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An inversion method for harmonic functions reconstruction
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DOI：10.1016/S1290-0729(02)01344-3.png)
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We are interested in this paper in recovering an harmonic function from the knowledge of Cauchy data on some pan of the boundary. The inverse scheme reduces the Cauchy problem resolution to a fixed point process. It is proved, when the data are compatible, this fixed point process converges to the Cauchy problem solution. The algorithm is implemented in both situations, firstly in the framework of boundary elements and secondly in a finite element one. Displayed numerical results highlight their accuracy, as well as their robustness to noisy data. Finally we present the contribution of the method to solve an engineering problem which consists in determining temperature and heat flux on the inner cylinder wall from the knowledge of temperatures and heat flux on the whole outer wall. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.
Keyword:
inverse problem
Laplace's equation
Cauchy problem
fixed point process
finite element method
boundary element method
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