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Keywords:
wavelet-Galerkin discretization; fictitious domain method; saddle-point system; conjugate gradient method; circulant matrix; fast Fourier transform; Kronecker product
wavelet-Galerkin discretization; fictitious domain method; saddle-point system; conjugate gradient method; circulant matrix; fast Fourier transform; Kronecker product
Summary:
The paper deals with fast solving of large saddle-point systems arising in wavelet-Galerkin discretizations of separable elliptic PDEs. The periodized orthonormal compactly supported wavelets of the tensor product type together with the fictitious domain method are used. A special structure of matrices makes it possible to utilize the fast Fourier transform that determines the complexity of the algorithm. Numerical experiments confirm theoretical results.
References:
[1] F. Brezzi, M. Fortin: Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York, 1991. MR 1115205
[2] P. G. Ciarlet: The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978. MR 0520174 | Zbl 0383.65058
[3] M. Fortin, R. Glowinski: Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems. North-Holland, Amsterdam, 1983. MR 0724072
[4] I. Daubechies: Ten Lectures on Wavelets. SIAM, Philadelphia, 1992. MR 1162107 | Zbl 0776.42018
[5] R. Glowinski, T. Pan, and J. Periaux: A fictitious domain method for Dirichlet problem and applications. Comput. Methods Appl. Mech. Eng. 111 (1994), 283–303. DOI 10.1016/0045-7825(94)90135-X | MR 1259864
[6] R. Glowinski, T. Pan, R. O. Wells, X. Zhou: Wavelets methods in computational fluid dynamics. In: Proc. Algorithms Trends in Computational Dynamics (1993), M. Y. Hussaini, A. Kumar, and M. D. Salas (eds.), Springer-Verlag, New York, pp. 259–276. MR 1295640
[7] G. H. Golub, C. F. Van Loan: Matrix Computation. The Johns Hopkins University Press, Baltimore, 1996, 3rd ed.
[8] N. I. M. Gould: On practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem. Math. Program. 32 (1985), 90–99. DOI 10.1007/BF01585660 | MR 0787745 | Zbl 0591.90068
[9] R. Kučera: Wavelet solution of elliptic PDEs. In: Proc. Matematyka v Naukach Technicznych i Przyrodniczych (2000), S. Bialas (ed.), AGH Krakow, pp. 55–62.
[10] W. Rudin: Real and Complex Analysis. McGraw-Hill, New York, 1987, 3rd ed. MR 0924157 | Zbl 0925.00005
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