Year: 2007
International Journal of Numerical Analysis and Modeling, Vol. 4 (2007), Iss. 1 : pp. 74–99
Abstract
In this paper we propose a variant of a binary level set approach for solving elliptic problems with piecewise constant coefficients. The inverse problem is solved by a variational augmented Lagrangian approach with a total variation regularisation. In the binary formulation, the sought interfaces between the domains with different values of the coefficient are represented by discontinuities of the level set functions. The level set functions shall only take two discrete values, i.e. 1 and -1, but the minimisation functional is smooth. Our formulation can, under moderate amount of noise in the observations, recover rather complicated geometries without requiring any initial curves of the geometries, only a reasonable guess of the constant levels is needed. Numerical results show that our implementation of this formulation has a faster convergence than the traditional level set formulation used on the same problems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2007-IJNAM-852
International Journal of Numerical Analysis and Modeling, Vol. 4 (2007), Iss. 1 : pp. 74–99
Published online: 2007-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: inverse problems parameter identification elliptic equation augmented Lagrangian optimisation level set methods total variation regularisation.