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Title: Frequency filtering decompositions for unsymmetric matrices and matrices with strongly varying coefficients

Abstract

In 1992, Wittum introduced the frequency filtering decompositions (FFD), which yield a fast method for the iterative solution of large systems of linear equations. Based on this method, the tangential frequency filtering decompositions (TFFD) have been developed. The TFFD allow the robust and efficient treatment of matrices with strongly varying coefficients. The existence and the convergence of the TFFD can be shown for symmetric and positive definite matrices. For a large class of matrices, it is possible to prove that the convergence rate of the TFFD and of the FFD is independent of the number of unknowns. For both methods, schemes for the construction of frequency filtering decompositions for unsymmetric matrices have been developed. Since, in contrast to Wittums`s FFD, the TFFD needs only one test vector, an adaptive test vector can be used. The TFFD with respect to the adaptive test vector can be combined with other iterative methods, e.g. multi-grid methods, in order to improve the robustness of these methods. The frequency filtering decompositions have been successfully applied to the problem of the decontamination of a heterogeneous porous medium by flushing.

Authors:
Publication Date:
Research Org.:
Front Range Scientific Computations, Inc., Lakewood, CO (United States)
OSTI Identifier:
440703
Report Number(s):
CONF-9604167-Vol.2
ON: DE96015307; TRN: 97:000721-0025
Resource Type:
Conference
Resource Relation:
Conference: Copper Mountain conference on iterative methods, Copper Mountain, CO (United States), 9-13 Apr 1996; Other Information: PBD: [1996]; Related Information: Is Part Of Copper Mountain conference on iterative methods: Proceedings: Volume 2; PB: 242 p.
Country of Publication:
United States
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; ITERATIVE METHODS; EFFICIENCY; SOILS; REMEDIAL ACTION; CONVERGENCE; MATRICES; MATHEMATICAL SPACE; POROUS MATERIALS; MATHEMATICAL MODELS

Citation Formats

Wagner, C. Frequency filtering decompositions for unsymmetric matrices and matrices with strongly varying coefficients. United States: N. p., 1996. Web.
Wagner, C. Frequency filtering decompositions for unsymmetric matrices and matrices with strongly varying coefficients. United States.
Wagner, C. 1996. "Frequency filtering decompositions for unsymmetric matrices and matrices with strongly varying coefficients". United States. https://www.osti.gov/servlets/purl/440703.
@article{osti_440703,
title = {Frequency filtering decompositions for unsymmetric matrices and matrices with strongly varying coefficients},
author = {Wagner, C},
abstractNote = {In 1992, Wittum introduced the frequency filtering decompositions (FFD), which yield a fast method for the iterative solution of large systems of linear equations. Based on this method, the tangential frequency filtering decompositions (TFFD) have been developed. The TFFD allow the robust and efficient treatment of matrices with strongly varying coefficients. The existence and the convergence of the TFFD can be shown for symmetric and positive definite matrices. For a large class of matrices, it is possible to prove that the convergence rate of the TFFD and of the FFD is independent of the number of unknowns. For both methods, schemes for the construction of frequency filtering decompositions for unsymmetric matrices have been developed. Since, in contrast to Wittums`s FFD, the TFFD needs only one test vector, an adaptive test vector can be used. The TFFD with respect to the adaptive test vector can be combined with other iterative methods, e.g. multi-grid methods, in order to improve the robustness of these methods. The frequency filtering decompositions have been successfully applied to the problem of the decontamination of a heterogeneous porous medium by flushing.},
doi = {},
url = {https://www.osti.gov/biblio/440703}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue Dec 31 00:00:00 EST 1996},
month = {Tue Dec 31 00:00:00 EST 1996}
}

Conference:
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