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

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.