Investigation of regularized techniques for boundary knot method. (English) Zbl 1208.65173

Wang, Fuzhang; Chen, Wen; Jiang, Xinrong

Int. J. Numer. Methods Biomed. Eng. 26, No. 12, 1868-1877 (2010).

Summary: This study investigates regularization techniques for the boundary knot method (BKM). We consider three regularization methods and two approaches for the determination of the regularization parameter. Our numerical experiments show that Tikhonov regularization in conjunction with generalized cross-validation approach outperforms the other regularization techniques in the BKM solution of Helmholtz and modified Helmholtz problems.

MSC:

65N35	Spectral, collocation and related methods for boundary value problems involving PDEs
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65F20	Numerical solutions to overdetermined systems, pseudoinverses

Keywords:

boundary knot method; regularization method; singular value decomposition; Helmholtz problem; numerical experiments; Tikhonov regularization; generalized cross-validation

Software:

Regularization tools

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