TY - EJOU
AU - Shi, C.
AU - Wang, C.
AU - Wei, T.
TI - Numerical Reconstruction of a Space-Dependent Heat Source Term in a Multi-Dimensional Heat Equation
T2 - Computer Modeling in Engineering \& Sciences
PY - 2012
VL - 86
IS - 2
SN - 1526-1506
AB - 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.
KW - Inverse heat source
KW - ill-posed problem
KW - the method of fundamental solution
KW - Tikhonov regularization
DO - 10.3970/cmes.2012.086.071