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A nonlinear multigrid for imaging electrical conductivity and permittivity at low frequency. (English) Zbl 0981.65126
Summary: We propose a nonlinear multigrid approach for imaging the electrical conductivity and permittivity of a body Ω, given partial, usually noisy knowledge of the Neumann-to-Dirichlet map at the boundary. The algorithm is a nested iteration, where the image is constructed on a sequence of grids in Ω, starting from the coarsest grid and advancing towards the finest one. We show various numerical examples that demonstrate the effectiveness and robustness of the algorithm and prove local convergence.
MSC:
65N21Inverse problems (BVP of PDE, numerical methods)
65N55Multigrid methods; domain decomposition (BVP of PDE)
35R30Inverse problems for PDE