This article discusses the results of solving the problem of electrical exploration using direct current. The developed methods and algorithms for solving the direct and inverse exploration tasks are tested on several inhomogeneous models of the environment. The task is considered in three-dimensional approximation. To solve using the finite element method. Based on direct problem algorithm, a method for solving the inverse problem was implemented, which consists in finding the minimum of the deviation functional, which in turn leads to the multiple solution of the direct problem. The results were analyzed in order to identify disadvantages and advantages. An analysis was also made of the search time for optimal solutions, and the dependence of the accuracy of the solution on the thickening of the mesh when solving the problem by the finite element method was discussed.
This article describes solutions to the direct and inverse problems of the three-dimensional non-stationary heat conduction problem in a three-layer structure, using the finite element method for the direct problem and the gradient descent method for the inverse problem. A comparison of the FEM-solution and the analytical solution for a solid with a simple geometry is presented. Here are presented solutions of the direct and inverse three-dimensional non-stationary heat conductivity problem for a free three-stage turbine. The accuracy of the found and exact solutions is compared.
The proposed work deals with the problem of finding the geometric dimensions of a cavity-type defect by measuring the thermal fields. As a structural element, a plate with a rectangular cavity is considered.
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