Advanced Numerical Methods in the Mathematical Sciences
- Bandar Bin-Mohsin, King Saud University (Saudi Arabia)
- Determination of Inner Boundaries in Modified Helmholtz Inverse Geometric Problems Using the MFS
- B. Bin-Mohsin, King Saud University (Saudi Arabia)
- D. Lesnic, University of Leeds (United Kingdom)
In this study, an inverse geometric problem for the modified Helmholtz equation arising in heat conduction in a fin, which consists of determining an unknown inner boundary (rigid inclusion or cavity) of an annular domain from a single pair of boundary Cauchy data is solved numerically using the method of fundamental solutions (MFS). A nonlinear minimization of the objective function is regularized when noise is added into the input boundary data. The stability of numerical results is investigated for several test examples.