Numerical Method for solving an inverse Cauchy problem for Helmholtz equationusing CGLS, BICGSTABand PCG

Abstract

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