Numerical Implementation of a Conformable Two-Dimensional Radiation Boundary Condition

In open region di erential equation problems it is common to limit the computational domain by introducing an arti cial boundary. The arti cal boundary condition must be chosen to produce as little re ection as possible. Numerous ideas have been employed in the search of accurate and e cient radiation boundary conditions (RBCs). A nite element method (FEM) formulation that encompasses many di erent RBCs is presented. The computational domain can be a general convex two-dimensional domain containing the scatterer. The resulting system of linear equations is sparse and, in general, non-Hermitian. Examples using a generalization of the second order Bayliss Turkel RBC with both circular and non-circular arti cial boundaries are also discussed. The results from these tests both validate the present computational system and illustrate some of the computational savings (time and memory) that can be obtained by selecting an arti cial boundary conformal with the scatterer. 0This work was partially supported by the Semiconductor Research Corporation under Contract 93-DJ-211 and by the NSF under grant DMS-9404488.