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
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
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权重调整间断伽辽金方法：异质介质中的矩阵定值权重和弹性波传播：权重调整间断伽辽金方法：异质介质中的矩阵定值权重和弹性波传播
DOI：
10.1002/nme.5720
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发表时间：
2018
影响因子：
2.9
通讯作者：
Chan, Jesse
中科院分区：
文献类型：
--
作者：
Chan, Jesse
加权调整的内积很容易是加权L2内积的可逆近似。这些近似可以与不连续Galerkin(DG)离散相结合，产生一种适用于任意非均匀介质和曲线网格的低存储、能量稳定和高精度的波传播的时域方法。在这项工作中，我们将加权调整的DG方法推广到矩阵赋权的情况，并以线弹性波动方程为应用。我们给出了对称形式的线弹性波动方程的DG形式，并通过简单的惩罚通量合并了类似迎风的耗散。对弹性波传播中的几个问题进行了半离散收敛分析，数值结果证实了加权调整DG的稳定性和高阶精度。
Weight‐adjusted inner products are easily invertible approximations to weightedL2inner products. These approximations can be paired with a discontinuous Galerkin (DG) discretization to produce a time‐domain method for wave propagation which is low storage, energy stable, and high‐order accurate for arbitrary heterogeneous media and curvilinear meshes. In this work, we extend weight‐adjusted DG methods to the case of matrix‐valued weights, with the linear elastic wave equation as an application. We present a DG formulation of the symmetric form of the linear elastic wave equation, with upwind‐like dissipation incorporated through simple penalty fluxes. A semidiscrete convergence analysis is given, and numerical results confirm the stability and high‐order accuracy of weight‐adjusted DG for several problems in elastic wave propagation.