Boundary Reconstruction in Two-Dimensional Functionally Graded Materials Using a Regularized MFS
Liviu Marin;

doi:10.3970/cmes.2009.046.221
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 46, No. 3, pp. 221-254, 2009
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Keywords Functionally Graded Materials (FGMs); Inverse Geometric Problem; Method of Fundamental Solutions (MFS); Regularization.
Abstract We investigate the stable numerical reconstruction of an unknown portion of the boundary of a two-dimensional domain occupied by a functionally graded material (FGM) from a given boundary condition on this part of the boundary and additional Cauchy data on the remaining known portion of the boundary. The aforementioned inverse geometric problem is approached using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. The optimal value of the regularization parameter is chosen according to Hansen's L-curve criterion. Various examples are considered in order to show that the proposed method is numerically stable with respect to decreasing the amount of noise added into the Cauchy data, accurate and computationally very efficient.
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