Leevan Ling1, Tomoya Takeuchi2
CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 99-110, 2007, DOI:10.3970/cmes.2007.020.099
Abstract We aim to identify the unknown source locations in a two-dimensional heat equation from scattered measurements. In [Inverse Problems, 22(4):1289--1305, 2006], we proposed a numerical procedure that identifies the unknown source locations of 2D heat equation solely based on three measurement points. Due to the nonlinearity and complexity of the problem, the quality of the resulting estimations is often poor especially when the number of unknown is large. In this paper, we purpose a linear refinement scheme that takes the outputs of the existing nonlinear algorithm as initial guesses and iteratively improves on the accuracy of the estimations; the convergence… More >
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