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The method of fundamental solutions for the inverse heat source problem. (English) Zbl 1244.80026
Summary: In this paper a meshless numerical scheme for solving the inverse heat source problem is proposed. The numerical solution is developed by using the fundamental solution of the heat equation as a basis function. Since the resulting matrix equation is badly ill-conditioned, a regularized solution is obtained by employing the Tikhonov regularization method, while the choice of the regularization parameter is based on generalized cross-validation criterion. Both continuous and discontinuous numerical examples are given to verify the efficiency and accuracy of the proposed computational method.
MSC:
80M25Other numerical methods (thermodynamics)
80A23Inverse problems (thermodynamics)
80A20Heat and mass transfer, heat flow
65M80Fundamental solutions, Green’s function methods, etc. (IVP of PDE)