Electrical Conductivity Reconstruction Using Nonlocal Boundary Conditions
Copyright policy )Electrical Conductivity Reconstruction Using Nonlocal Boundary Conditions
Summary: We study existence, uniqueness, and solution estimates to the mixed problem \(\nabla\cdot\sigma\nabla u=0\) with Dirichlet to Neumann map boundary conditions and Neumann boundary conditions. We then show how this can be used in the reconstruction of \(\sigma\), given the relationship between u and its normal derivative on the boundary portion where we do not apply the Dirichlet to Neumann map. A numerical reconstruction scheme is also derived.
Inverse problems for PDEs, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Biomedical imaging and signal processing, impedance imaging, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, finite element method, existence, uniqueness, solution estimates, Dirichlet to Neumann map
Inverse problems for PDEs, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Biomedical imaging and signal processing, impedance imaging, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, finite element method, existence, uniqueness, solution estimates, Dirichlet to Neumann map
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