# Parallel space-time solutions for the linear visco-acoustic and visco-elastic wave equation

Dörfler, Willy; Wieners, Christian; Ziegler, Daniel

##### Abstract:
We present parallel adaptive results for a discontinuous Galerkin space-time discretization for acoustic and elastic waves with attenuation. The method is based on $p$-adaptive polynomial discontinuous ansatz and test spaces and a first-order formulation with full upwind fluxes. Adaptivity is controlled by dual-primal error estimation, and the full linear system is solved by a Krylov method with space-time multilevel preconditioning. The discretization and solution method is introduced in Dörfler-Findeisen-Wieners (Comput. Meth. Appl. Math. 2016) for general linear hyperbolic systems and applied to acoustic and elastic waves in Dörfler-Findeisen-Wieners-Ziegler (Radon Series Comp. Appl. Math. 2019); attenuation effects were included in Ziegler (PhD thesis 2019, Karlsruhe Institute of Technology). Here, we consider the evaluation of this method for a benchmark configuration in geophysics, where the convergence is tested with respect to seismograms. We consider the scaling on parallel machines and we show that the adaptive method based on goal-oriented error estimation is able to reduce the computational effort substantially.

 Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)Sonderforschungsbereich 1173 (SFB 1173) Publikationstyp Forschungsbericht/Preprint Publikationsmonat/-jahr 12.2020 Sprache Englisch Identifikator ISSN: 2365-662X KITopen-ID: 1000127990 Verlag Karlsruher Institut für Technologie (KIT) Umfang 10 S. Serie CRC 1173 Preprint ; 2020/40 Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019) Externe Relationen Siehe auch
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