In this paper, we consider a typical ill-posed inverse heat source problem, that is, we determine a space-dependent heat source term in a multi-dimensional heat equation from a pair of Cauchy data on a part of boundary. By a simple transformation, the inverse heat source problem is changed into a Cauchy problem of a homogenous heat conduction equation. We use the method of fundamental solutions (MFS) coupled with the Tikhonov regularization technique to solve the ill-conditioned linear system of equations resulted from the MFS discretization. The generalized cross-validation rule for determining the regularization parameter is used. Numerical results for four examples in 1D, 2D and 3D cases show that the proposed method is effective and feasible.
Shi, C., Wang, C., Wei, T. (2012). Numerical Reconstruction of a Space-Dependent Heat Source Term in a Multi-Dimensional Heat Equation. CMES-Computer Modeling in Engineering & Sciences, 86(2), 71–92.
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