Evolutionary-numerical algorithm for unsteady inverse geometric problems in double-connected domains

Numerical solution of the problem of reconstruction of the inner boundary of the double-connected domain from the given Cauchy data on the outer part of the domain, for the heat and wave equations is considered. The inverse problem is reformulated as a minimization of the nonlinear functional. A real-valued genetic algorithm is used for the minimization. A tness function of the individual is proposed, for the calculation of which it is necessary to solve the non-stationary Dirichlet problem. For this problem, rst a semi discretization by the time variable is performed using the Rothe's method, and then the method of fundamental solutions is applied to the obtained recurrent sequence of stationary inhomogeneous problems. The proposed approach is easy to extend to the case of higher dimensions, therefore two dimensional and three dimensional domains are considered. The algorithm is tested on several examples for both equations and the stability of the method is con rmed for the noised input data.