Generalized Multiscale Finite Element Methods for Wave Propagation in Heterogeneous Media

DOI10.1137/130926675zbMath1315.65085arXiv1307.0123OpenAlexW2963710982MaRDI QIDQ5251790

Eric T. Chung, Wing Tat Leung, Yalchin R. Efendiev

Publication date: 21 May 2015

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.0123

zbMATH Keywords

stabilityconvergencenumerical examplewave propagationheterogeneous mediamodel reductioninterior penalty discontinuous Galerkin methodmultiscale finite element method

Mathematics Subject Classification ID

Wave equation (35L05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

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Cites Work

• Unnamed Item
• Unnamed Item
• Generalized multiscale finite element methods (GMsFEM)
• Generalized multiscale finite element method. Symmetric interior penalty coupling
• Optimal error estimates for the fully discrete interior penalty DG method for the wave equation
• A new high accuracy locally one-dimensional scheme for the wave equation
• A staggered discontinuous Galerkin method for wave propagation in media with dielectrics and meta-materials
• Exact nonreflecting boundary conditions for three dimensional poroelastic wave equations
• Convergence and superconvergence of staggered discontinuous Galerkin methods for the three-dimensional Maxwell's equations on Cartesian grids
• High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster
• A staggered discontinuous Galerkin method for the convection–diffusion equation
• A staggered discontinuous Galerkin method for the curl-curl operator
• Optimal Discontinuous Galerkin Methods for the Acoustic Wave Equation in Higher Dimensions
• AN ENERGY-CONSERVING DISCONTINUOUS MULTISCALE FINITE ELEMENT METHOD FOR THE WAVE EQUATION IN HETEROGENEOUS MEDIA
• A Coarse Space Construction Based on Local Dirichlet-to-Neumann Maps
• Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
• Efficient Simulation of Wave Propagation with Implicit Finite Difference Schemes
• Two-Level Overlapping Schwarz Algorithms for a Staggered Discontinuous Galerkin Method
• A Sub-Grid Structure Enhanced Discontinuous Galerkin Method for Multiscale Diffusion and Convection-Diffusion Problems
• Generalized Multiscale Finite Element Methods. Nonlinear Elliptic Equations
• Optimal Discontinuous Galerkin Methods for Wave Propagation