A semi-implicit binary level set method for source reconstruction problems
C. Liu 1, S. Zhu 21 Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, Zhejiang, P.R. China.
2 Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, P.R. China.
Received by the editors January 20, 2010 and, in revised form, November 26, 2010.
The aim of this paper is to investigate the application of a semi-implicit additive operator splitting scheme based binary level set method to source reconstruction problems. We reformulate the original model to be a new constrained optimization problem under the binary level set framework and solve it by the augmented Lagrangian method. Then we propose an efficient gradient-type algorithm based on the additive operator splitting scheme. The proposed algorithm can create new holes during the evolution. Topological changes can be handled automatically and complex geometry can be recovered under a certain amount of noise in the observation data. Numerical examples are presented to show the effectiveness and efficiency of our method.AMS subject classifications: 49N45, 65N21
Key words: source reconstruction, binary level set method, augmented Lagrangian method, additive operator splitting.
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