A SPATIALLY EXACT NONREFLECTING BOUNDARY-CONDITION FOR TIME-DEPENDENT PROBLEMS

A special artificial boundary condition is devised and incorporated in a finite element scheme for use in the numerical solution of exterior two-dimensional time-dependent wave problems. The time-dependent wave equation is first discretized in time, leading to a sequence of boundary value problems in an unbounded domain. Then an artificial boundary is introduced, and a spatially exact boundary condition is derived on it. This boundary condition, which is non-local in space but local in time, is employed in conjunction with a finite element scheme in the interior domain. In the proposed method the artificial boundary may be set very close to the scatterer without reducing the accuracy of the numerical results. The spatially exact boundary condition is compared to two commonly used local boundary conditions.