A high order discontinuous Galerkin method for the symmetric form of the anisotropic viscoelastic wave equation. (1st October 2021)

• Record Type: Journal Article
• Authors: Shukla, Khemraj; Chan, Jesse; de Hoop, Maarten V.
• Is Part Of: Computers & mathematics with applications. Volume 99(2021)
• Page Start: 113
• Page End: 132
• Publication Date: 2021-10-01
• Subjects: Discontinuous Galerkin -- Viscoelastic -- Energy stability -- Unstructured meshes -- Wave propagation; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.08.003
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We introduce a new symmetric treatment of anisotropic viscous terms in the viscoelastic wave equation. An appropriate memory variable treatment of stress-strain convolution terms, result into a symmetric system of first order linear hyperbolic partial differential equations, which we discretize using a high-order discontinuous Galerkin finite element method. The accuracy of the resulting numerical scheme is verified using convergence studies against analytical plane wave solutions and analytical solutions of the viscoelastic wave equation. Computational experiments are shown for various combinations of homogeneous and heterogeneous viscoelastic media in two and three dimensions.