Nonlocal Wave Propagation in Unbounded Multi-Scale Media

Abstract

This paper focuses on the simulation of nonlocal wave propagations in unbounded multi-scale mediums. To this end, we consider two issues: (a) the design of artificial/absorbing boundary conditions; and (b) the construction of an asymptotically compatible (AC) scheme for the nonlocal operator with general kernels. The design of ABCs facilitates us to reformulate unbounded domain problems into bounded domain problems. The construction of AC scheme facilitates us to simulate nonlocal wave propagations in multi-scale mediums. By applying the proposed ABCs and the proposed AC scheme, we investigate different wave propagation behaviors in the "local" and nonlocal mediums through numerical examples.