Recovery of an Interface From Boundary Measurement in an Elliptic Differential Equation
We study the inverse problem of recovering an interior interface from a boundary measurement in an elliptic boundary value problem arising from a semiconductor transistor model. We set up a nonlinear least-squares formulation for solving the inverse problem, and establish the necessary derivatives with respect to the interface. We then propose both the Gauss–Newton iterative method and the conjugate gradient method for the least-squares problem, and present implementation of these methods using integral equations.
& Zeng, S.
(2011). Recovery of an Interface From Boundary Measurement in an Elliptic Differential Equation. Advances in Computational Mathematics, 36, 201-220.