Daniel Lesnic

TL;DR: In this article, the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions of the direct problem and a supplementary condition, called an overdetermination, is investigated.

TL;DR: The method of fundamental solutions (MFS) is a relatively new method for the numerical solution of boundary value problems and initial/boundary value problems governed by certain partial differential equations as discussed by the authors.

TL;DR: In this article, a variational formulation of the Cauchy problem for the Laplace equation is studied and an efficient conjugate gradient method based on an optimal-order stopping criterion is presented together with its numerical implementation.

TL;DR: In this article, the authors investigated the inverse problem of determining a spacewise dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from a supplementary temperature measurement at a given single instant of time.

TL;DR: In this article, the application of the method of fundamental solutions to the Cauchy problem associated with two-dimensional Helmholtz-type equations is investigated, where the resulting system of linear algebraic equations is ill-conditioned and therefore its solution is regularized by employing the first-order Tikhonov functional, while the choice of the regularization parameter is based on the L-curve method.