A fundamental solution method for inverse heat conduction problem

By Yiu Chung Benny Hon, Ting Wei. 2004

223 citations recorded by the source corpus.

Abstract In this paper, we develop a new meshless and integration-free numerical scheme for solving an inverse heat conduction problem. The numerical scheme is developed based on the use of the fundamental solution as a radial basis function. To regularize the resultant ill-conditioned linear system of equations, we apply successfully both the Tikhonov regularization technique and the L-curve method to obtain a stable numerical approximation to the solution. The approach is readily extendable to solve high-dimensional problems under irregular domain.

Subfields: Mathematical Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/536ab5effdb501d390a04edf5f71c8c463a4a4be

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In Mathematical Physics

In Mechanics of Materials

Citations in the corpus

Applicability of the method of fundamental solutions (2009, methodology): “The method of fundamental solutions (MFS) introduced by Kupradze and Aleksidze [1] has become a popular meshless method for solving various partial differential equations (PDEs) of practical importance; for example, Poisson equations [2], nonlinear Poisson problems [3], nonlinear thermal explosions ”
Some comments on the ill-conditioning of the method of fundamental solutions (2006, background): “In [14,15], the authors have discussed the details on how to choose the regularization parameters using various techniques.”
Reconstruction of a moving boundary from Cauchy data in one-dimensional heat equation (2009, methodology): “Inverse Problems in Science and Engineering Vol. 17, No. 4, June 2009, 551–567 Reconstruction of a moving boundary from Cauchy data in one-dimensional heat equation T. Weia* and M. Yamamotob aSchool of Mathematics and Statistics, Lanzhou University, Lanzhou, China; bDepartment of Mathematical Scienc”
Kernel techniques: From machine learning to meshless methods (2006, background): “…fundamental solutions (Kythe 1996, Golberg and Chen 1999, Chen, Marcozzi and Choi 1999a, Balakrishnan and Ramachandran 2000, Alves, Chen and Šarler 2002, Poullikkas, Karageorghis and Georgiou 2002, Hon and Wei 2004), where we again picked out just a few cases from different application areas.”