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  • 1
    Electronic Resource
    Electronic Resource
    Automatic domain decomposition on unstructured grids (DOUG) (1998)
    Springer
    Advances in computational mathematics 9 (1998), S. 281-310 
    Details
    ISSN: 1572-9044
    Keywords: partial differential equations ; finite elements ; unstructured grids ; parallel solver ; domain decomposition ; additive Schwarz ; MPI ; general purpose software ; 65F10 ; 65N22 ; 65N55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper describes a parallel iterative solver for finite element discretisations of elliptic partial differential equations on 2D and 3D domains using unstructured grids. The discretisation of the PDE is assumed to be given in the form of element stiffness matrices and the solver is automatic in the sense that it requires minimal additional information about the PDE and the geometry of the domain. The solver parallelises matrix–vector operations required by iterative methods and provides parallel additive Schwarz preconditioners. Parallelisation is implemented through MPI. The paper contains numerical experiments showing almost optimal speedup on unstructured mesh problems on a range of four platforms and in addition gives illustrations of the use of the package to investigate several questions of current interest in the analysis of Schwarz methods. The package is available in public domain from the home page http://www.maths.bath.ac.uk/∼mjh/.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018997725374
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  • 2
    Electronic Resource
    Electronic Resource
    Finite element analysis of a static contact problem with Coulomb friction (2000)
    Springer
    Applications of mathematics 45 (2000), S. 357-379 
    Details
    ISSN: 1572-9109
    Keywords: unilateral contact ; Coulomb friction ; finite elements ; existence proofs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A unilateral contact problem with a variable coefficient of friction is solved by a simplest variant of the finite element technique. The coefficient of friction may depend on the magnitude of the tangential displacement. The existence of an approximate solution and some a priori estimates are proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022220711369
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  • 3
    Electronic Resource
    Electronic Resource
    On equilibrium finite elements in three-dimensional case (1997)
    Springer
    Applications of mathematics 42 (1997), S. 233-242 
    Details
    ISSN: 1572-9109
    Keywords: divergence-free functions ; finite elements ; internal approximation ; stream function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The space of divergence-free functions with vanishing normal flux on the boundary is approximated by subspaces of finite elements that have the same property. The easiest way of generating basis functions in these subspaces is considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022421722236
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  • 4
    Electronic Resource
    Electronic Resource
    Algebraic domain decomposition solver for linear elasticity (1999)
    Springer
    Applications of mathematics 44 (1999), S. 435-458 
    Details
    ISSN: 1572-9109
    Keywords: algebraic multigrid ; zero energy modes ; convergence theory ; finite elements ; computational mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We generalize the overlapping Schwarz domain decomposition method to problems of linear elasticity. The convergence rate independent of the mesh size, coarse-space size, Korn's constant and essential boundary conditions is proved here. Abstract convergence bounds developed here can be used for an analysis of the method applied to singular perturbations of other elliptic problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022272804816
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  • 5
    Electronic Resource
    Electronic Resource
    On superconvergence techniques (1987)
    Springer
    Acta applicandae mathematicae 9 (1987), S. 175-198 
    Details
    ISSN: 1572-9036
    Keywords: 65D ; 65J ; 65L ; 65M ; 65N ; 65P ; 65R ; Superconvergence ; finite elements ; differential and integral equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A brief survey with a bibliography of superconvergence phenomena in finding a numerical solution of differential and integral equations is presented. A particular emphasis is laid on superconvergent schemes for elliptic problems in the plane employing the finite element method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00047538
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  • 6
    Electronic Resource
    Electronic Resource
    Numerical analysis of the radiated fields of ultrasonic transducers (1995)
    Springer
    Journal of nondestructive evaluation 14 (1995), S. 137-146 
    Details
    ISSN: 1573-4862
    Keywords: Ultrasonic transducers ; acoustic medium ; nearfield ; farfield ; finite elements
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract A finite element model is implemented for simulating the radiated fields of both planar and curved transducers in acoustic media. The approach is based on general finite element analysis developed for solving the governing equations of elastic wave propagation. The distributions of the wave fields are presented for both the nearfield and farfield regions of the transducer. Three excitation pulses with the same center frequency but different bandwidths are examined and the accuracy is indicated by a comparison of the simulation results for the axial and transverse fields with the analytical results for continuous wave excitation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01183119
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  • 7
    Electronic Resource
    Electronic Resource
    Finite-element modeling of eddy-current nondestructive evaluation (NDE) (1988)
    Springer
    Journal of nondestructive evaluation 7 (1988), S. 55-69 
    Details
    ISSN: 1573-4862
    Keywords: Nondestructive evaluation (NDE) ; eddy currents ; finite elements ; computational modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract Quantitative eddy-current nondestructive evaluation is hampered by the lack of suitable models to describe the field/defect interaction. The governing partial differential equations admit of closed-form algebraic solution only in the most trivial of geometries. Finite-element methods hold out the hope of providing numerical solutions for more complex cases. In this paper certain effectively two-dimensional eddy-current problems are considered, previous analytical results being used to validate the computations wherever feasible. The extension to three-dimensional fields, which is outlined here, is treated in detail in a subsequent paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00565777
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  • 8
    Electronic Resource
    Electronic Resource
    Tensor product type subspace splittings and multilevel iterative methods for anisotropic problems (1995)
    Springer
    Advances in computational mathematics 4 (1995), S. 171-206 
    Details
    ISSN: 1572-9044
    Keywords: Anisotropic elliptic equations ; finite elements ; wavelets ; preconditioners ; multi-level methods ; AMS(MOS) 65F10 ; 65F35 ; 65N20 ; 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We describe tensor product type techniques to derive robust solvers for anisotropic elliptic model problems on rectangular domains in ℝ d . Our analysis is based on the theory of additive subspace correction methods and applies to finite element and prewavelet schemes. We present multilevel- and prewavelet-based methods that are robust for anisotropic diffusion operators with additional Helmholtz term. Furthermore, the resulting convergence rates are independent of the discretization level. Beside their theoretical foundation, we also report on the results of various numerical experiments to compare the different methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02123478
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  • 9
    Electronic Resource
    Electronic Resource
    From Single-Phase to Compositional Flow: Applicability of Mixed Finite Elements (1997)
    Springer
    Transport in porous media 27 (1997), S. 225-242 
    Details
    ISSN: 1573-1634
    Keywords: fractional flow ; mixed methods ; finite elements ; multiphase flow ; porous media.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract In this paper we discuss the formulation of the governing equations that describe flow of fluids in porous media. Various types of fluid flow, ranging from single-phase flow to compositional flow, are considered. It is shown that all the differential equations governing these types of flow can be effectively rewritten in a fractional flow formulation; i.e., in terms of a global pressure and saturation (or saturations), and that mixed finite element methods can be accurately exploited to solve the pressure equation. Numerical results are presented to see the performance of the mixed methods for the flow equations in three space dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006507816183
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  • 10
    Electronic Resource
    Electronic Resource
    Ultrasonic modeling and experiments: An industrial case: Bimetallic weld in nuclear power plant (1990)
    Springer
    Journal of nondestructive evaluation 9 (1990), S. 145-153 
    Details
    ISSN: 1573-4862
    Keywords: Modeling ; ultrasonic testing ; finite elements
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract To improve the ultrasonic inspection of the safe ends connecting the nuclear vessel to the piping, we are conducting modeling studies using two models: PROMANIS, a ray tracing code, and ULTSON, a 2-D finite element code. The study has shown a great interest in combining modeling and experiments to improve the codes and react to the experimental conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00566390
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