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Determination of inner boundaries in modified Helmholtz inverse geometric problems using the method of fundamental solutions

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  • Bin-Mohsin, B.
  • Lesnic, D.

Abstract

In this paper, 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 minimisation of the objective function is regularised when noise is added into the input boundary data. The stability of numerical results is investigated for several test examples.

Suggested Citation

  • Bin-Mohsin, B. & Lesnic, D., 2012. "Determination of inner boundaries in modified Helmholtz inverse geometric problems using the method of fundamental solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1445-1458.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:8:p:1445-1458
    DOI: 10.1016/j.matcom.2012.02.002
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    Cited by:

    1. Ivanyshyn Yaman, Olha & Özdemir, Gazi, 2021. "Numerical solution of a generalized boundary value problem for the modified Helmholtz equation in two dimensions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 181-191.

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