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The method of fundamental solutions for the inverse space-dependent heat source problem. (English) Zbl 1180.80054
Summary: In this study, the inverse heat source problem in which the heat source is space-dependent is treated. The method proposed in L. Yan et al. [The method of fundamental solutions for the inverse heat source problem. Eng. Anal. Boundary Elem. 32, 216–222 (2008; doi:10.1016/j.enganabound.2007.08.002)] where the heat source is considered to be only time-dependent, is modified so that it can be applied to only space-dependent problems. We have used a new transformation to simplify the problem.

##### MSC:
 80A23 Inverse problems in thermodynamics and heat transfer 35R30 Inverse problems for PDEs 58J35 Heat and other parabolic equation methods for PDEs on manifolds 58J90 Applications of PDEs on manifolds
##### Software:
Regularization tools
Full Text:
##### References:
 [1] Cannon, J.R., Determination of an unknown heat source from overspecified boundary data, SIAM J numer anal, 5, 275-286, (1968) · Zbl 0176.15403 [2] Cannon, J.R.; Duchateau, P., Structural identification of an unknown source term in a heat equation, Inv probl, 14, 535-551, (1998) · Zbl 0917.35156 [3] Savateev, E.G., On problems of determining the source function in a parabolic equation, J inv ill-posed probl, 3, 83-102, (1995) · Zbl 0828.35142 [4] Farcas, A.; Lesnic, D., The boundary-element method for the determination of a heat source dependent on one variable, J eng math, 54, 375-388, (2006) · Zbl 1146.80007 [5] Yan, L.; Fu, C.L.; Yang, F.L., The method of fundamental solutions for the inverse heat source problem, Eng anal boundary elem, 32, 216-222, (2008) · Zbl 1244.80026 [6] Ling, L.; Yamamoto, M.; Hon, Y.C.; Takeuchi, T., Identification of source locations in two-dimensional heat equations, Inv probl, 22, 1289-1305, (2006) · Zbl 1112.35147 [7] Yi, Zh.; Murio, D.A., Source term identification in 1-d IHCP, Comput math appl, 47, 1921-1933, (2004) · Zbl 1063.65102 [8] Kupradze, V.D.; Aleksidze, M.A., The method of functional equations for the approximate solution of certain boundary value problems, USSR comput math math phys, 4, 82-126, (1964) · Zbl 0154.17604 [9] Mathon, R.; Johnston, H., The approximate solution of elliptic boundary-value problems by fundamental solutions, SIAM J numer anal, 14, 4, 638-650, (1977) · Zbl 0368.65058 [10] Kress, R.; Mohsen, A., On the simulation source technique for exterior problems in acoustics, Math methods appl sci, 8, 585-597, (1986) · Zbl 0626.35019 [11] Karageorghis, A.; Fairweather, G., The method of fundamental solutions for the numerical solution of the biharmonic equation, J comput phys, 69, 434-459, (1987) · Zbl 0618.65108 [12] Chen, C.S., The method of fundamental solutions for nonlinear thermal explosion, Commun numer methods eng, 11, 675-681, (1995) · Zbl 0839.65143 [13] Fairweather, G.; Karageorghis, A., The method of fundamental solutions for elliptic boundary value problems, Adv comput math, 9, 1-2, 69-95, (1998) · Zbl 0922.65074 [14] Golberg, M.A.; Chen, C.S., The method of fundamental solutions for potential, hemholtz and diffusion problems, (), 103-176 · Zbl 0945.65130 [15] Hon, Y.C.; Wei, T., A fundamental solution method for inverse heat conduction problem, Eng anal boundary elem, 28, 489-495, (2004) · Zbl 1073.80002 [16] Mera, N.S., The method of fundamental solutions for the backward heat conduction problem, Inv probl sci eng, 13, 65-78, (2005) · Zbl 1194.80107 [17] Marin, L.; Lesnic, D., The method of fundamental solutions for the Cauchy problem in two-dimensional linear elasticity, Int J solids struct, 41, 13, 3425-3438, (2004) · Zbl 1071.74055 [18] Marin, L.; Lesnic, D., The method of fundamental solutions for the Cauchy problem associated with two-dimensional Helmholtz-type equations, Comput struct, 83, 4-5, 267-278, (2005) · Zbl 1088.35079 [19] Jin, B.; Zheng, Y., A meshless method for some inverse problems associated with the Helmholtz equation, Comput methods appl mech eng, 195, 19-22, 2270-2288, (2006) · Zbl 1123.65111 [20] Hansen, P.C., Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems, Numer algorithms, 6, 1-35, (1994) · Zbl 0789.65029
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