Simultaneous Recovery of Robin Boundary and Coefficient for the Laplace Equation by Shape Derivative
We study the simultaneous recovery of the boundary and coefficient of the Robin boundary condition for the Laplace equation from a pair of solution measurements on another part of the boundary. We derive the variational derivatives of the data-fitting objective functional with respect to the Robin boundary and coefficient, which are then used to device a nonlinear conjugate gradient iterative scheme for the numerical recovery of both the Robin boundary and coefficient together. Numerical examples are presented to illustrate the effectiveness of the recovery algorithms.
(2022). Simultaneous Recovery of Robin Boundary and Coefficient for the Laplace Equation by Shape Derivative. Journal of Computational and Applied Mathematics, 413, 114376.