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 - <p style="text-align: justify;">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.</p>