@Article{cmes.2012.086.071,
AUTHOR = {C.  Shi, C.  Wang, T.  Wei},
TITLE = {Numerical Reconstruction of a Space-Dependent Heat Source Term in a Multi-Dimensional Heat Equation},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {86},
YEAR = {2012},
NUMBER = {2},
PAGES = {71--92},
URL = {http://www.techscience.com/CMES/v86n2/25858},
ISSN = {1526-1506},
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 examples in 1D, 2D and 3D cases show that the proposed method is effective and feasible.},
DOI = {10.3970/cmes.2012.086.071}
}