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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.