Exact non-reflecting boundary conditions

An exact non-reflecting boundary condition is devised for use in solving the reduced wave equation in an infinite domain. The domain is made finite by the introduction of an artificial boundary on which this exact condition is imposed. In the finite domain a finite element method is employed. Although the boundary condition is non-local, that does not affect the efficiency of the computational scheme. Numerical examples are presented which show that the use of the exact non-local boundary condition yields results which are much more accurate than those obtained with various approximate local conditions. The method can also be used to solve problems in large finite domains by reducing them to smaller domains, and it can be adapted to other differential equations.