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- W4221151305 abstract "In this paper, we propose and analyze a reconstruction algorithm for imaging an anisotropic conductivity tensor in a second-order elliptic PDE with a nonzero Dirichlet boundary condition from internal current densities. It is based on a regularized output least-squares formulation with the standard $L^2(Omega)^{d,d}$ penalty, which is then discretized by the standard Galerkin finite element method. We establish the continuity and differentiability of the forward map with respect to the conductivity tensor in the $L^p(Omega)^{d,d}$-norms, the existence of minimizers and optimality systems of the regularized formulation using the concept of H-convergence. Further, we provide a detailed analysis of the discretized problem, especially the convergence of the discrete approximations with respect to the mesh size, using the discrete counterpart of H-convergence. In addition, we develop a projected Newton algorithm for solving the first-order optimality system. We present extensive two-dimensional numerical examples to show the efficiency of the proposed method." @default.
- W4221151305 created "2022-04-03" @default.
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- W4221151305 date "2022-06-01" @default.
- W4221151305 modified "2023-10-15" @default.
- W4221151305 title "Imaging Anisotropic Conductivities from Current Densities" @default.
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- W4221151305 doi "https://doi.org/10.1137/21m1437810" @default.
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