Owusu Amponsah, Charles Oduro〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Urbanisation in the cities of Sub-Saharan Africa has been associated with urban sprawl and increased vehicular traffic, which undermine the agglomeration effects of the cities on socioeconomic development. These adverse effects will exacerbate as the human population of the region continues to increase. Some scholars argue that making the cities mobility-smart could mitigate the adverse effects of urbanisation in the region. However, the conventional literature on smart mobility in Sub-Saharan Africa does little to demonstrate how the concept can be applied. In this regard, the purpose of this study is two pronged: a) to assess the mobility smartness of Ghanaian cities and b) to demonstrate how the concept can be operationalised to mitigate some of the adverse effects of urbanisation in the cities. The research process began with a review of relevant literature to conceptualise smart mobility. The conceptual framework was then used to assess the mobility-smartness of Ghanaian cities, which was followed by a discussion of how the concept of smart cities can be operationalised in Ghanaian cities. The results show that the cities in Ghana, like many cities in Sub-Saharan Africa, depend mainly on the road sub-sector for the movement of people and freight. The rapid increases in vehicular population without a commensurate expansion in road infrastructure have undermined the cities’ productivity. The conclusion from this is that the cities are not mobility-smart and for this to change, the paper argues that efforts should be made to improve people mobility, information logistic mobility and information mobility. These require technological literate and receptive population and investments in transport infrastructure.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Computers & Geosciences, Volume 123〈/p〉 〈p〉Author(s): Timothy J. Naegeli, Jason Laura〈/p〉 〈div xml:lang="en"〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper we present an extension to the Large Crater Clustering (LCC) tool set which places a cone of uncertainty around the trajectories of secondary impact craters to determine potential locations of source craters. The LCC tool set was a first step in the spatial quantification of primary and secondary cratering processes, which allows planetary geologists to accurately estimate the geologic age of a celestial surface. This work builds on the LCC tool set by accounting for the ambiguity of flight path trajectories through a Python script that leverages ArcGIS's ArcPy library. We chronicle the mechanics of the script, which creates geodetically correct cones then counts them within equally sized cells of a vector grid. We describe the process that was used to derive the shape of the cone and provide parameters for the sizes of the cones and the grid. We demonstrate that the cone of uncertainty has the ability to compensate for error in secondary crater trajectories by introducing deviation in the trajectory bearing and comparing the predicted primary crater location. We use two study areas on Mars as well as the entire lunar surface to illustrate the usefulness of the extension as an aid to human interpretation of back-projections.〈/p〉〈/div〉 〈/div〉

Beschreibung: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): Hong Fang, Yikun Hu, Caihui Yu, Ming Tie, Jie Liu, Chunye Gong〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The mesh deformation method based on radial basis functions (RBF) has many advantages and is widely used. RBF based mesh deformation method mainly has two steps: data reduction and displacement interpolation. The data reduction step includes solving interpolation weight coefficients and searching for the node with the maximum interpolation error. The data reduction schemes based on greedy algorithm is used to select an optimum reduced set of surface mesh nodes. In this paper, a parallel mesh deformation method based on parallel data reduction and displacement interpolation is proposed. The proposed recurrence Choleskey decomposition method (RCDM) can decrease the computational cost of solving interpolation weight coefficients from 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi〉O〈/mi〉〈mrow〉〈mo stretchy="true"〉(〈/mo〉〈msubsup〉〈mrow〉〈mi〉N〈/mi〉〈/mrow〉〈mrow〉〈mi〉c〈/mi〉〈/mrow〉〈mrow〉〈mn〉4〈/mn〉〈/mrow〉〈/msubsup〉〈mo stretchy="true"〉)〈/mo〉〈/mrow〉〈/math〉 to 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈mi〉O〈/mi〉〈mrow〉〈mo stretchy="true"〉(〈/mo〉〈msubsup〉〈mrow〉〈mi〉N〈/mi〉〈/mrow〉〈mrow〉〈mi〉c〈/mi〉〈/mrow〉〈mrow〉〈mn〉3〈/mn〉〈/mrow〉〈/msubsup〉〈mo stretchy="true"〉)〈/mo〉〈/mrow〉〈/math〉, where 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉N〈/mi〉〈/mrow〉〈mrow〉〈mi〉c〈/mi〉〈/mrow〉〈/msub〉〈/math〉 denotes the number of support nodes. The technology of parallel computing is used to accelerate the searching for the node with the maximum interpolation error and displacement interpolation. The combination of parallel data reduction and parallel interpolation can greatly improve the efficiency of mesh deformation. Two typical deformation problems of the ONERA M6 and DLR-F6 wing-body-Nacelle-Pylon configuration are taken as the test cases to validate the proposed approach and can get up to 19.57 times performance improvement with the proposed approach. Finally, the aeroelastic response of HIRENASD wing-body configuration is used to verify the efficiency and robustness of the proposed method.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Daniil Bochkov, Frederic Gibou〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present two finite volume schemes to solve a class of Poisson-type equations subject to Robin boundary conditions in irregular domains with 〈em〉piecewise smooth〈/em〉 boundaries. The first scheme results in a symmetric linear system and produces second-order accurate numerical solutions with first-order accurate gradients in the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mo〉∞〈/mo〉〈/mrow〉〈/msup〉〈/math〉-norm (for solutions with two bounded derivatives). The second scheme is nonsymmetric but produces second-order accurate numerical solutions as well as second-order accurate gradients in the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msup〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mo〉∞〈/mo〉〈/mrow〉〈/msup〉〈/math〉-norm (for solutions with three bounded derivatives). Numerical examples are given in two and three spatial dimensions.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: Available online 19 October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics〈/p〉 〈p〉Author(s): Mandeep Deka, Shuvayan Brahmachary, Ramakrishnan Thirumalaisamy, Amaresh Dalal, Ganesh Natarajan〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We describe a new and simple strategy based on the Gauss divergence theorem for obtaining centroidal gradients on unstructured meshes. Unlike the standard Green–Gauss (SGG) reconstruction which requires face values of quantities whose gradients are sought, the proposed approach reconstructs the gradients using the normal derivative(s) at the faces. The new strategy, referred to as the Modified Green–Gauss (MGG) reconstruction results in consistent gradients which are at least first-order accurate on arbitrary polygonal meshes. We show that the MGG reconstruction is linearity preserving independent of the mesh topology and retains the consistent behaviour of gradients even on meshes with large curvature and high aspect ratios. The gradient accuracy in MGG reconstruction depends on the accuracy of discretisation of the normal derivatives at faces and this necessitates an iterative approach for gradient computation on non-orthogonal meshes. Numerical studies on different mesh topologies demonstrate that MGG reconstruction gives accurate and consistent gradients on non-orthogonal meshes, with the number of iterations proportional to the extent of non-orthogonality. The MGG reconstruction is found to be consistent even on meshes with large aspect ratio and curvature with the errors being lesser than those from linear least-squares reconstruction. A non-iterative strategy in conjunction with MGG reconstruction is proposed for gradient computations in finite volume simulations that achieves the accuracy and robustness of MGG reconstruction at a cost equivalent to that of SGG reconstruction. The efficacy of this strategy for fluid flow problems is demonstrated through numerical investigations in both incompressible and compressible regimes. The MGG reconstruction may, therefore, be viewed as a novel and promising blend of least-squares and Green–Gauss based approaches which can be implemented with little effort in open-source finite-volume solvers and legacy codes.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: Available online 18 July 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics〈/p〉 〈p〉Author(s): Marvin Bohm, Andrew R. Winters, Gregor J. Gassner, Dominik Derigs, Florian Hindenlang, Joachim Saur〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉The first paper of this series presents a discretely entropy stable discontinuous Galerkin (DG) method for the resistive magnetohydrodynamics (MHD) equations on three-dimensional curvilinear unstructured hexahedral meshes. Compared to other fluid dynamics systems such as the shallow water equations or the compressible Navier–Stokes equations, the resistive MHD equations need special considerations because of the divergence-free constraint on the magnetic field. For instance, it is well known that for the symmetrization of the ideal MHD system as well as the continuous entropy analysis a non-conservative term proportional to the divergence of the magnetic field, typically referred to as the Powell term, must be included. As a consequence, the mimicry of the continuous entropy analysis in the discrete sense demands a suitable DG approximation of the non-conservative terms in addition to the ideal MHD terms.〈/p〉 〈p〉This paper focuses on the 〈em〉resistive〈/em〉 MHD equations: Our first contribution is a proof that the resistive terms are symmetric and positive-definite when formulated in entropy space as gradients of the entropy variables, which enables us to show that the entropy inequality holds for the resistive MHD equations. This continuous analysis is the key for our DG discretization and guides the path for the construction of an approximation that discretely mimics the entropy inequality, typically termed 〈em〉entropy stability〈/em〉. Our second contribution is a detailed derivation and analysis of the discretization on three-dimensional curvilinear meshes. The discrete analysis relies on the summation-by-parts property, which is satisfied by the DG spectral element method (DGSEM) with Legendre–Gauss–Lobatto (LGL) nodes. Although the divergence-free constraint is included in the non-conservative terms, the resulting method has no particular treatment of the magnetic field divergence errors, which might pollute the solution quality. Our final contribution is the extension of the standard resistive MHD equations and our DG approximation with a divergence cleaning mechanism that is based on a generalized Lagrange multiplier (GLM).〈/p〉 〈p〉As a conclusion to the first part of this series, we provide detailed numerical validations of our DGSEM method that underline our theoretical derivations. In addition, we show a numerical example where the entropy stable DGSEM demonstrates increased robustness compared to the standard DGSEM.〈/p〉 〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): James F. Kelly, Harish Sankaranarayanan, Mark M. Meerschaert〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉This paper develops appropriate boundary conditions for the two-sided fractional diffusion equation, where the usual second derivative in space is replaced by a weighted average of positive (left) and negative (right) fractional derivatives. Mass preserving, reflecting boundary conditions for two-sided fractional diffusion involve a balance of left and right fractional derivatives at the boundary. Stable, consistent explicit and implicit Euler methods are detailed, and steady state solutions are derived. Steady state solutions for two-sided fractional diffusion equations using both Riemann–Liouville and Caputo flux are computed. For Riemann–Liouville flux and reflecting boundary conditions, the steady-state solution is singular at one or both of the end-points. For Caputo flux and reflecting boundary conditions, the steady-state solution is a constant function. Numerical experiments illustrate the convergence of these numerical methods. Finally, the influence of the reflecting boundary on the steady-state behavior subject to both the Riemann–Liouville and Caputo fluxes is discussed.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): N. Saini, C. Kleinstreuer〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉All natural and a growing number of manufactured solid particles are non-spherical. Interesting fluid–particle dynamics applications include the transport of granular material, piling of seeds or grains, inhalation of toxic aerosols, use of nanofluids for enhanced cooling or improved lubrication, and optimal drug-targeting of tumors. A popular approach for computer simulations of such scenarios is the multi-sphere (MS) method, where any non-spherical particle is represented by an assemblage of spheres. However, the MS approach may lead to multiple sphere-to-sphere contact points during collision, and subsequently to erroneous particle transport and deposition. In cases where non-spherical particles can be approximated as ellipsoids with arbitrary aspect ratios, a new theory for particle transport, collision and wall interaction is presented which is more accurate computationally and more efficient than the MS method. In general, with the new ellipsoidal particle interaction (EPI) model, contact points and planes of ellipsoids, rather than spheres, are obtained based on a geometric potential algorithm. Then, interaction forces and torques of the colliding particles are determined via inscribed ‘pseudo-spheres’, employing the soft-particle approach. The off-center forces and moments are then transferred to the mass center of the ellipsoids to solve the appropriate translatory and angular equations of motion. Considering ellipses to illustrate the workings and predictive power of the new collision model, turbulent fluid–particle flow with the EPI model in a 2-D channel is simulated and compared with 3-D numerical benchmark results which relied on the MS method. The 2-D concentrations of micron particles with different aspect ratios matched closely with the 3-D cases. However, interesting differences occurred when comparing the particle-velocity profiles for which the 2-D EPI model generated somewhat larger particle velocities due to out-of-plane collisions, slightly higher particle–wall interactions, and two-way coupling effects.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Kyongmin Yeo, Igor Melnyk〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present a deep learning model, DE-LSTM, for the simulation of a stochastic process with an underlying nonlinear dynamics. The deep learning model aims to approximate the probability density function of a stochastic process via numerical discretization and the underlying nonlinear dynamics is modeled by the Long Short-Term Memory (LSTM) network. It is shown that, when the numerical discretization is used, the function estimation problem can be solved by a multi-label classification problem. A penalized maximum log likelihood method is proposed to impose a smoothness condition in the prediction of the probability distribution. We show that the time evolution of the probability distribution can be computed by a high-dimensional integration of the transition probability of the LSTM internal states. A Monte Carlo algorithm to approximate the high-dimensional integration is outlined. The behavior of DE-LSTM is thoroughly investigated by using the Ornstein–Uhlenbeck process and noisy observations of nonlinear dynamical systems; Mackey–Glass time series and forced Van der Pol oscillator. It is shown that DE-LSTM makes a good prediction of the probability distribution without assuming any distributional properties of the stochastic process. For a multiple-step forecast of the Mackey–Glass time series, the prediction uncertainty, denoted by the 95% confidence interval, first grows, then dynamically adjusts following the evolution of the system, while in the simulation of the forced Van der Pol oscillator, the prediction uncertainty does not grow in time even for a 3,000-step forecast.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 15 February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 379〈/p〉 〈p〉Author(s): Christopher Eldred, Thomas Dubos, Evaggelos Kritsikis〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The rotating shallow water (RSW) equations are the usual testbed for the development of numerical methods for three-dimensional atmospheric and oceanic models. However, an arguably more useful set of equations are the thermal shallow water equations (TSW), which introduce an additional thermodynamic scalar but retain the single layer, two-dimensional structure of the RSW. As a stepping stone towards a three-dimensional atmospheric dynamical core, this work presents a quasi-Hamiltonian discretization of the thermal shallow water equations using compatible Galerkin methods, building on previous work done for the shallow water equations. Structure-preserving or quasi-Hamiltonian discretizations methods, that discretize the Hamiltonian structure of the equations of motion rather than the equations of motion themselves, have proven to be a powerful tool for the development of models with discrete conservation properties. By combining these ideas with an energy-conserving Poisson time integrator and a careful choice of Galerkin spaces, a large set of desirable properties can be achieved. In particular, for the first time total mass, buoyancy and energy are conserved to machine precision in the fully discrete model.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 15 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 377〈/p〉 〈p〉Author(s): Fang Qing, Xijun Yu, Zupeng Jia〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The MoF (Moment of Fluid) method is an accurate approach for interface reconstruction in numerical simulation of multi-material fluid flow. So far, most works focus on improving its accuracy and efficiency, such as developing analytic reconstruction method and deducing the iteration schemes based on high order derivatives of the objective function. In this paper, we mainly concern on improving its robustness, especially for severely deformed polygonal meshes, in which case the objective function has multiple minimum value points. By using an efficient method for solving multiple roots of the nonlinear equation in large scope, a new algorithm is developed to enhance robustness of the MoF method. The main idea of this algorithm is as follows. The first derivative of the objective function is continuous, so the minimum value points of the objective function must be the zero points of the first derivative. Instead of finding the zero points of the first derivative directly, we turn to calculating the minimum value points (also zero points) of the square of the first derivative, which is a convex function on a neighborhood of each zero point. Applying the properties of convex function, the neighbor of each extreme minimum point of it can be obtained efficiently. Then each zero point of the square of the first derivative can be obtained using the iterative formula in its neighbor. Finally, by comparing the values of the objective function at these zero points of the first derivative, the global minimum value point of the objective function can be found and is the desired solution. The new algorithm only uses the first derivative of the objective function. It doesn't need an initial guess for the solution, which has to be carefully chosen in previous works. Numerical results are presented to demonstrate the accuracy and robustness of this new algorithm. The results show that it is applicable to severely deformed polygonal mesh, even with concave cells.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: Available online 22 March 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics〈/p〉 〈p〉Author(s): Savio Poovathingal, Eric C. Stern, Ioannis Nompelis, Thomas E. Schwartzentruber, Graham V. Candler〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Micro scale simulations are performed of flow through porous (pyrolyzing) thermal protection system (TPS) materials using the direct simulation Monte Carlo (DSMC) method. DSMC results for permeability are validated with computational fluid dynamics (CFD) calculations and theory, for simple porous geometries under continuum flow conditions. An artificial fiber-microstructure generation code FiberGen is used to create triangulated surface geometry representative of FiberForm® (FiberForm) material. DSMC results for permeability of FiberForm are validated for a range of pressures (transitional flow conditions) and agree with experimental measurements. Numerical uncertainty is determined to be within 2% if sufficiently large portions of the microstructure are included in the computation. However, small variations in fiber size and angle bias can combine to give 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mo〉+〈/mo〉〈mn〉30〈/mn〉〈mtext〉%〈/mtext〉〈/math〉 uncertainty when comparing with experimental permeability data. X-ray microtomography scans of FiberForm are used to create microstructure geometry for incorporation within DSMC simulations of coupled oxygen diffusion and gas-surface chemistry in the presence of a blowing pyrolysis gas. In-depth penetration of atomic oxygen is limited to 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈mn〉0.2〈/mn〉〈mtext〉–〈/mtext〉〈mn〉0.4〈/mn〉〈/math〉 mm for the range of Knudsen number and pyrolysis gas conditions studied.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: Available online 30 August 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation〈/p〉 〈p〉Author(s): Péter Kutas〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We propose an algorithm for finding zero divisors in quaternion algebras over quadratic number fields, or equivalently, solving homogeneous quadratic equations in three variables over 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi mathvariant="double-struck"〉Q〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈msqrt〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msqrt〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 where 〈em〉d〈/em〉 is a square-free integer. The algorithm is randomized and runs in polynomial time if one is allowed to call oracles for factoring integers.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: May–June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 92〈/p〉 〈p〉Author(s): Maria Alberich-Carramiñana, Josep Àlvarez Montaner, Guillem Blanco〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We provide an algorithm that allows to describe the minimal log-resolution of an ideal in a smooth complex surface from the minimal log-resolution of its generators. In order to make this algorithm effective we present a modified version of the Newton–Puiseux algorithm that computes the Puiseux decomposition of a product of not necessarily reduced or irreducible elements together with their algebraic multiplicity in each factor.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: March–April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 91〈/p〉 〈p〉Author(s): 〈/p〉

Beschreibung: 〈p〉Publication date: Available online 15 June 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation〈/p〉 〈p〉Author(s): Wayne Eberly〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Initial findings in a study of the automatic selection of algorithms for matrix computations are reported. These include the presentation and analysis of algorithms for the detection and certification of matrix properties allowing the reliable use of a variety of special-purpose algorithms for sparse and structured matrix computations.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: March–April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 91〈/p〉 〈p〉Author(s): Alexandru Dimca, Gabriel Sticlaru〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We describe an algorithm computing the monodromy and the pole order filtration on the Milnor fiber cohomology of any reduced projective plane curve 〈em〉C〈/em〉. The relation to the zero set of Bernstein–Sato polynomial of the defining homogeneous polynomial for 〈em〉C〈/em〉 is also discussed. When 〈em〉C〈/em〉 has some non-weighted homogeneous singularities, then we have to assume that a conjecture holds in order to get some of our results. In all the examples computed so far this conjecture holds.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: March–April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 91〈/p〉 〈p〉Author(s): Simon Hampe, Michael Joswig, Benjamin Schröter〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We describe a new method for computing tropical linear spaces and more general duals of polyhedral subdivisions. This is based on an algorithm of Ganter for finite closure systems.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: May–June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 92〈/p〉 〈p〉Author(s): Jinwang Liu, Dongmei Li, Weijun Liu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉We consider the following two problems: Let 〈em〉f〈/em〉 and 〈em〉g〈/em〉 be two polynomials over a field 〈em〉K〈/em〉.〈/p〉 〈dl〉 〈dt〉P1.〈/dt〉 〈dd〉〈p〉When is 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mo stretchy="false"〉{〈/mo〉〈mi〉f〈/mi〉〈mo〉+〈/mo〉〈mi〉s〈/mi〉〈mo〉,〈/mo〉〈mi〉g〈/mi〉〈mo〉+〈/mo〉〈mi〉t〈/mi〉〈mo stretchy="false"〉}〈/mo〉〈/math〉 a Gröbner basis for all 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"〉〈mi〉s〈/mi〉〈mo〉,〈/mo〉〈mi〉t〈/mi〉〈mo〉∈〈/mo〉〈mi〉K〈/mi〉〈/math〉?〈/p〉〈/dd〉 〈dt〉P2.〈/dt〉 〈dd〉〈p〉When is 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈mo stretchy="false"〉{〈/mo〉〈msup〉〈mrow〉〈mi〉f〈/mi〉〈/mrow〉〈mrow〉〈mi〉λ〈/mi〉〈/mrow〉〈/msup〉〈mo〉,〈/mo〉〈msup〉〈mrow〉〈mi〉g〈/mi〉〈/mrow〉〈mrow〉〈mi〉σ〈/mi〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉}〈/mo〉〈/math〉 a Gröbner basis for all 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.gif" overflow="scroll"〉〈mi〉λ〈/mi〉〈mo〉,〈/mo〉〈mi〉σ〈/mi〉〈mo〉∈〈/mo〉〈mi mathvariant="double-struck"〉N〈/mi〉〈/math〉?〈/p〉〈/dd〉 〈/dl〉 We provide a simpler proof of Hoon's criterion for P1 and a new criterion for P2. The two criteria are applied to the theory of Gröbner bases under composition.〈/div〉

Beschreibung: 〈p〉Publication date: May–June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 92〈/p〉 〈p〉Author(s): Rok Požar〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Let 〈em〉U〈/em〉 be a finitely presented group with a normal subgroup 〈em〉F〈/em〉, and let 〈em〉H〈/em〉 be a finite group. We present an effective method for constructing all 〈em〉U〈/em〉-stable epimorphisms from 〈em〉F〈/em〉 onto 〈em〉H〈/em〉; that is, epimorphisms whose kernels are normal in 〈em〉U〈/em〉. Our strategy is an adaptation of the algorithm for determining all epimorphisms from a finitely presented group onto a finite group. As an application, we construct all admissible regular graph covering projections with a given deck transformation group.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: January–February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 90〈/p〉 〈p〉Author(s): Pascal Schreck, Pascal Mathis〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In most cases in geometry, applying analytic or algebraic tools on coordinates helps to solve some difficult problems. For instance, proving that a geometrical construction problem is solvable using ruler and compass is often impossible within a synthetic geometry framework. But in an analytic geometry framework, it is a direct application of Galois theory after performing triangularizations. However, these algebraic tools lead to a large amount of computation. Their implementation in modern Computer Algebra Systems (CAS) are still too time consuming to provide an answer in a reasonable time. In addition, they require a lot of memory space which can grow exponentially with the size of the problem. Fortunately, some geometrical properties can be used to setup the algebraic systems so that they can be more efficiently computed. These properties turn polynomials into new ones so as to reduce both the degrees and the number of monomials. The present paper promotes this approach by considering two corpora of geometric construction problems, namely Wernick's and Connely's lists. These lists contain about 280 problems. The purpose is to determine their status i.e. whether they are constructible or not with ruler and compass. Some of these problems had unknown status that will be settled in this paper. More generally, the status of all problems of these corpora are fully automatically given by an approach combining geometry and algebra.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: May–June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 92〈/p〉 〈p〉Author(s): Grégoire Lecerf〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In their 1996 article, Lickteig and Roy introduced a fast “divide and conquer” variant of the subresultant algorithm which avoids coefficient growth in defective cases. The present article concerns the complexity analysis of their algorithm over effective rings endowed with the partially defined division routine. We achieve essentially the same kind of complexity bound as over effective fields. As a consequence we obtain new convenient complexity bounds for gcds, especially when coefficients are in abstract polynomial rings where evaluation/interpolation schemes are not supposed to be available.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: March–April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 91〈/p〉 〈p〉Author(s): Xavier Allamigeon, Stéphane Gaubert, Mateusz Skomra〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Helton and Nie conjectured that every convex semialgebraic set over the field of real numbers can be written as the projection of a spectrahedron. Recently, Scheiderer disproved this conjecture. We show, however, that the following result, which may be thought of as a tropical analogue of this conjecture, is true: over a real closed nonarchimedean field of Puiseux series, the convex semialgebraic sets and the projections of spectrahedra have precisely the same images by the nonarchimedean valuation. The proof relies on game theory methods.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: March–April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 91〈/p〉 〈p〉Author(s): Michela Ceria〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The aim of this paper is to count 0-dimensional stable and strongly stable ideals in 2 and 3 variables, given their (constant) affine Hilbert polynomial 〈em〉p〈/em〉, by means of a bijection between these ideals and some integer partitions of 〈em〉p〈/em〉, which can be counted via determinantal formulas. This will be achieved by the 〈em〉Bar Code〈/em〉, a bidimensional diagram that allows to represent any finite set of terms 〈em〉M〈/em〉 and desume many properties of the corresponding monomial ideal 〈em〉I〈/em〉, if 〈em〉M〈/em〉 is an order ideal.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: May–June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 92〈/p〉 〈p〉Author(s): Scott McCallum, Adam Parusiński, Laurentiu Paunescu〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In 1994 Lazard proposed an improved method for cylindrical algebraic decomposition (CAD). The method comprised a simplified projection operation together with a generalized cell lifting (that is, stack construction) technique. For the proof of the method's validity Lazard introduced a new notion of valuation of a multivariate polynomial at a point. However a gap in one of the key supporting results for his proof was subsequently noticed. In the present paper we provide a complete validity proof of Lazard's method. Our proof is based on the classical parametrized version of Puiseux's theorem and basic properties of Lazard's valuation. This result is significant because Lazard's method can be applied to any finite family of polynomials, without any assumption on the system of coordinates. It therefore has wider applicability and may be more efficient than other projection and lifting schemes for CAD.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: March–April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 91〈/p〉 〈p〉Author(s): Thomas Bauer, Sandra Di Rocco, David Schmitz, Tomasz Szemberg, Justyna Szpond〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In the present note we show that the union of 〈em〉r〈/em〉 general lines and one fat line in 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msup〉〈mrow〉〈mi mathvariant="double-struck"〉P〈/mi〉〈/mrow〉〈mrow〉〈mn〉3〈/mn〉〈/mrow〉〈/msup〉〈/math〉 imposes independent conditions on forms of sufficiently high degree 〈em〉d〈/em〉, where the bound is independent of the number of lines. This extends former results of Hartshorne and Hirschowitz on unions of general lines, and of Aladpoosh on unions of general lines and one double line.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: January–February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 90〈/p〉 〈p〉Author(s): Manfred Schmidt-Schauß, David Sabel, Yunus D.K. Kutz〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉The problem of nominal unification where variables are allowed for atoms, and computing a complete set of unifiers is considered. The complexity is shown to be NP-complete, while for special cases there are polynomial time algorithms. The main result is a novel algorithm to compute a complete set of unifiers which performs lazy guessing of equality or disequality of atom-variables, runs in NP time, and the collecting variant has more chances to keep the complete set of unifiers small. Applications of this algorithm are in reasoning about program transformations in higher order functional languages. We also present a variant of the unification algorithm that delays guessing and checking solvability, and produces a single most general unifier.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: Available online 19 June 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation〈/p〉 〈p〉Author(s): Angel Blasco, Sonia Pérez-Díaz〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Let 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi mathvariant="script"〉P〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉t〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉∈〈/mo〉〈msup〉〈mrow〉〈mi mathvariant="double-struck"〉P〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉(〈/mo〉〈mi mathvariant="double-struck"〉K〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉t〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 be a rational projective parametrization of a plane curve 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si138.gif" overflow="scroll"〉〈mi mathvariant="script"〉C〈/mi〉〈/math〉. In this paper, we introduce the notion of 〈em〉limit point〈/em〉, 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉P〈/mi〉〈/mrow〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈/msub〉〈/math〉, of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si147.gif" overflow="scroll"〉〈mi mathvariant="script"〉P〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉t〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, and some remarkable properties of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉P〈/mi〉〈/mrow〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈/msub〉〈/math〉 are obtained. In particular, if the singularities of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si138.gif" overflow="scroll"〉〈mi mathvariant="script"〉C〈/mi〉〈/math〉 are 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si174.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉P〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈mo〉…〈/mo〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉P〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉P〈/mi〉〈/mrow〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈/msub〉〈/math〉 (all of them ordinary) and their respective multiplicities are 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si175.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉m〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈mo〉,〈/mo〉〈mo〉…〈/mo〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉m〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si182.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉m〈/mi〉〈/mrow〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈/msub〉〈/math〉, we show that 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si8.gif" overflow="scroll"〉〈mi〉T〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉s〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉=〈/mo〉〈msubsup〉〈mrow〉〈mo〉∏〈/mo〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈mo〉=〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msubsup〉〈msub〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉P〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈msup〉〈mrow〉〈mo stretchy="false"〉(〈/mo〉〈mi〉s〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉m〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈/mrow〉〈/msub〉〈mo〉−〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈/msup〉〈msub〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉P〈/mi〉〈/mrow〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈msup〉〈mrow〉〈mo stretchy="false"〉(〈/mo〉〈mi〉s〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉m〈/mi〉〈/mrow〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈/msub〉〈mo〉−〈/mo〉〈mn〉1〈/mn〉〈/mrow〉〈/msup〉〈/math〉, where 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si9.gif" overflow="scroll"〉〈mi〉T〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉s〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 is the univariate resultant of two polynomials obtained from 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si147.gif" overflow="scroll"〉〈mi mathvariant="script"〉P〈/mi〉〈mo stretchy="false"〉(〈/mo〉〈mi〉t〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉, and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si10.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉P〈/mi〉〈/mrow〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈mi〉s〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉,〈/mo〉〈mo〉…〈/mo〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉P〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈mi〉s〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈mo〉,〈/mo〉〈msub〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈msub〉〈mrow〉〈mi〉P〈/mi〉〈/mrow〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈/msub〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈mi〉s〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 are the 〈em〉fibre functions〈/em〉 of the singularities. The fibre function of a point 〈em〉P〈/em〉 is a polynomial 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si11.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈mi〉P〈/mi〉〈/mrow〉〈/msub〉〈mo stretchy="false"〉(〈/mo〉〈mi〉s〈/mi〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 whose roots are the fibre of 〈em〉P〈/em〉. Thus, a complete classification of the singularities of a given plane curve, via the factorization of a resultant, is obtained.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: March–April 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 91〈/p〉 〈p〉Author(s): Hannah Markwig, Bernard Mourrain, Giorgio Ottaviani〈/p〉

Beschreibung: 〈p〉Publication date: Available online 17 July 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation〈/p〉 〈p〉Author(s): Cristina Bertone, Francesca Cioffi, Davide Franco〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉A classical approach to investigate a closed projective scheme 〈em〉W〈/em〉 consists of considering a general hyperplane section of 〈em〉W〈/em〉, which inherits many properties of 〈em〉W〈/em〉. The inverse problem that consists in finding a scheme 〈em〉W〈/em〉 starting from a possible hyperplane section 〈em〉Y〈/em〉 is called a 〈em〉lifting problem〈/em〉, and every such scheme 〈em〉W〈/em〉 is called a 〈em〉lifting〈/em〉 of 〈em〉Y〈/em〉. Investigations in this topic can produce methods to obtain schemes with specific properties. For example, any smooth point for 〈em〉Y〈/em〉 is smooth also for 〈em〉W〈/em〉.〈/p〉 〈p〉We characterize all the liftings of 〈em〉Y〈/em〉 with a given Hilbert polynomial by a parameter scheme that is obtained by gluing suitable affine open subschemes in a Hilbert scheme and is described through the functor it represents. We use constructive methods from Gröbner and marked bases theories. Furthermore, by classical tools we obtain an analogous result for equidimensional liftings. Examples of explicit computations are provided.〈/p〉 〈/div〉

Beschreibung: 〈p〉Publication date: May–June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 92〈/p〉 〈p〉Author(s): James East, Attila Egri-Nagy, James D. Mitchell, Yann Péresse〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to which these results apply include many important classes: transformation semigroups, partial permutation semigroups and inverse semigroups, partition monoids, matrix semigroups, and subsemigroups of finite regular Rees matrix and 0-matrix semigroups over groups. For any subsemigroup of such a semigroup, it is possible to, among other things, efficiently compute its size and Green's relations, test membership, factorize elements over the generators, find the semigroup generated by the given subsemigroup and any collection of additional elements, calculate the partial order of the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mi mathvariant="script"〉D〈/mi〉〈/math〉-classes, test regularity, and determine the idempotents. This is achieved by representing the given subsemigroup without exhaustively enumerating its elements. It is also possible to compute the Green's classes of an element of such a subsemigroup without determining the global structure of the semigroup.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: May–June 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 92〈/p〉 〈p〉Author(s): Ivan Marin〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We prove two new cases of the Broué–Malle–Rouquier freeness conjecture for the Hecke algebras associated to complex reflection groups, using methods inspired by non-commutative Gröbner bases. These two cases are the complex reflection groups of rank 2 called 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mn〉20〈/mn〉〈/mrow〉〈/msub〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si16.gif" overflow="scroll"〉〈msub〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mn〉21〈/mn〉〈/mrow〉〈/msub〉〈/math〉 in the Shephard and Todd classification. This reduces the number of remaining unproven cases to 3.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: January–February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Symbolic Computation, Volume 90〈/p〉 〈p〉Author(s): Adnan Rashid, Osman Hasan〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉To study the dynamical behavior of the engineering and physical systems, we often need to capture their continuous behavior, which is modeled using differential equations, and perform the frequency-domain analysis of these systems. Traditionally, Fourier transform methods are used to perform this frequency domain analysis using paper-and-pencil based analytical techniques or computer simulations. However, both of these methods are error prone and thus are not suitable for analyzing systems used in safety-critical domains, like medicine and transportation. In order to provide an accurate alternative, we propose to use higher-order-logic theorem proving to conduct the frequency domain analysis of these systems. For this purpose, the paper presents a higher-order-logic formalization of Fourier transform using the HOL-Light theorem prover. In particular, we use the higher-order-logic based formalizations of differential, integral, transcendental and topological theories of multivariable calculus to formally define Fourier transform and reason about the correctness of its classical properties, such as existence, linearity, time shifting, frequency shifting, modulation, time scaling, time reversal and differentiation in time domain, and its relationships with Fourier Cosine, Fourier Sine and Laplace transforms. We use our proposed formalization for the formal verification of the frequency response of a generic n-order linear system, an audio equalizer and a MEMs accelerometer, using the HOL-Light theorem prover.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Sustainable Cities and Society, Volume 44〈/p〉 〈p〉Author(s): Ning Wang, Linhao Tang, Huizhong Pan〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Environmental issues and energy security have led governments to introduce lots of incentive policies on electric vehicle promotion. Benefiting from policy dividend, the global threshold of 1 million electric cars on the road had been exceeded in 2015, closing at 1.26 million. Among these incentive policies, subsidy scheme was regarded as the most important and effective. However, many governments intend to abrogate subsidy for electric vehicle, such as China, America and Germany. It`s worth finding out the key factors including incentive measures and additional socio-economic factors that promote electric vehicle adoption. Utilizing multiple linear regression method, we explore the relationship between those variables and 30 national electric vehicle market shares for the year 2015. The results show that chargers` density, fuel price and road priority are significantly positive factors correlated with a country`s electric vehicle market share. Nevertheless, fiscal incentives are no longer the reasons for the huge differences of electric vehicle promotion over countries. This paper is helpful for policymakers to adjust and improve their policy for electric mobility.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: January–June 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 SoftwareX, Volume 7〈/p〉 〈p〉Author(s): Martin Masek, Chiou Peng Lam, Cameron Tranthim-Fryer, Bas Jansen, Kevin Baptist〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present a software package for analysing body positions of a subject when they are lying or sleeping in their bed. The software is designed to interface to inexpensive sensors, such as the Microsoft Kinect, and is thus suitable for monitoring at the subjects own home, rather than a dedicated sleep lab. The system is invariant to bed clothing and levels of ambient lighting. Analysis time for a single night session is under five minutes, a significant improvement over the 30–60 min analysis time reported in the literature.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: March 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Pattern Recognition, Volume 87〈/p〉 〈p〉Author(s): Jimin Xiao, Yanchun Xie, Tammam Tillo, Kaizhu Huang, Yunchao Wei, Jiashi Feng〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Person search in real-world scenarios is a new challenging computer version task with many meaningful applications. The challenge of this task mainly comes from: (1) unavailable bounding boxes for pedestrians and the model needs to search for the person over the whole gallery images; (2) huge variance of visual appearance of a particular person owing to varying poses, lighting conditions, and occlusions. To address these two critical issues in modern person search applications, we propose a novel Individual Aggregation Network (IAN) that can accurately localize persons by learning to minimize intra-person feature variations. IAN is built upon the state-of-the-art object detection framework, i.e., faster R-CNN, so that high-quality region proposals for pedestrians can be produced in an online manner. In addition, to relieve the negative effect caused by varying visual appearances of the same individual, IAN introduces a novel center loss that can increase the intra-class compactness of feature representations. The engaged center loss encourages persons with the same identity to have similar feature characteristics. Extensive experimental results on two benchmarks, i.e., CUHK-SYSU and PRW, well demonstrate the superiority of the proposed model. In particular, IAN achieves 77.23% mAP and 80.45% top-1 accuracy on CUHK-SYSU, which outperform the state-of-the-art by 1.7% and 1.85%, respectively.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): A. Belme, F. Alauzet, A. Dervieux〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present a goal-oriented error analysis for the calculation of low Reynolds steady compressible flows with anisotropic mesh adaptation. The error analysis is of 〈em〉a priori〈/em〉 type. Its central principle is to express the right-hand side of the error equation, often referred as the local error, as a function of the interpolation error of a collection of fields present in the nonlinear Partial Differential Equations. This goal-oriented error analysis is the extension of [39] done for inviscid flows to laminar viscous flows by adding viscous terms. The main benefits of this approach, in comparison to other error estimates in the literature, is that the optimal anisotropy of the mesh directly appears in the error analysis and is not obtained from an ad hoc variable nor a local analysis. As a consequence, an optimum is obtained and the convergence of the mesh adaptive process is very fast, 〈em〉i.e.,〈/em〉 generally the convergence is obtained after 5 to 10 mesh adaptation cycle. Then, using the continuous mesh framework, an optimal metric is analytically obtained from the error estimation. Applications to mesh adaptive calculations of flows past airfoils are presented.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 15 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 375〈/p〉 〈p〉Author(s): Pablo Miguel Ramos, Nikos Ch. Karayiannis, Manuel Laso〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A new algorithmic approach is presented for the generation and successive equilibration of polymer configurations under conditions of extreme confinement where the inter-wall distance, in at least one dimension, approaches the diameter of the spherical monomers. It significantly improves on the Monte Carlo (MC) protocol described in Karayiannis and Laso (2008) [126]. The algorithm is designed to generate highly confined packings of freely-jointed chains of hard spheres of uniform size. Spatial confinement is achieved by including flat, parallel impenetrable walls in one or more dimensions of the simulation box. The present MC scheme allows the systematic study of the effect of chain length, polydispersity, volume fraction, bond tolerance (gap), cell aspect ratio and level of confinement on the short- and long-range structure of polymer chains near and far from the confining planes. In the present study we focus on the efficiency of the MC protocol in generating, equilibrating, and configurationally decorrelating chain assemblies with average lengths ranging from 〈em〉N〈/em〉 = 12 to 1000 monomers and at volume fractions from dilute up to the maximally random jammed (MRJ) state. Starting from cubic amorphous cells filled with polymer chains, the MC algorithm is able to reach quasi 2-d (plate-like) and 1-d (tube-like) states under conditions of extreme confinement and/or cell aspect ratio where the inter-wall distance approaches the diameter of beads forming the chains. A comparison with corresponding bulk packings shows the similarities and differences produced by extreme spatial confinement.〈/p〉〈/div〉 〈h5〉Graphical abstract〈/h5〉 〈div〉〈p〉Snapshots of computer-generated athermal polymer configurations under full confinement with increasing cell aspect ratio starting from 3-d cubic cells and leading to 2-d templates.〈/p〉〈/div〉 〈figure〉〈img src="https://ars.els-cdn.com/content/image/1-s2.0-S0021999118305850-gr001.jpg" width="452" alt="Graphical abstract for this article" title=""〉〈/figure〉

Beschreibung: 〈p〉Publication date: 15 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 375〈/p〉 〈p〉Author(s): Gaddiel Y. Ouaknin, Nabil Laachi, Kris Delaney, Glenn H. Fredrickson, Frederic Gibou〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We introduce a level-set strategy to find the geometry of confinement that will guide the self-assembly of block copolymers to a given target design in the context of lithography. The methodology is based on a shape optimization algorithm, where the level-set normal velocity is defined as the pressure field computed through a self-consistent field theory simulation. We present numerical simulations that demonstrate that this methodology is capable of finding guiding templates for a variety of target arrangements of cylinders and thus is an effective approach to the inverse directed self-assembly problem.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Complexity, Volume 48〈/p〉 〈p〉Author(s): Alexander E. Litvak, Anna Lytova, Konstantin Tikhomirov, Nicole Tomczak-Jaegermann, Pierre Youssef〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Let 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈mi〉d〈/mi〉〈/math〉 be a (large) integer. Given 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si2.gif"〉〈mi〉n〈/mi〉〈mo〉≥〈/mo〉〈mn〉2〈/mn〉〈mi〉d〈/mi〉〈/math〉, let 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si3.gif"〉〈msub〉〈mrow〉〈mi〉A〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈/math〉 be the adjacency matrix of a random directed 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈mi〉d〈/mi〉〈/math〉-regular graph on 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si5.gif"〉〈mi〉n〈/mi〉〈/math〉 vertices, with the uniform distribution. We show that the rank of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si3.gif"〉〈msub〉〈mrow〉〈mi〉A〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈/math〉 is at least 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si7.gif"〉〈mi〉n〈/mi〉〈mo〉−〈/mo〉〈mn〉1〈/mn〉〈/math〉 with probability going to one as 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si5.gif"〉〈mi〉n〈/mi〉〈/math〉 grows to infinity. The proof combines the well known method of simple switchings and a recent result of the authors on delocalization of eigenvectors of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si3.gif"〉〈msub〉〈mrow〉〈mi〉A〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈/math〉.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Complexity, Volume 49〈/p〉 〈p〉Author(s): Hongzhi Tong, Michael Ng〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we study and analyze the regularized least squares for functional linear regression model. The approach is to use the reproducing kernel Hilbert space framework and the integral operators. We show with a more general and realistic assumption on the reproducing kernel and input data statistics that the rate of excess prediction risk by the regularized least squares is minimax optimal.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Complexity, Volume 50〈/p〉 〈p〉Author(s): Jia Chen, Heping Wang〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we investigate optimal linear approximations (〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈mi〉n〈/mi〉〈/math〉-approximation numbers) of the embeddings from the Sobolev spaces 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si2.gif"〉〈msup〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈mi〉r〈/mi〉〈/mrow〉〈/msup〉〈mspace width="0.33em"〉〈/mspace〉〈mrow〉〈mo〉(〈/mo〉〈mi〉r〈/mi〉〈mo〉〉〈/mo〉〈mn〉0〈/mn〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉 for various equivalent norms and the Gevrey type spaces 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si3.gif"〉〈msup〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mi〉α〈/mi〉〈mo〉,〈/mo〉〈mi〉β〈/mi〉〈/mrow〉〈/msup〉〈mspace width="0.33em"〉〈/mspace〉〈mrow〉〈mo〉(〈/mo〉〈mi〉α〈/mi〉〈mo〉,〈/mo〉〈mi〉β〈/mi〉〈mo〉〉〈/mo〉〈mn〉0〈/mn〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉 on the sphere 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si4.gif"〉〈msup〉〈mrow〉〈mi mathvariant="double-struck"〉S〈/mi〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msup〉〈/math〉 and on the ball 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si5.gif"〉〈msup〉〈mrow〉〈mi mathvariant="double-struck"〉B〈/mi〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msup〉〈/math〉, where the approximation error is measured in the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si6.gif"〉〈msub〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈/math〉-norm. We obtain preasymptotics, asymptotics, and strong equivalences of the above approximation numbers as a function in 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈mi〉n〈/mi〉〈/math〉 and the dimension 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si8.gif"〉〈mi〉d〈/mi〉〈/math〉. We emphasize that all equivalence constants in the above preasymptotics and asymptotics are independent of the dimension 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si8.gif"〉〈mi〉d〈/mi〉〈/math〉 and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈mi〉n〈/mi〉〈/math〉. As a consequence we obtain that for the absolute error criterion the approximation problems 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si11.gif"〉〈msub〉〈mrow〉〈mi〉I〈/mi〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msub〉〈mo〉:〈/mo〉〈msup〉〈mrow〉〈mi〉H〈/mi〉〈/mrow〉〈mrow〉〈mi〉r〈/mi〉〈/mrow〉〈/msup〉〈mo〉→〈/mo〉〈msub〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈/math〉 are weakly tractable if and only if 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si12.gif"〉〈mi〉r〈/mi〉〈mo〉〉〈/mo〉〈mn〉1〈/mn〉〈/math〉, not uniformly weakly tractable, and do not suffer from the curse of dimensionality. We also prove that for any 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si13.gif"〉〈mi〉α〈/mi〉〈mo〉,〈/mo〉〈mi〉β〈/mi〉〈mo〉〉〈/mo〉〈mn〉0〈/mn〉〈/math〉, the approximation problems 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si14.gif"〉〈msub〉〈mrow〉〈mi〉I〈/mi〉〈/mrow〉〈mrow〉〈mi〉d〈/mi〉〈/mrow〉〈/msub〉〈mo〉:〈/mo〉〈msup〉〈mrow〉〈mi〉G〈/mi〉〈/mrow〉〈mrow〉〈mi〉α〈/mi〉〈mo〉,〈/mo〉〈mi〉β〈/mi〉〈/mrow〉〈/msup〉〈mo〉→〈/mo〉〈msub〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msub〉〈/math〉 are uniformly weakly tractable, not polynomially tractable, and quasi-polynomially tractable if and only if 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si15.gif"〉〈mi〉α〈/mi〉〈mo〉≥〈/mo〉〈mn〉1〈/mn〉〈/math〉.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Complexity, Volume 49〈/p〉 〈p〉Author(s): Domingo Gómez-Pérez, Min Sha, Andrew Tirkel〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper, we define the linear complexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linear complexity and 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈mi〉k〈/mi〉〈/math〉-error linear complexity of multidimensional periodic sequences.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Complexity, Volume 48〈/p〉 〈p〉Author(s): Robert J. Kunsch〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We study the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si2.gif"〉〈msub〉〈mrow〉〈mi〉L〈/mi〉〈/mrow〉〈mrow〉〈mi〉∞〈/mi〉〈/mrow〉〈/msub〉〈/math〉-approximation of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si3.gif"〉〈mi〉d〈/mi〉〈/math〉-variate functions from Hilbert spaces via linear functionals as information. It is a common phenomenon in tractability studies that unweighted problems (with each dimension being equally important) suffer from the curse of dimensionality in the deterministic setting, that is, the number 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si4.gif"〉〈mi〉n〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉ϵ〈/mi〉〈mo〉,〈/mo〉〈mi〉d〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉 of information needed in order to solve a problem within a given accuracy 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si5.gif"〉〈mi〉ϵ〈/mi〉〈mo〉〉〈/mo〉〈mn〉0〈/mn〉〈/math〉 grows exponentially in 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si3.gif"〉〈mi〉d〈/mi〉〈/math〉. We show that for certain approximation problems in periodic tensor product spaces, in particular Korobov spaces with smoothness  〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si7.gif"〉〈mi〉r〈/mi〉〈mo〉〉〈/mo〉〈mn〉1〈/mn〉〈mo〉∕〈/mo〉〈mn〉2〈/mn〉〈/math〉, switching to the randomized setting can break the curse of dimensionality, now having polynomial tractability, namely 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si8.gif"〉〈mi〉n〈/mi〉〈mrow〉〈mo〉(〈/mo〉〈mi〉ϵ〈/mi〉〈mo〉,〈/mo〉〈mi〉d〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈mo〉⪯〈/mo〉〈msup〉〈mrow〉〈mi〉ϵ〈/mi〉〈/mrow〉〈mrow〉〈mo〉−〈/mo〉〈mn〉2〈/mn〉〈/mrow〉〈/msup〉〈mspace width="0.16667em"〉〈/mspace〉〈mi〉d〈/mi〉〈mspace width="0.16667em"〉〈/mspace〉〈mrow〉〈mo〉(〈/mo〉〈mn〉1〈/mn〉〈mo〉+〈/mo〉〈mo〉log〈/mo〉〈mi〉d〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉. Similar benefits from Monte Carlo methods in terms of tractability have only been known for integration problems so far.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: October 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Complexity, Volume 48〈/p〉 〈p〉Author(s): Kateryna Tatarko〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Let 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈mi〉A〈/mi〉〈mo〉=〈/mo〉〈mrow〉〈mo〉(〈/mo〉〈msub〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mi〉i〈/mi〉〈mi〉j〈/mi〉〈/mrow〉〈/msub〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉 be a square 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si2.gif"〉〈mi〉n〈/mi〉〈mo〉×〈/mo〉〈mi〉n〈/mi〉〈/math〉 matrix with i.i.d. zero mean and unit variance entries. It was shown by Rudelson and Vershynin in 2008 that the upper bound for the smallest singular value 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si3.gif"〉〈msub〉〈mrow〉〈mi〉s〈/mi〉〈/mrow〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈/msub〉〈mrow〉〈mo〉(〈/mo〉〈mi〉A〈/mi〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉 is of order 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si4.gif"〉〈msup〉〈mrow〉〈mi〉n〈/mi〉〈/mrow〉〈mrow〉〈mo〉−〈/mo〉〈mfrac〉〈mrow〉〈mn〉1〈/mn〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/mfrac〉〈/mrow〉〈/msup〉〈/math〉 with probability close to one under the additional assumption that the entries of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si5.gif"〉〈mi〉A〈/mi〉〈/math〉 satisfy 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si6.gif"〉〈mi mathvariant="double-struck"〉E〈/mi〉〈msubsup〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mn〉11〈/mn〉〈/mrow〉〈mrow〉〈mn〉4〈/mn〉〈/mrow〉〈/msubsup〉〈mo〉〈〈/mo〉〈mi〉∞〈/mi〉〈/math〉. We remove the assumption on the fourth moment and show the upper bound assuming only 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si7.gif"〉〈mi mathvariant="double-struck"〉E〈/mi〉〈msubsup〉〈mrow〉〈mi〉a〈/mi〉〈/mrow〉〈mrow〉〈mn〉11〈/mn〉〈/mrow〉〈mrow〉〈mn〉2〈/mn〉〈/mrow〉〈/msubsup〉〈mo〉=〈/mo〉〈mn〉1〈/mn〉〈mo〉.〈/mo〉〈/math〉〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Complexity, Volume 50〈/p〉 〈p〉Author(s): Yoshihito Kazashi, Quoc T. Le Gia〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We investigate a discretization of a class of stochastic heat equations on the unit sphere with multiplicative noise. A spectral method is used for the spatial discretization and the truncation of the Wiener process, while an implicit Euler scheme with non-uniform steps is used for the temporal discretization. Some numerical experiments inspired by Earth’s surface temperature data analysis GISTEMP provided by NASA are given.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: February 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Complexity, Volume 50〈/p〉 〈p〉Author(s): Shao-Bo Lin〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Needlets have been recognized as state-of-the-art tools to tackle spherical data, due to their excellent localization properties in both spacial and frequency domains. This paper considers developing kernel methods associated with the needlet kernel for nonparametric regression problems whose predictor variables are defined on a sphere. Due to the localization property in the frequency domain, we prove that the regularization parameter of the kernel ridge regression associated with the needlet kernel can decrease arbitrarily fast. A natural consequence is that the regularization term for the kernel ridge regression is not necessary in the sense of rate optimality. Based on the excellent localization property in the spacial domain further, we prove that all 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si1.gif"〉〈msup〉〈mrow〉〈mi〉l〈/mi〉〈/mrow〉〈mrow〉〈mi〉q〈/mi〉〈/mrow〉〈/msup〉〈/math〉〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si2.gif"〉〈mrow〉〈mo〉(〈/mo〉〈mn〉0〈/mn〉〈mo〉〈〈/mo〉〈mi〉q〈/mi〉〈mo〉≤〈/mo〉〈mn〉2〈/mn〉〈mo〉)〈/mo〉〈/mrow〉〈/math〉 kernel regularization estimates associated with the needlet kernel, including the kernel lasso estimate and kernel bridge estimate, possess almost same generalization capability for a large range of regularization parameters in the sense of rate optimality. This finding tentatively reveals that, if the needlet kernel is utilized, then the choice of 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si3.gif"〉〈mi〉q〈/mi〉〈/math〉 might not have a strong impact on the generalization capability in some modeling contexts. The above two properties reveal the theoretical advantages of the needlet kernel in kernel methods for spherical nonparametric regression problems.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Complexity, Volume 49〈/p〉 〈p〉Author(s): Janak Raj Sharma, Deepak Kumar〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉An iterative method with fifth order of convergence for solving systems of nonlinear equations is presented. The scheme is composed of three steps, of which the first two steps are that of double Newton’s method with frozen derivative and third step is second derivative-free modification of Chebyshev’s method. The semilocal convergence of the method in Banach spaces is established by using a system of recurrence relations. Then an existence and uniqueness theorem is given to show the 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="si98.gif"〉〈mi〉R〈/mi〉〈/math〉-order of the method to be five and a priori error bounds. Computational complexity is discussed and compared with existing methods. Numerical results are included to confirm theoretical results. A comparison with the existing methods shows that the new method is more efficient than existing ones and hence use the minimum computing time in multiprecision arithmetic.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Gautier Dakin, Bruno Després, Stéphane Jaouen〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Staggered grids schemes, formulated in internal energy, are commonly used for CFD applications in industrial context. Here, we prove the consistency of a class of high-order Lagrange-Remap staggered schemes for solving the Euler equations in 1D and 2D on Cartesian grids. The main result of the paper is that using an 〈em〉a posteriori〈/em〉 internal energy corrector, the Lagrangian schemes are proved to be conservative in mass, momentum and total energy and to be weakly consistent with the 1D Lagrangian formulation of the Euler equations. Extension in 2D is done using directional splitting methods and face-staggering. Numerical examples in both 1D and 2D illustrate the accuracy, the convergence and the robustness of the schemes.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 15 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 375〈/p〉 〈p〉Author(s): Florian Monteghetti, Denis Matignon, Estelle Piot〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Time-domain impedance boundary conditions (TDIBCs) can be enforced using the impedance, the admittance, or the scattering operator. This article demonstrates the computational advantage of the last, even for nonlinear TDIBCs, with the linearized Euler equations. This is achieved by a systematic semi-discrete energy analysis of the weak enforcement of a generic nonlinear TDIBC in a discontinuous Galerkin finite element method. In particular, the analysis highlights that the sole definition of a discrete model is not enough to fully define a TDIBC. To support the analysis, an elementary physical nonlinear scattering operator is derived and its computational properties are investigated in an impedance tube. Then, the derivation of time-delayed broadband TDIBCs from physical reflection coefficient models is carried out for single degree of freedom acoustical liners. A high-order discretization of the derived time-local formulation, which consists in composing a set of ordinary differential equations with a transport equation, is applied to two flow ducts.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): C. Cheng, A.P. Bunger〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉A new reduced order model (ROM) provides rapid and reasonably accurate prediction of the complex behavior of multiple, simultaneously growing radial hydraulic fractures. The method entails vastly reducing the degrees of freedom typically associated with fully-coupled simulations of this multiple moving boundary problem by coupling together an approximation of the influence of the stress interaction among the fractures (“stress shadow”) with an approximation of fluid flow and elasticity, ensuring preservation of global volume balance, global energy balance, elasticity, and compatibility of the crack opening with the inlet fluid flux. Validating with large scale (“high-fidelity”) simulations shows the ROM solution captures not only the basic suppression of interior hydraulic fractures in a uniformly-spaced array due to the well-known stress shadowing phenomenon, but also complex behaviors arising when the spacing among the hydraulic fractures is non-uniform. The simulator's usefulness is demonstrated through a proof-of-concept optimization whereby non-uniform spacing and stage length are chosen to maximize the fracture surface area and/or the uniformity of growth associated with each stimulation treatment.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 15 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 375〈/p〉 〈p〉Author(s): Rohit K. Tripathy, Ilias Bilionis〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉State-of-the-art computer codes for simulating real physical systems are often characterized by vast number of input parameters. Performing uncertainty quantification (UQ) tasks with Monte Carlo (MC) methods is almost always infeasible because of the need to perform hundreds of thousands or even millions of forward model evaluations in order to obtain convergent statistics. One, thus, tries to construct a cheap-to-evaluate surrogate model to replace the forward model solver. For systems with large numbers of input parameters, one has to address the curse of dimensionality through suitable dimensionality reduction techniques. A popular class of dimensionality reduction methods are those that attempt to recover a low-dimensional representation of the high-dimensional feature space. However, such methods often tend to overestimate the intrinsic dimensionality of the input feature space. In this work, we demonstrate the use of deep neural networks (DNN) to construct surrogate models for numerical simulators. We parameterize the structure of the DNN in a manner that lends the DNN surrogate the interpretation of recovering a low-dimensional nonlinear manifold. The model response is a parameterized nonlinear function of the low-dimensional projections of the input. We think of this low-dimensional manifold as a nonlinear generalization of the notion of the 〈em〉active subspace〈/em〉. Our approach is demonstrated with a problem on uncertainty propagation in a stochastic elliptic partial differential equation (SPDE) with uncertain diffusion coefficient. We deviate from traditional formulations of the SPDE problem by lifting the assumption of fixed lengthscales of the uncertain diffusion field. Instead we attempt to solve a more challenging problem of learning a map between an arbitrary snapshot of the diffusion field and the response.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 15 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 375〈/p〉 〈p〉Author(s): Jordi Casacuberta, Koen J. Groot, Henry J. Tol, Stefan Hickel〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Selective Frequency Damping (SFD) is a popular method for the computation of globally unstable steady-state solutions in fluid dynamics. The approach has two model parameters whose selection is generally unclear. In this article, a detailed analysis of the influence of these parameters is presented, answering several open questions with regard to the effectiveness, optimum efficiency and limitations of the method. In particular, we show that SFD is always capable of stabilising a globally unstable systems ruled by one unsteady unstable eigenmode and derive analytical formulas for optimum parameter values. We show that the numerical feasibility of the approach depends on the complex phase angle of the most unstable eigenvalue. A numerical technique for characterising the pertinent eigenmodes is presented. In combination with analytical expressions, this technique allows finding optimal parameters that minimise the spectral radius of a simulation, without having to perform an independent stability analysis. An extension to multiple unstable eigenmodes is derived. As computational example, a two-dimensional cylinder flow case is optimally stabilised using this method. We provide a physical interpretation of the stabilisation mechanism based on, but not limited to, this Navier–Stokes example.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 15 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 375〈/p〉 〈p〉Author(s): M. Esmaeilbeigi, O. Chatrabgoun, M. Cheraghi〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In the interpolation method, in some cases, one often has a number of data points and its derivatives, which are obtained by sampling or experimentation. In this case, the problem of finding an approximating function passing through these points and coinciding with given values of its derivatives at these points is generally known as “Hermite interpolation”. The Hermite interpolation is mostly a method of interpolating data points as a polynomial function that is faced with some challenges in high dimensions and on irregular domains. Radial basis functions take advantage of being flexible with respect to geometry, easy to implement in higher dimensions, and can also provide high order convergence. So, they can be applied as a suitable tool to high dimensional Hermite interpolation problem on irregular domains. In many applied systems, commonly available derivatives information is presented using fractional order derivatives instead of integer ones. For this purpose, in this paper, we assume that the values of an unknown function and its fractional derivatives at some distinct points are presented. Therefore, we intend to apply a new approach, which we call it as “fractional Hermite interpolation” with radial basis functions in high dimensions. Optimal recovery conditions for the fractional Hermite interpolant are investigated. Then, the existence and uniqueness of the solution in this type of generalized interpolation are proved. In order to increase the accuracy and stability of the method, Hilbert Schmidt's theory has also been used. The main advantages of the used method are its simplicity and efficiency in high dimensions, and over irregular domains. Finally, numerical results in one, two and three dimensions and a real-world problem are presented to support our theoretical analysis.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Majid Haghshenas, James A. Wilson, Ranganathan Kumar〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this work, we implement interfacial forces (surface tension, hydrostatic and viscous forces) by enlisting the finite volume discretization of GFM (Ghost Fluid Method) using A-CLSVOF (Algebraic Coupled Level-Set/Volume-of-Fluid) method for the mass conservative, and smooth interface description. The widely used PISO momentum solution to resolve the pressure–velocity coupling is presented along with the present GFM discretization and its placement within the PISO loop. The pressure jump at the interface due to the interfacial forces is made sharp via direct calculation of the modified pressure matrix coefficients corresponding to targeted interfacial cells, and as a source term for the jump value itself. The Level-Set field is enlisted for curvature computation in A-CLSVOF and for the interpolation and weighting of the relative contribution of the capillary force in adjacent for the matrix coefficients in the FV framework. To assess the A-CLSVOF/GFM performance, four canonical cases were studied. In the case of a static droplet in suspension, A-CLSVOF/GFM produces a sharp and accurate pressure jump compared to the traditional CSF implementation of A-CLSVOF. The interaction of viscous and capillary forces is proven to be accurate and consistent with theoretical results for the classical capillary wave. For the linear two-layer shear flow, GFM sharp treatment of the viscosity captured the velocity gradient across the interface and removed the diffusion of the viscous stresses caused by the discontinuous material properties. Finally, the combination of all GFM improvements proposed in this study are compared to experimental findings of terminal velocity for a gaseous bubble rising in a viscous fluid. GFM outperforms CSF with errors of 4.6% and 14.0% respectively.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Samira Nikkar, Jan Nordström〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉 〈p〉In this article, well-posedness and dual consistency of the linearized constant coefficient incompressible Navier–Stokes equations posed on time-dependent spatial domains are studied. To simplify the derivation of the dual problem and improve the accuracy of gradients, the second order formulation is transformed to first order form. Boundary conditions that simultaneously lead to boundedness of the primal and dual problems are derived.〈/p〉 〈p〉Fully discrete finite difference schemes on summation-by-parts form, in combination with the simultaneous approximation technique, are constructed. We prove energy stability and discrete dual consistency and show how to construct the penalty operators such that the scheme automatically adjusts to the variations of the spatial domain. As a result of the aforementioned formulations, stability and discrete dual consistency follow simultaneously.〈/p〉 〈p〉The method is illustrated by considering a deforming time-dependent spatial domain in two dimensions. The numerical calculations are performed using high order operators in space and time. The results corroborate the stability of the scheme and the accuracy of the solution. We also show that linear functionals are superconverging. Additionally, we investigate the convergence of non-linear functionals and the divergence of the solution.〈/p〉 〈/div〉

Beschreibung: 〈p〉Publication date: 15 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 375〈/p〉 〈p〉Author(s): Chris J. Budd, Andrew T.T. McRae, Colin J. Cotter〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In the context of numerical solution of PDEs, dynamic mesh redistribution methods (r-adaptive methods) are an important procedure for increasing the resolution in regions of interest, without modifying the connectivity of the mesh. Key to the success of these methods is that the mesh should be sufficiently refined (locally) and flexible in order to resolve evolving solution features, but at the same time not introduce errors through skewness and lack of regularity. Some state-of-the-art methods are bottom-up in that they attempt to prescribe both the local cell size and the alignment to features of the solution. However, the resulting problem is overdetermined, necessitating a compromise between these conflicting requirements. An alternative approach, described in this paper, is to prescribe only the local cell size and augment this an optimal transport condition to provide global regularity. This leads to a robust and flexible algorithm for generating meshes fitted to an evolving solution, with minimal need for tuning parameters. Of particular interest for geophysical modelling are meshes constructed on the surface of the sphere. The purpose of this paper is to demonstrate that meshes generated on the sphere using this optimal transport approach have good a-priori regularity and that the meshes produced are naturally aligned to various simple features. It is further shown that the sphere's intrinsic curvature leads to more regular meshes than the plane. In addition to these general results, we provide a wide range of examples relevant to practical applications, to showcase the behaviour of optimally transported meshes on the sphere. These range from axisymmetric cases that can be solved analytically to more general examples that are tackled numerically. Evaluation of the singular values and singular vectors of the mesh transformation provides a quantitative measure of the mesh anisotropy, and this is shown to match analytic predictions.〈/p〉〈/div〉 〈h5〉Graphical abstract〈/h5〉 〈div〉〈p〉〈/p〉〈/div〉 〈figure〉〈img src="https://ars.els-cdn.com/content/image/1-s2.0-S0021999118305515-gr001.jpg" width="494" alt="Graphical abstract for this article" title=""〉〈/figure〉

Beschreibung: 〈p〉Publication date: 15 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 375〈/p〉 〈p〉Author(s): Ahmad Al Takash, Marianne Beringhier, Mohammad Hammoud, Jean-Claude Grandidier〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉Large computation time is widely considered to be the most important issue in scientific research especially in solving structural evolution problems. Recent developments in this domain have shown that the use of non-incremental schemes through Model Order Reduction led to important results in saving time. Yet, the question arises here how to obtain more time-saving. This paper examines an approach based on a collection of significant modes given by Proper Generalized Decomposition (PGD) solution for different time scales in order to save more computation time. The dictionary of the significant modes allows to construct an accurate solution for different characteristic times and different boundary problems compared to the full solution with a relative error rate less than 5% and with a large time saving of order 50 compared to Finite Element Method (FEM). The ability of the approach with respect to cycle time is discussed.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 15 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 375〈/p〉 〈p〉Author(s): Christopher Lester, Christian A. Yates, Ruth E. Baker〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this work, we consider the problem of estimating summary statistics to characterise biochemical reaction networks of interest. Such networks are often described using the framework of the Chemical Master Equation (CME). For physically-realistic models, the CME is widely considered to be analytically intractable. A variety of Monte Carlo algorithms have therefore been developed to explore the dynamics of such networks empirically. Amongst them is the multi-level method, which uses estimates from multiple ensembles of sample paths of different accuracies to estimate a summary statistic of interest. In this work, we develop the multi-level method in two directions: (1) to increase the robustness, reliability and performance of the multi-level method, we implement an improved variance reduction method for generating the sample paths of each ensemble; and (2) to improve computational performance, we demonstrate the successful use of a different mechanism for choosing which ensembles should be included in the multi-level algorithm.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 1 January 2019〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 376〈/p〉 〈p〉Author(s): Dong-Yeop Na, Ben-Hur V. Borges, Fernando L. Teixeira〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉We present a finite-element time-domain (FETD) Maxwell solver for the analysis of body-of-revolution (BOR) geometries based on discrete exterior calculus (DEC) of differential forms and transformation optics (TO) concepts. We explore TO principles to map the original 3-D BOR problem to a 2-D one in the meridian 〈em〉ρz〈/em〉-plane based on a Cartesian coordinate system where the cylindrical metric is fully embedded into the constitutive properties of an effective inhomogeneous and anisotropic medium that fills the domain. The proposed solver uses a 〈math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"〉〈mo stretchy="false"〉(〈/mo〉〈msup〉〈mrow〉〈mtext〉TE〈/mtext〉〈/mrow〉〈mrow〉〈mi〉ϕ〈/mi〉〈/mrow〉〈/msup〉〈mo〉,〈/mo〉〈msup〉〈mrow〉〈mtext〉TM〈/mtext〉〈/mrow〉〈mrow〉〈mi〉ϕ〈/mi〉〈/mrow〉〈/msup〉〈mo stretchy="false"〉)〈/mo〉〈/math〉 field decomposition and an appropriate set of DEC-based basis functions on an irregular grid discretizing the meridian plane. A symplectic time discretization based on a leap-frog scheme is applied to obtain the full-discrete marching-on-time algorithm. We validate the algorithm by comparing the numerical results against analytical solutions for resonant fields in cylindrical cavities and against pseudo-analytical solutions for fields radiated by cylindrically symmetric antennas in layered media. We also illustrate the application of the algorithm for a particle-in-cell (PIC) simulation of beam-wave interactions inside a high-power backward-wave oscillator.〈/p〉〈/div〉

Beschreibung: 〈p〉Publication date: 15 December 2018〈/p〉 〈p〉〈b〉Source:〈/b〉 Journal of Computational Physics, Volume 375〈/p〉 〈p〉Author(s): Vamsi Spandan, Detlef Lohse, Marco D. de Tullio, Roberto Verzicco〈/p〉 〈h5〉Abstract〈/h5〉 〈div〉〈p〉In this paper we propose and test the validity of simple and easy-to-implement algorithms within the immersed boundary framework geared towards large scale simulations involving thousands of deformable bodies in highly turbulent flows. First, we introduce a fast moving least squares (fast-MLS) approximation technique with which we speed up the process of building transfer functions during the simulations which leads to considerable reductions in computational time. We compare the accuracy of the fast-MLS against the exact moving least squares (MLS) for the standard problem of uniform flow over a sphere. In order to overcome the restrictions set by the resolution coupling of the Lagrangian and Eulerian meshes in this particular immersed boundary method, we present an adaptive Lagrangian mesh refinement procedure that is capable of drastically reducing the number of required nodes of the basic Lagrangian mesh when the immersed boundaries can move and deform. Finally, a coarse-grained collision detection algorithm is presented which can detect collision events between several Lagrangian markers residing on separate complex geometries with minimal computational overhead.〈/p〉〈/div〉