Potential Field Distribution Modeling in a Heterogeneous Medium by Near-Boundary Elements and Non-classical Finite Differences

Abstract

A generalized scheme for finding solutions of potential theory problems in two-dimensional piecewise homogeneous media containing local regions with coordinate-dependent physical characteristics has been given. To describe the additional influence of these local areas, along with the indirect method of near-boundary elements, a non-classical finite-difference method, which is based on asymmetric finite-difference relations, was used. The software implementation of the developed approach for finding the potential of the direct current electric field in a mountain heterogeneous ridge was carried out.