A direct solution of the Robin inverse problem

Fang, Weifu; Zeng, Suxing

doi:10.1216/jie-2009-21-4-545

Cited by 8 publications

(7 citation statements)

References 10 publications

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“…It is well known that the Robin boundary-value problem (2.1) admits unique solution 0 U ≥ in Ω for given nonnegative model parameters p and g on Γ , and thus the equivalent boundary integral equation (2.1) yields nonnegative solution u on Γ as well (see e.g. [11]).…”

Section: Integral Equation Formulationmentioning

confidence: 99%

Numerical Solutions to the Robin Inverse Problem with Nonnegativity Constraints

Fang,

Lin

2022

JAMP

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We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results.

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Section: Integral Equation Formulationmentioning

confidence: 99%

Numerical Solutions to the Robin Inverse Problem with Nonnegativity Constraints

Fang,

Lin

2022

JAMP

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“…However, this approach would only lead to another variant of the above direct method and would not serve as a preparatory step towards an iterative method for the inverse problem IP2. For a related method solving a two-dimensional inverse impedance problem for the Laplace equation we refer to Fang and Zeng [9]. To solve the above nonlinear system numerically we apply an iterative method suggested by Kress and Rundell [15] based on a simultaneous linearization of both equations with respect to both unknowns.…”

Section: Pmentioning

confidence: 99%

Inverse scattering for surface impedance from phase-less far field data

Ivanyshyn

Kreß

2011

Journal of Computational Physics

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“…A lot of research over recent years has been devoted to developing a numerical solution to the inverse problem [9][10][11][12][13]. Lin and Fang transformed the Robin inverse problem into a linear integral equation by introducing a new variable v, then located a way of regularizing v [14].…”

Section: Introductionmentioning

confidence: 99%

The numerical solution of forward and inverse Robin problems for Laplace’s equation

2019

Bound Value Probl

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The Robin boundary value problem for Laplace's equation in the elliptic region (which is a forward problem) and its related inverse problem can be used to reconstruct Robin coefficients from measurements on a partial boundary (inverse problem). We present a numerical solution of the forward problem that uses a boundary integral equation method, and we propose a fast solver based on one that reduces the computational complexity to O(N log(N)), where N is the size of the data. We compute the solution of the inverse problem using a preconditioned Krylov subspace method where the preconditioner is based on a block matrix decomposition. The structure of the matrix is then exploited to solve the direct problem. Numerical examples are presented to illustrate the effectiveness of the proposed approach.

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A direct solution of the Robin inverse problem

Cited by 8 publications

References 10 publications

Numerical Solutions to the Robin Inverse Problem with Nonnegativity Constraints

Numerical Solutions to the Robin Inverse Problem with Nonnegativity Constraints

Inverse scattering for surface impedance from phase-less far field data

The numerical solution of forward and inverse Robin problems for Laplace’s equation

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