A general approach for high order absorbing boundary conditions for the Helmholtz equation (Q401549)

This paper gives an overview of various {absorbing boundary conditions (ABC)} for Helmholtz equations on unbounded domains and presents a new method to construct high-order ABCs. From this general method, ABCs for 2D and 3D Helmholtz equations are derived, which are based on different series representations of the solution in polar, elliptical and spherical coordinates. Some of these ABCs are generalizations of previously known and some are new. They produce more accurate solutions to the Helmholtz equation, which are much less dependent on parameters of the problem, such as the wave number. The method sheds light on the connections between different ABCs. Computations confirm the high accuracy of these new ABCs.