Abstract
The adaptive filtering decompositions are based on the tangential frequency filtering decompositions (TFFD). During the iteration with a preliminary preconditioner, the adaptive test vector method calculates new test vectors for additional TFFDs. The adaptive test vector iterative method allows the combination of the tangential frequency decomposition and other iterative methods such as multi-grid. The connection with the TFFD improves the robustness of these iterative methods with respect to varying coefficients. Realistic numerical experiments confirm the efficiency of the presented algorithms.
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References
H. Brakhage, Über die numerische Behandlung von Integralgleichungen nach der Quaraturformelmethode, Numerische Mathematik 2, pp. 183–196, 1960.
R. P. Fedorenko, A relaxation method for solving elliptic difference equations, USSR Comput. Math, and Math. Phys. 1, 5, pp. 1092–1096, 1961.
W. Hackbusch AND U. Trottenberg, Multigrid methods, Proceedings Köln-Porz 1981, Springer-Verlag, Berlin, 1982.
W. Hackbusch, Multi-grid methods and applications, Springer-Verlag, Berlin, 1985.
P.W. Hemker and P. Wesseling, eds., Multigrid methods. Proceedings of the fourth European Multigrid Conference, INSM, Birkhäuser, Basel, 1994.
W. Kinzelbach, Numerische Methoden zur Modellierung des Transports von Schadstoffen im Grundwasser, Oldenbourg Verlag, München, 1992.
A. Reusken, Multigrid with matrix-dependent transfer operators for convection-diffusion problems, in [5], 1994.
M.J.L. Robin, A.L. Gutjahr, E. A. Sudicky AND J.L. Wilson, Cross-correlated random field generation with the direct Fourier transform method, Water Resources Research, Vol. 29, No. 7, pp. 2385–2397, 1993.
E. Stiefel, Über einige Methoden der Relaxationsrechnung, Z. Angew. Math. Phys. 3, pp. 1–33, 1952.
THE UG GROUP, ug — a flexible toolbox for the adaptive multigrid solution of partial differential equations, Stuttgart, 1995.
C. Wagner, W. Kinzelbach AND G.WITTUM, Schur-complement multgrid — a robust method for groundwater flow and transport problems, ICA-Preprint 95/1, Stuttgart, 1995; to be published in Numerische Mathematik, 1997.
C. Wagner, Frequenzfilternde Zerlegungen für unsymmetrische Matrizen und Matrizen mit stark variierenden Koeffizienten, Ph. D. thesis Universität Stuttgart, ICA-Bericht 95/7, Stuttgart, 1995.
C. Wagner, Tangential frequency filtering decompositions for symmetric matrices, ICA-Bericht 96/4, Stuttgart, 1996; to appear in Numerische Mathematik.
C. Wagner, Tangential frequency filtering decompositions for unsymmetric matrices, ICA-Bericht 96/5, Stuttgart, 1996; to appear in Numerische Mathematik.
C. Wagner AND G. Wittum, Adaptive Filtering, ICA-Bericht 96/8, Stuttgart, 1996; to appear in Numerische Mathematik.
G. Wittum, Filternde Zerlegungen — Schnelle Löser für große Gleichungssysteme. Teubner Skrioten zur Numerik Band 1. Teubner-Verlag. Stuttgart. 1992.
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Wagner, C., Wittum, G. (1998). Filtering Decompositions with Respect to Adaptive Test Vectors. In: Hackbusch, W., Wittum, G. (eds) Multigrid Methods V. Lecture Notes in Computational Science and Engineering, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58734-4_19
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DOI: https://doi.org/10.1007/978-3-642-58734-4_19
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