Genetic programming with a method of fundamental solutions for solving the steady-state inverse geometric problem

Ihor Borachok, Arkadii Marchenko

Анотація


It is proposed to use genetic programming to reconstruct the interior boundary of a double-connected domain by the known Cauchy data of the harmonic function on the exterior boundary. In this approach, the individual fitness function is evaluated by solving the mixed boundary value problem for the Laplace equation using the method of fundamental solutions. Then the unknown function is represented as a linear combination of fundamental solutions, and the unknown coefficients are found using the collocation method. The proposed method is easy to implement in higher dimensions, so we consider both two-dimensional and three-dimensional domains. The inverse problem is known to be a non-linear ill-posed problem, and the proposed scheme and its robustness are tested on several numerical examples with exact given data and with data with random noise.

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DOI: http://dx.doi.org/10.30970/vam.2024.33.12373

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