A hybrid method for inverse boundary value problems in potential theory

R. Chapko 1  and R. Kress 2
  • 1 Department of Applied Mathematics and Computer Science, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine. E-mail: chapko@is.lviv.ua
  • 2 Institut für Numerische und Angewandte Mathematik, Universität Göttingen, 37083 Göttingen, Germany. E-mail: kress@math.uni-goettingen.de.

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.

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This journal presents original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published.