Nonlinear integral equations and the iterative solution for an inverse boundary value problem
Copyright policy )Nonlinear integral equations and the iterative solution for an inverse boundary value problem
Summary: Determining the shape of a perfectly conducting inclusion within a conducting medium from voltage and current measurements on the accessible boundary of the medium can be modelled as an inverse boundary value problem for harmonic functions. We present a novel solution method for such inverse boundary value problems via a pair of nonlinear and ill-posed integral equations for the unknown boundary that can be solved by linearization, i.e., by regularized Newton iterations. We present a mathematical foundation of the method and illustrate its feasibility by numerical examples.
- University of Göttingen Germany
- Texas A&M University United States
- The University of Texas System United States
Inverse problems for PDEs, ill-posed integral equations, Inverse problems for integral equations, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, nondestructive testing, Laplace equation, Numerical methods for integral equations, inverse conductivity problem, Boundary value problems for second-order elliptic equations, regularized Newton iterations, unknown inclusion, Numerical methods for inverse problems for integral equations
Inverse problems for PDEs, ill-posed integral equations, Inverse problems for integral equations, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, nondestructive testing, Laplace equation, Numerical methods for integral equations, inverse conductivity problem, Boundary value problems for second-order elliptic equations, regularized Newton iterations, unknown inclusion, Numerical methods for inverse problems for integral equations
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