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Volume 35, Issue 3
Solution of Inverse Geometric Problems Using a Non-Iterative MFS

Andreas Karageorghis, Daniel Lesnic & Liviu Marin

DOI: 10.4208/cicp.OA-2023-0207

Commun. Comput. Phys., 35 (2024), pp. 553-578.

Published online: 2024-04

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  • Abstract

In most of the method of fundamental solutions (MFS) approaches employed so far for the solution of inverse geometric problems, the MFS implementation typically leads to non-linear systems which were solved by standard nonlinear iterative least squares software. In the current approach, we apply a three-step non-iterative MFS technique for identifying a rigid inclusion from internal data measurements, which consists of: (i) a direct problem to calculate the solution at the set of measurement points, (ii) the solution of an ill-posed linear problem to determine the solution on a known virtual boundary and (iii) the solution of a direct problem in the virtual domain which leads to the identification of the unknown curve using the ${\rm MATLAB}^®$ functions contour in 2D and isosurface in 3D. The results of several numerical experiments for steady-state heat conduction and linear elasticity in two and three dimensions are presented and analyzed.

  • Keywords

Void detection, inverse problem, method of fundamental solutions.

  • AMS Subject Headings

65N35, 65N21, 65N38

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-35-553, author = {Karageorghis , AndreasLesnic , Daniel and Marin , Liviu}, title = {Solution of Inverse Geometric Problems Using a Non-Iterative MFS}, journal = {Communications in Computational Physics}, year = {2024}, volume = {35}, number = {3}, pages = {553--578}, abstract = {

In most of the method of fundamental solutions (MFS) approaches employed so far for the solution of inverse geometric problems, the MFS implementation typically leads to non-linear systems which were solved by standard nonlinear iterative least squares software. In the current approach, we apply a three-step non-iterative MFS technique for identifying a rigid inclusion from internal data measurements, which consists of: (i) a direct problem to calculate the solution at the set of measurement points, (ii) the solution of an ill-posed linear problem to determine the solution on a known virtual boundary and (iii) the solution of a direct problem in the virtual domain which leads to the identification of the unknown curve using the ${\rm MATLAB}^®$ functions contour in 2D and isosurface in 3D. The results of several numerical experiments for steady-state heat conduction and linear elasticity in two and three dimensions are presented and analyzed.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0207}, url = {http://global-sci.org/intro/article_detail/cicp/23052.html} }
TY - JOUR T1 - Solution of Inverse Geometric Problems Using a Non-Iterative MFS AU - Karageorghis , Andreas AU - Lesnic , Daniel AU - Marin , Liviu JO - Communications in Computational Physics VL - 3 SP - 553 EP - 578 PY - 2024 DA - 2024/04 SN - 35 DO - http://doi.org/10.4208/cicp.OA-2023-0207 UR - https://global-sci.org/intro/article_detail/cicp/23052.html KW - Void detection, inverse problem, method of fundamental solutions. AB -

In most of the method of fundamental solutions (MFS) approaches employed so far for the solution of inverse geometric problems, the MFS implementation typically leads to non-linear systems which were solved by standard nonlinear iterative least squares software. In the current approach, we apply a three-step non-iterative MFS technique for identifying a rigid inclusion from internal data measurements, which consists of: (i) a direct problem to calculate the solution at the set of measurement points, (ii) the solution of an ill-posed linear problem to determine the solution on a known virtual boundary and (iii) the solution of a direct problem in the virtual domain which leads to the identification of the unknown curve using the ${\rm MATLAB}^®$ functions contour in 2D and isosurface in 3D. The results of several numerical experiments for steady-state heat conduction and linear elasticity in two and three dimensions are presented and analyzed.

Andreas Karageorghis, Daniel Lesnic & Liviu Marin. (2024). Solution of Inverse Geometric Problems Using a Non-Iterative MFS. Communications in Computational Physics. 35 (3). 553-578. doi:10.4208/cicp.OA-2023-0207
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