two-dimensional problem of potential theory

Potential field modeling by combination of near-boundary and contact elements with non-classical finite differences in a heterogeneous medium

In this paper, 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 presented.  To describe the additional influence of these local areas, along with the indirect methods of near-boundary and contact elements, a non-classical finite-difference method based on asymmetric finite-difference relations has been used.  The software implementation of the developed approach for finding the potential of the direct current electric

Using of partly-boundary elements as a version of the indirect near-boundary element method for potential field modeling

In this paper, the partly-boundary elements as a version of the indirect near-boundary element method has been considered.  Accuracy and effectiveness of their using for 2D problems of potential theory have been investigated.  It is shown that using of partly-boundary elements for objects of canonical shape (circle, square, rectangle, ellipse) and arbitrary polygons allows us to achieve the solution accuracy, which is comparable with the accuracy of the indirect near-boundary element method, and its order of magnitude is higher than in the indirect boundary element method.  In this case, th