Implicit/explicit, BEM/FEM coupled scheme for acoustic waves with the wave equation in the second order formulation

2022/03/02 by Banjai, Lehel
#35L05 #65M38 #65M60 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2203.00986

Abstract

Acoustic scattering of waves by bounded inhomogeneities in an unbounded homogeneous domain is considered. A symmetric coupled system of time-domain boundary integral equations and the second order formulation of the wave equation is described. A fully discrete system consists of spatial discretization by boundary and finite element methods (BEM/FEM), leapfrog time-stepping in the interior, and convolution quadrature for the boundary integral equations. Convolution quadrature is based on BDF2, trapezoidal rule, or a newly introduced truncated trapezoidal rule that has some favourable properties for both the implementation and quality of approximate solution. We give a stability and convergence analysis under a CFL conditon of the fully discrete system. The theoretical results are illustrated by numerical experiments in two dimensions.

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