Numerical Solution of a Two-Dimensional Nonlocal Wave Equation on Unbounded Domains

Abstract

We are concerned with the numerical solution of a nonlocal wave equation in an infinite two-dimensional space. The contribution of this paper is the derivation of an absorbing boundary condition which allows the wave field defined on the finite computational domain to retain the same feature as that defined on the original infinite domain. We resort to the idea of a first-kind integral equation method and develop a solution formulation in terms of a potential summation on a surrounding ghost region. This new formulation can be taken as an absorbing boundary condition of generalized Dirichlet-to-Dirichlet type. The accuracy and effectiveness of our approach are illustrated by some numerical examples.