Complementary operators: a method to annihilate artificial reflections arising from the truncation of the computational domain in the solution of partial differential equations

Abstract

The ease and simplicity with which the finite difference time domain (FDTD) or the finite elements (FE) techniques can handle complex radiation or scattering problems have lead to a remarkable surge in the use of these methods. While execution time is becoming less of an impediment when solving large problems, the biggest constraint remains the memory needed to run the FDTD or the FE methods. It is precisely this limitation that the article addresses. A boundary operation is developed to minimize the artificial reflections that arise when truncating the computational domain of an open region scattering or radiation problem. The method is based on the use of two boundary operators that are complementary in their action. By solving the problem with each of the two operators and then averaging the two solutions, the first-order reflections that arise from the artificial boundary can be completely eliminated. Numerical results are presented to show that this new technique gives significant reduction in the error when compared to other widely used boundary conditions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>