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  • 1
    Call number: PIK Q 200-97-0045
    In: ZIB-Report SC
    Type of Medium: Monograph available for loan
    Pages: 19 p.
    Series Statement: ZIB-Report SC 96-38
    Branch Library: PIK Library
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 72 (1996), S. 481-499 
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65N30, 65N55, 35J85
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We derive globally convergent multigrid methods for discrete elliptic variational inequalities of the second kind as obtained from the approximation of related continuous problems by piecewise linear finite elements. The coarse grid corrections are computed from certain obstacle problems. The actual constraints are fixed by the preceding nonlinear fine grid smoothing. This new approach allows the implementation as a classical V-cycle and preserves the usual multigrid efficiency. We give $1-O(j^{-3})$ estimates for the asymptotic convergence rates. The numerical results indicate a significant improvement as compared with previous multigrid approaches.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Induction heating of large steel slabs can be described by a coupled system of non-linear evolution equations of Stefan type represnting the temporal and spatial distribution of the induced magnetic field and the generated temperature within the slab. Discretizing these equations implicitly in time and by finite differences in space, at each time step the solution of a system of difference inclusions is required. For the solution of that system two multi-grid algorithms are given which, combined with a nested iteration type continuation strategy to proceed in time, result in computationally highly efficient schemes for the numerical simulation of the induction heating process.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider the approximate solution of self-adjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly non-uniform tetrahedral mesh which is generated adaptively. The arising linear systems are solved iteratively by the conjugate gradient method provided with a multilevel preconditioner. Here, the accuracy of the iterative solution is coupled with the discretization error. As the performance of hierarchical bases preconditioners deteriorates in three space dimensions, the BPX preconditioner is used, taking special care of an efficient implementation. Reliable a posteriori estimates for the discretization error are derived from a local comparison with the approximation resulting from piecewise quadratic elements. To illustrate the theoretical results, we consider a familiar model problem involving reentrant corners and a real-life problem arising from hyperthermia, a recent clinical method for cancer therapy.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The potential distribution of bipolar, strongly reverse-biased pn-junctions can be described by a double obstacle problem for the Laplacian. The problem is solved by a self-adaptive finite-element method involving automatic termination criteria for the iterative solver, local error estimation and local mesh refinement. Special attention is paid to the efficient resolution of the geometries typically arising in semiconductor device simulation. The algorithm is applied to a reverse-biased pn-junction with multistep field plate and stop electrode to illustrate its efficiency and reliability.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Publication Date: 2019-11-28
    Description: Abstract
    Description: This data set provides data from subduction zone earthquake experiments and analysis described in Rosenau et al. (2019). In the experiments analogue seismotectonic scale models of subduction zones characterized by two seismogenic asperities are used to study the interaction of asperities over multiple seismic cycles by means of static (Coulomb failure) stress transfer. Various asperity geometries (lateral/along-strike of the subduction zone distance and vertical/across-strike of the subduction zone offset) are tested on their effect on recurrence pattern of simulated great (M8+) earthquakes.The results demonstrate the role of stress coupling in the synchronization of asperities leading to multi-asperity M9+ events in nature. The data set contains time series of experimental surface velocities from which analogue earthquakes are detected and classified into synchronized events and solo events. The latter are subcategorized into main events and aftershocks and into normal and thrust events. An analogue earthquake catalogue lists all categorized events of the 12 experiments used for statistical analysis. Moreover, results from elastic dislocation modelling aimed ate quantifying the stress coupling between the asperities for the various geometries are summarized. Basic statistics of classified events (e.g. percentage of categorized events, coefficient of variation in size and recurrence time etc.) are documented. Matlab scripts are provided to visualize the data as in the paper.
    Keywords: multi-scale laboratories ; Megathrust earthquakes ; computational statistics ; analogue models of geologic processes ; analogue modelling results ; software tools ; EPOS ; European Plate Observing System ; EARTH SCIENCE SERVICES 〉 MODELS 〉 GEOLOGIC/TECTONIC/PALEOCLIMATE MODELS ; EARTH SCIENCE 〉 SOLID EARTH 〉 TECTONICS 〉 PLATE TECTONICS ; EARTH SCIENCE 〉 SOLID EARTH 〉 TECTONICS 〉 PLATE TECTONICS 〉 PLATE BOUNDARIES ; tectonic setting 〉 plate margin setting 〉 forearc setting ; tectonic setting 〉 plate margin setting 〉 subduction zone setting ; deformation ; tectonic process 〉 subduction ; megathrust ; Silicon/Silly putty/PDMS ; Sugar ; Rubber ; Earthquake simulator ; Digital Image Correlation (DIC) / Particle Image Velocimetry (PIV) 〉 StrainMaster (La Vision GmbH) ; Time lapse camera
    Language: English
    Type: Dataset , Dataset
    Format: 3 Files
    Format: application/octet-stream
    Format: application/octet-stream
    Format: application/octet-stream
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  • 7
    Publication Date: 2016-02-04
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
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  • 8
    Publication Date: 2019-04-01
    Description: The magnitude of great subduction megathrust earthquakes is controlled mainly by the number of adjacent asperities failing synchronously and the resulting rupture length. Here we investigate experimentally the long-term recurrence behavior of a pair of asperities coupled by static stress transfer over hundreds of seismic cycles. We statistically analyze long (c. 500 ka) time series of M8-9 analogue earthquakes simulated using a seismotectonic scale model approach with two aims: First, to constrain probabilistic measures (frequency-size distribution, variability) useful for hazard assessment and, second, to relate them with geometric observables (coseismic slip pattern, locking pattern). We find that the number of synchronized asperity failures relative to the number of individual asperity failures as well as the coefficients of variation of recurrence intervals and seismic moment scale with the logarithm of stress coupling between the asperities. Accordingly, tighter packed asperities tend to recur more periodically and with a more characteristic magnitude while more distant asperities show clustering of more variable sized events. The probability of synchronized failures seems to be controlled to first order by geometrical relations (i.e., spacing and offset of asperities). The effects of rheological properties are evident but it remains to be explored to which extent they vary in nature and how sensitive the system is to those.
    Print ISSN: 2169-9313
    Electronic ISSN: 2169-9356
    Topics: Geosciences , Physics
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