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Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients. (English) Zbl 1197.65191
Summary: We present a new technique to accelerate the convergence of a FFT-based solver for numerical homogenization of complex periodic media proposed by H. Moulinec and P. Suquet [C. R. Acad. Sci., Paris, Sér. II 318, No. 11, 1417–1423 (1994; Zbl 0799.73077)]. The approach proceeds from discretization of the governing integral equation by the trigonometric collocation method due to G. Vainikko [in: Direct and inverse problems of mathematical physics. Papers presented at special sessions of the ISAAC’97 congress, University of Delaware, Newark, DE, USA, June 2–7, 1997. Dordrecht: Kluwer Academic Publishers. Int. Soc. Anal. Appl. Comput. 5, 423–440 (2000; Zbl 0962.65097)] to give a linear system which can be efficiently solved by conjugate gradient methods. Computational experiments confirm robustness of the algorithm with respect to its internal parameters and demonstrate significant increase of the convergence rate for problems with high-contrast coefficients at a low overhead per iteration.

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
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