Exact non-reflecting boundary conditions (Q1119370)

The reduced wave equation with source term is considered on an exterior domain in \(R^ n\) with \(n=2\) or 3. For numerical computations the domain must be truncated, and in this paper the exterior bounding surface is taken to be a circle or sphere, depending on the value of n. The boundary condition on this exterior boundary is nonlocal in nature, and it is derived from the eigenfunction expansion of the source-free problem exterior to a circle or sphere. Such practical issues as the size of the bounding sphere and the number of terms to be retained in the eigenfunction expansion are also discussed.