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A Coarse-fine mesh approach for improved solution of 3-D inverse problems in unbounded media
(IEEE, 2020) Aydoğan, Ahmet; Kılıç, Emre; Taygur, Mehmet Mert; Eibert, Thomas F.
A coarse-fine mesh approach is proposed to enhance the inverse scattering method for a three-dimensional problem. The problem is decomposed into exterior and interior problems to reduce the computational cost by invoking the equivalence principle. The exterior radiation problem is formulated by a boundary integral equation which enables to estimate the unknown surface current densities. The estimated current densities form the boundary conditions of the interior problem to extract the dielectric profile. The interior problem is formulated by the finite element technique and solved by the Gauss-Newton method. The associated surfaces and volumes are respectively discretized by triangular and tetrahedral meshes in the decomposed problems. The interior problem is solved with increasingly finer meshes and restricted iteration numbers for the coarser meshes. The exterior problem is solved for each mesh to form the boundary conditions with the associated discretization while the extracted profile in the previous step is used as the initial solution in the interior problem.