Parallel Space-Time Solutions for the Linear Visco-Acoustic and Visco-Elastic Wave Equation

Abstract

We present parallel adaptive results for a discontinuous Galerkin spacetime 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.

Dynamic Phase‐Field Fracture in Viscoelastic Materials using a First‐Order Formulation

“…h is attained by solving a Riemann problem locally between faces of neighbouring finite element cells to find a good approximation for the crossing flux (see details in [1], derivation for linear elasticity in [15,16]). Depending on the phase field z h ∈ V cf h the operators…”