An estimation method for point sources of multidimensional diffusion equation

An inverse source problem is considered for the multidimensional diffusion equation. The source term is expressed by a sum of unknown point sources, and the number of these point sources is also unknown. Our problem is to estimate the unknown source term under the condition that the potential and fl...

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Bibliographic Details
Published in:Applied mathematical modelling 1997-02, Vol.21 (2), p.77-84
Main Authors: Yamatani, Katsu, Ohnaka, Kohzaburo
Format: Article
Language:English
Subjects:
boundary integral equation
inverse source problem
multidimensional diffusion equation
point source
weighted residual approach
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Summary:An inverse source problem is considered for the multidimensional diffusion equation. The source term is expressed by a sum of unknown point sources, and the number of these point sources is also unknown. Our problem is to estimate the unknown source term under the condition that the potential and flux are observed on the boundary. We propose a numerical method that need not use a direct analysis for the governing equation. Our method is based on a weighted residual approach with suitable weighting functions analogized from the fundamental solution of the one-dimensional case. The effectiveness of the method is shown by numerical examples.
ISSN:0307-904X
DOI:10.1016/S0307-904X(96)00148-5