Nonreflecting Boundary Conditions for Time-Dependent Scattering

of the ordinary differential equation which occurs in the boundary condition. An exact nonreflecting boundary condition was derived previously for use with the time dependent wave equation in three Finally, we shall solve a sequence of scattering problems space dimensions. Here it is shown how to combine that boundary by using an explicit finite difference method and our condition with finite difference methods and finite element methboundary condition. We shall also solve the same problems ods. Uniqueness of the solution is proved, stability issues are disby using two of the standard artificial boundary conditions. cussed, and improvements are proposed for numerical computaComparison of these solutions with the ‘‘exact’’ solution, tion. Numerical examples are presented which demonstrate the improvement in accuracy over standard methods. Q 1996 Academic obtained by computing in a very large domain so that