Parallel additive Schwarz methods for elastic wave equations

Andrew T. Barker

Department of Applied Mathematics
University of Colorado at Boulder
Boulder, CO 80309-0526

Xiao-Chuan Cai
Department of Computer Science
University of Colorado at Boulder
Boulder, CO 80309


Abstract

We develop a scalable parallel finite element solver for the elastic wave equation discretized using an implicit Newmark scheme in time on unstructured meshes. The resulting system of linear equations is solved with an additive Schwarz preconditioned Krylov subspace method. We present numerical and analytical evidence to explain the behavior of the algorithms and discuss applications to a fluid-structure interaction algorithm that implicitly couples the elasticity equation with the Navier-Stokes equations to simulate blood flow in compliant arteries.