Hybrid topological derivative-gradient based methods for nondestructive testing. (English) Zbl 1470.78009

Carpio, A.; Rapún, M.-L.

Abstr. Appl. Anal. 2013, Article ID 816134, 20 p. (2013).

Summary: This paper is devoted to the reconstruction of objects buried in a medium and their material properties by hybrid topological derivative-gradient based methods. After illustrating the techniques in time-harmonic acoustic problems with different boundary conditions and in electrical impedance tomography problems with continuous Neumann conditions, we extend the hybrid method for a realistic model in tomography where the boundary conditions are given at a discrete set of electrodes.

MSC:

78M99	Basic methods for problems in optics and electromagnetic theory
74J25	Inverse problems for waves in solid mechanics
65N21	Numerical methods for inverse problems for boundary value problems involving PDEs
74P15	Topological methods for optimization problems in solid mechanics
78A46	Inverse problems (including inverse scattering) in optics and electromagnetic theory
78A55	Technical applications of optics and electromagnetic theory
35R30	Inverse problems for PDEs
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

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