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    Numerical Reconstruction of a Space-Dependent Heat Source Term in a Multi-Dimensional Heat Equation

    C. Shi1, C. Wang1, T. Wei1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.2, pp. 71-92, 2012, DOI:10.3970/cmes.2012.086.071

    Abstract 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… More >

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