Galerkin Differences for acoustic and elastic wave equations in two space dimensions

The Galerkin Difference method, a finite element method built using standard Galerkin projection techniques but employing nonstandard basis functions, was originally developed for one space dimension in [1]. Here the method is extended to two space dimensions using a tensor product construction. The...

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Bibliographic Details
Published in:Journal of computational physics Vol. 372; no. C; pp. 864 - 892
Main Authors: Banks, J.W., Hagstrom, T., Jacangelo, J.
Format: Journal Article
Language:English
Published: Cambridge Elsevier Inc 01.11.2018
Elsevier Science Ltd
Elsevier
Subjects:
Acoustic mapping
Acoustics
Basis functions
Boundary value problems
Computational physics
Convergence
Difference methods
Elastic waves
Finite element method
Forecasting
Free surfaces
Galerkin method
Galerkin methods
Initial–boundary value problems
Mass matrix
Matrix methods
Wave equations
Waveform analysis
Difference methods
Initial–boundary value problems
Galerkin methods
Wave equations
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:The Galerkin Difference method, a finite element method built using standard Galerkin projection techniques but employing nonstandard basis functions, was originally developed for one space dimension in [1]. Here the method is extended to two space dimensions using a tensor product construction. Theoretical and computational evidence shows the method behaves as expected for the acoustic wave equation. For the elastic wave equation, the approximations are found to be at least as accurate as predicted, but with a free surface the scheme may exhibit an unexpected superconvergence. Extension to curvilinear mapped grids is also considered for acoustics. In all cases, the use of a tensor product construction allows for efficient solution of the linear system involving the mass matrix, which implies optimal linear time solutions with respect to the number of degrees of freedom. •Galerkin Difference schemes for 2D wave equations are developed.•Schemes for acoustics and elasticity are presented.•A tensor-product formulation enables optimal linear time algorithms.•Extension to mapped curvilinear domains is performed.•Comprehensive numerical studies illustrate the theoretical predictions.
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USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2018.06.029