Open Access

ARTICLE

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

C. Shi¹, C. Wang¹, T. Wei^1,2

1 School of mathematics and statistics, Lanzhou University, Lanzhou 730000, China
2 Corresponding author.

Computer Modeling in Engineering & Sciences 2012, 86(2), 71-92. https://doi.org/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 examples in 1D, 2D and 3D cases show that the proposed method is effective and feasible.

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Keywords

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