The Method of Fundamental Solutions for the 3D Laplace Inverse Geometric Problem on an Annular Domain

In this paper, we are interested in an inverse geometric problem for the three-dimensional Laplace equation to recover an inner boundary of an annular domain. This work is based on the method of fundamental solutions (MFS) by imposing the boundary Cauchy data in a least-square sense and minimisation of the objective function. This approach can also be considered with noisy boundary Cauchy data. The simplicity and efficiency of this method is illustrated in several numerical examples.

Automated summary

This paper discusses an inverse geometric problem for the three-dimensional Laplace equation to recover an inner boundary of an annular domain using the method of fundamental solutions (MFS). It works by imposing the boundary Cauchy data in a least-square sense and minimizing the objective function. The simplicity and efficiency of this method is demonstrated in several numerical examples.