Method of Generalized and Combined Computational Grids for Restoration of the Parameters of Inhomogeneities of a Body Based on the Results of Measurements of the Electromagnetic Field

This paper presents a method for finding inhomogeneities inside a body located in free space based on the results of measuring the electromagnetic field. This problem is relevant, for example, in flaw detection and medical diagnostics. It is assumed that it is possible to use a noninvasive approach, meaning the use of methods or procedures that do not require penetration or intervention inside the studied object to measure the parameters of inhomogeneities. The formulation of the problem at the electrodynamic level of rigor is described by Maxwell’s equations with all the necessary conditions. Maxwell’s system of equations is reduced to a volumetric singular equation on the body. Next, using the resulting integral equation, the field values outside the body at observation points are modeled. Instead of a real experiment, in this study a mathematical model of the physical process is built. To find inhomogeneities, a two-step procedure for determining inhomogeneities is applied, in which the original nonlinear problem is rewritten as a solution of a linear integral equation and a conversion formula. This procedure works well when calculating a small number of inhomogeneities not exceeding 1000 values. To determine a larger number of inhomogeneities, the solution of the problem on combined and generalized computational grids is used, which makes it possible to calculate inhomogeneities on large-sized computational grids containing 10 000 or more elements. The proposed approach allows us to better describe the physical phenomena under consideration.