Explicit Polynomial Trefftz-DG Method for Space-Time Elasto-Acoustics [chapter]

H. Barucq, H. Calandra, J. Diaz, E. Shishenina
2020 Lecture Notes in Computational Science and Engineering  
Trefftz methods are particular finite element methods where the basis and test functions are locally solutions to the partial differential equation that governs the problem to be solved. Compared to the existing literature for solving frequency problems, space-time Trefftz methods are still not widely used. One reason could be that they require using space-time meshes [6, 12]. To our knowledge, few references on Trefftz approximations of time-dependent wave equations are available and they
more » ... lable and they mainly address theoretical properties in the case of Acoustics and Electromagnetism [4, 8, 10, 11]. They provide convergence and stability studies and some numerical results are displayed by using plane wave bases in 1D + time dimension. Numerical in 2D + time dimensions are proposed in [4] for electromagnetism. There are also some studies devoted to the second-order formulation of the acoustic wave equation approximated in Trefftz spaces by the mean of Lagrange multipliers [1, 13]. In [3], we have proposed a Trefftz-DG formulation for elasto-acoustic. The method required the inversion of a huge sparse matrix. The goal of this paper is to show how to derive a semi-explicit scheme, requiring only the inversion of a block-diagonal matrix on each element of the mesh.
doi:10.1007/978-3-030-39647-3_31 fatcat:jfx6uol55nfltmzskevwmgm56q