Method of generalized and combined computational grids for restoration the parameters of inhomogeneities of a body based on the results of measurements of the electromagnetic field

A. O. Lapich ; M. Y. Medvedik

Matematičeskoe modelirovanie, Tome 36 (2024) no. 4, pp. 24-36.

Résumé

The 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 non-invasive approach, meaning the use of methods or procedures that do not require penetration or intervention inside the object under study 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 work a mathematical model of the physical process was built. To find inhomogeneities, a two-step procedure for determining inhomogeneities was applied, in which the original nonlinear problem was rewritten as a solution of a linear integral equation and a conversion formula. This procedure worked 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 10000 or more elements. The proposed approach allows us to better describe the physical phenomena under consideration.

Détail

Keywords: Maxwell's system of equations, volume integral equation, numerical method, collocation method, combined computational grids, generalized computational grids.

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