Numerical Solutions to the Robin Inverse Problem with Nonnegativity Constraints  

作　　者：Weifu Fang Fu-Rong Lin Weifu Fang;Fu-Rong Lin(Department of Mathematics and Statistics, Wright State University, Dayton, USA;Department of Mathematics, Shantou University, Shantou, China)

机构地区：[1]Department of Mathematics and Statistics, Wright State University, Dayton, USA [2]Department of Mathematics, Shantou University, Shantou, China

出　　处：《Journal of Applied Mathematics and Physics》2022年第6期2015-2025,共11页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：Robin Inverse Problem Ill-Posed Problem Laplace Equation Boundary Inte-gral Equation Nonnegativity Constraint Penalty Method 

分 类 号：O17[理学—数学]