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Determination of an Unknown Heat Source Term from Boundary Data

Y. Hu1, T. Wei1,2

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

Computer Modeling in Engineering & Sciences 2012, 87(4), 307-326. https://doi.org/10.3970/cmes.2012.087.307

Abstract

This paper employ the method of fundamental solutions for determining an unknown heat source term in a heat equation from overspecified boundary measurement data. By a function transformation, the inverse source problem is changed into an inverse initial data problem which is solved by a method of fundamental solutions. The standard Tikhonov regularization technique with the generalized cross-validation criterion for choosing the regularization parameter is adopted for solving the resulting ill-conditioned system of linear algebraic equations. The effectiveness of the algorithm is illustrated by five numerical examples in one-dimensional and two-dimensional cases.

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Hu, Y., Wei, T. (2012). Determination of an Unknown Heat Source Term from Boundary Data. CMES-Computer Modeling in Engineering & Sciences, 87(4), 307–326.



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