Author(s)

Weifu Fang¹, Fu-Rong Lin²

¹Department of Mathematics and Statistics, Wright State University, Dayton, USA.
²Department of Mathematics, Shantou University, Shantou, China.

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.

Robin Inverse Problem, Ill-Posed Problem, Laplace Equation, Boundary Inte-gral Equation, Nonnegativity Constraint, Penalty Method

Fang, W. and Lin, F. (2022) Numerical Solutions to the Robin Inverse Problem with Nonnegativity Constraints. Journal of Applied Mathematics and Physics, 10, 2015-2025. doi: 10.4236/jamp.2022.106137.