Nonreflecting boundary conditions for time-dependent scattering
The paper presents a computational method for the calculation of a time dependent field scattered from a bounded scattering region in \(\mathbb{R}^3\). The model problem is described by the wave equation with a nonlinear source term and the exact nonreflecting boundary condition derived by the authors [SIAM J. Appl. Math. 55, No. 2, 280-297 (1995; Zbl 0817.35049)]. For this model the uniqueness of the solution is proved and both the finite element and the finite difference methods are applied. In the considered computational method, due to the truncation of an infinite sum to a finite value, the boundary condition becomes inexact. It is shown how to modify this boundary condition to improve its accuracy. Moreover, it is proved that despite the incorrect boundary condition, the energy of the solution remains bounded. The stability of the ordinary differential equation occurring in the boundary condition is also examined. Numerical examples demonstrate the long time stability of the proposed method and the improvement in accuracy over standard ones.
scientific article; zbMATH DE number 938007