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Reconstructing discontinuities using complex geometrical optics solutions. (English) Zbl 1146.35097

Summary: We provide a framework for constructing general complex geometrical optics solutions for several systems of two variables that can be reduced to a system with the Laplacian as the leading order term. We apply these special solutions to the problem of reconstructing inclusions with known conductivity inside a domain from local boundary measurements. Computational results demonstrate the versatility of these solutions to determine electrical inclusions.

MSC:

35R30 Inverse problems for PDEs
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
78A48 Composite media; random media in optics and electromagnetic theory
74B20 Nonlinear elasticity
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