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

作者：Bin Mohsin B; Lesnic D^*

来源：Mathematics and Computers in Simulation, 2012, 82(8): 1445-1458.

DOI：10.1016/j.matcom.2012.02.002

• Modified Helmholtz%26apos
• s equation
• Inverse problem
• Method of fundamental solutions
• Regularisation

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.

• 出版日期2012-4