Regularized MFS-Based Boundary Identification in Two-Dimensional Helmholtz-Type Equations
Liviu Marin; and Andreas Karageorghis;

doi:10.3970/cmc.2009.010.259
Source CMC: Computers, Materials, & Continua, Vol. 10, No. 3, pp. 259-294, 2009
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Keywords Helmholtz-Type Equations; Inverse Geometric Problem; Method of Fundamental Solutions (MFS); Regularization.
Abstract We study the stable numerical identification of an unknown portion of the boundary on which a given boundary condition is provided and additional Cauchy data are given on the remaining known portion of the boundary of a two-dimensional domain for problems governed by either the Helmholtz or the modified Helmholtz equation. This inverse geometric problem is solved using the method of fundamental solutions (MFS) in conjunction with the Tikhonov regularization method. The optimal value for the regularization parameter is chosen according to Hansen's L-curve criterion. The stability, convergence, accuracy and efficiency of the proposed method are investigated by considering several examples.
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