Numerical Solutions to the Robin Inverse Problem With Nonnegativity Constraints

Weifu Fang; Fu-Rong Lin

doi:10.4236/jamp.2022.106137

Numerical Solutions to the Robin Inverse Problem With Nonnegativity Constraints

Weifu Fang, Fu-Rong Lin

Wright State University

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	American English
Journal	Journal of Applied Mathematics and Physics
Volume	10
DOIs	https://doi.org/10.4236/jamp.2022.106137
State	Published - Jun 30 2022

Keywords

Boundary Integral Equation
Ill-Posed Problem
Laplace Equation
Nonnegativity Constraint
Penalty Method
Robin Inverse Problem

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title = "Numerical Solutions to the Robin Inverse Problem With Nonnegativity Constraints",

abstract = " 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.",

keywords = "Boundary Integral Equation, Ill-Posed Problem, Laplace Equation, Nonnegativity Constraint, Penalty Method, Robin Inverse Problem",

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N2 - 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.

AB - 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.

KW - Boundary Integral Equation

KW - Ill-Posed Problem

KW - Laplace Equation

KW - Nonnegativity Constraint

KW - Penalty Method

KW - Robin Inverse Problem

UR - https://corescholar.libraries.wright.edu/math/418

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DO - 10.4236/jamp.2022.106137

M3 - Article

VL - 10

JO - Journal of Applied Mathematics and Physics

JF - Journal of Applied Mathematics and Physics

ER -

Numerical Solutions to the Robin Inverse Problem With Nonnegativity Constraints

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Keywords

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