Numerical Method for Solving an inverse Cauchy problem for Helmholtz equation using CGLS, BICGSTAB and PCG

Abstract

In this work, an inverse Cauchy problem of Helmholtz equation for thermal conductivity at the edge of the target was considered. In this paper, temperature on the unknown boundary (the inner boundary)  is determined, by taking advantage of the  Cauchy data that can be obtained from the known part, the part that can be reached (the outer boundary), this problem is solved numerically using the proposed method, and the stability of the approximate solution has been confirmed by adding noise to the Cauchy data.