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Title: Weight-adjusted discontinuous Galerkin methods: Matrix-valued weights and elastic wave propagation in heterogeneous media: Weight-adjusted discontinuous Galerkin methods: Matrix-valued weights and elastic wave propagation in heterogeneous media
Award ID(s):
1712639 1719818
NSF-PAR ID:
10058378
Author(s) / Creator(s):
Date Published:
Journal Name:
International Journal for Numerical Methods in Engineering
Volume:
113
Issue:
12
ISSN:
0029-5981
Page Range / eLocation ID:
1779 to 1809
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  1. Abstract

    This article presents high order accurate discontinuous Galerkin (DG) methods for wave problems on moving curved meshes with general choices of basis and quadrature. The proposed method adopts an arbitrary Lagrangian–Eulerian formulation to map the wave equation from a time‐dependent moving physical domain onto a fixed reference domain. For moving curved meshes, weighted mass matrices must be assembled and inverted at each time step when using explicit time‐stepping methods. We avoid this step by utilizing an easily invertible weight‐adjusted approximation. The resulting semi‐discrete weight‐adjusted DG scheme is provably energy stable up to a term that (for a fixed time interval) converges to zero with the same rate as the optimal error estimate. Numerical experiments using both polynomial and B‐spline bases verify the high order accuracy and energy stability of proposed methods.

     
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