Hierarchical Absorbing Interface Conditions for Wave Propagation on Non-Uniform Meshes

Abstract

In this paper, we propose hierarchical absorbing interface conditions to solve the problem of wave propagation in domains with a non-uniform space discretization or grid size inhomogeneity using Padé Via Lanczos (PVL) method. The proposed interface conditions add an auxiliary variable in the wave system to eliminate the spurious reflection at the interface between regions with different mesh sizes. The auxiliary variable with proper boundary condition can suppress the spurious reflection by cancelling the boundary source term produced by the space inhomogeneity in variational perspective. The new hierarchical interface conditions with the help of PVL implementation can effectively reduce the degree of freedom in solving the wave propagation problem. AMS subject classifications: 65K10, 65N22, 35L05