potential theory

Solving inverse problem of the potential theory by the cascade algorithm and the near-boundary element method

The effectiveness of the indirect method of near-boundary elements (as a variant of the method of boundary integral equations) for constructing numerical solutions of direct and inverse problems of potential theory in a limited piecewise homogeneous object of arbitrary shape whose components are in ideal contact is substantiated.  The integral representation of the solution of the direct problem is constructed using the fundamental solution of the Laplace equation for the plane.  To find the intensities of unknown sources introduced in the near-boundary elements, the co

Recognition of Inclusion Characteristics Using Neural Network Methods in Stationary Process Modeling

Detection and identification of inclusions in the modeling of stationary processes is a crucial task in many technical fields, including materials science, electronics, and non-destructive testing. The presence of inclusions can affect the mechanical, thermal, and electrical properties of a material, making the accurate determination of their geometric and physical characteristics essential. The use of modern numerical methods and deep learning techniques opens new opportunities for improving the efficiency and accuracy of prediction results.

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.