A hybrid method for inverse boundary value problems in potential theory

A hybrid method for inverse boundary value problems in potential theory We describe a new method for solving an inverse Dirichlet problem for harmonic functions that arises in the mathematical modelling of electrostatic and thermal imaging methods. This method may be interpreted as a hybrid of a decomposition method, in the spirit of a method developed by Kirsch and Kress, and a regularized Newton method for solving a nonlinear ill-posed operator equation, in terms of the solution operator that maps the unknown boundary onto the solution of the direct problem. As opposed to the Newton iterations the new method does not require a forward solver. Its feasibility is demonstrated through numerical examples. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Inverse and Ill-Posed Problems de Gruyter

A hybrid method for inverse boundary value problems in potential theory

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Publisher
de Gruyter
Copyright
Copyright 2005, Walter de Gruyter
ISSN
0928-0219
eISSN
1569-3953
DOI
10.1515/1569394053583711
Publisher site
See Article on Publisher Site

Abstract

We describe a new method for solving an inverse Dirichlet problem for harmonic functions that arises in the mathematical modelling of electrostatic and thermal imaging methods. This method may be interpreted as a hybrid of a decomposition method, in the spirit of a method developed by Kirsch and Kress, and a regularized Newton method for solving a nonlinear ill-posed operator equation, in terms of the solution operator that maps the unknown boundary onto the solution of the direct problem. As opposed to the Newton iterations the new method does not require a forward solver. Its feasibility is demonstrated through numerical examples.

Journal

Journal of Inverse and Ill-Posed Problemsde Gruyter

Published: Jan 1, 2005

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