# piecewise homogeneous medium

## Algorithm for determining inclusion parameters in solving inverse problems of geoelectrical exploration using the profiling method

The paper aims to develop an algorithm for recognizing the physical and geometric parameters of inclusion, using indirect methods of boundary, near-boundary, and partially-boundary elements based on the data of the potential field. Methodology. The direct and inverse two-dimensional problems of the potential theory concerning geophysics were solved when modeling the earth's crust with a piecewise-homogeneous half-plane composed of a containing medium and inclusion that are an ideal contact.

## Mathematical modeling of fluid flows through the piecewise homogeneous porous medium by R-function method

The stationary fluid flow through a piecewise homogeneous porous medium is considered under the assumption that Darcy's law holds.  The mathematical model of this problem is defined as an elliptic equation for the stream function, supplemented by the second-type boundary conditions at the water boundaries and the first-type boundary conditions at the impervious to liquid boundaries.  The problem statement also includes the conditions of conjugation at the separation line between two soils and the unknown value of fluid discharge, which can be established from the additional integral ratio.

## Solving 3d problems of potential theory in piecewise homogeneous media by using indirect boundary and near-boundary element methods

Effective numerical-analytical approaches for solving the direct problem of electrical prospecting for the media with inclusions of arbitrary shape and constant electrical characteristics are suggested. They are based on the combination of a fundamental solution of Laplase’s equation and principal ideas of the method of boundary integral equations and that of collocation.