Computing Influence Functions for 2-D Compound Regions of Complex Configuration

Abstract

Utilization of influence (Green’s) functions may significantly increase the effectiveness of the existing softwares based on the boundary element method. In nowadays, however, practical use of Green’s functions is notably limited. One of the basic reasons for that is a lack of available representations of those functions in literature. The point is that their practical construction for partial differential equations is not a trivial exercise. In this paper, the emphasis is made on the developing the algorithm for computing influence functions to boundary value problems formulated for the equation of potential over compound regions of complex configuration. In many cases of great practical importance, media that are not homogeneous itself but consist of several zones each one being homogeneous (are referred to below as the compound media) must be analyzed. Some types of those problems formulated over compound media can be fruitfully studied by using the Green’s functions formalizm.