The method of fundamental solutions for a biharmonic inverse boundary determination problem

摘要

In this paper, a nonlinear inverse boundary value problem associated to the biharmonic equation is investigated. This problem consists of determining an unknown boundary portion of a solution domain by using additional data on the remaining known part of the boundary. The method of fundamental solutions (MFS), in combination with the Tikhonov zeroth order regularization technique, are employed. It is shown that the MFS regularization numerical technique produces a stable and accurate numerical solution for an optimal choice of the regularization parameter.