|
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 Penza State University, Penza
Abstract:
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.
Keywords:
Maxwell's system of equations, volume integral equation, numerical method, collocation method, combined computational grids, generalized computational grids.
Received: 04.12.2023 Revised: 04.12.2023 Accepted: 26.02.2024
Citation:
A. O. Lapich, M. Y. Medvedik, “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”, Mat. Model., 36:4 (2024), 24–36; Math. Models Comput. Simul., 16:6 (2024), 806–813
Linking options:
https://www.mathnet.ru/eng/mm4550 https://www.mathnet.ru/eng/mm/v36/i4/p24
|
Statistics & downloads: |
Abstract page: | 129 | Full-text PDF : | 2 | References: | 41 | First page: | 25 |
|