Abstract
This paper deals with nearly singular, possibly indefinite problems for which the usual multigrid solvers converge very slowly or even diverge. The main difficulty is related to some badly approximated smooth functions which correspond to eigenfunctions with nearly zero eigenvalues. A modification to the usual coarse-grid equations is derived, both in Correction Scheme and in Full Approximation Scheme. With this modification, the algorithm exhibits the usual multigrid efficiency.
Sponsored by the Air Force Wright Aeronautical Laboratories, Air Force Systems Command, Unites State Air Force under Grant AFOSR 84-0070.
Research was supported by the National Aeronautics and Space Administration under NASA Contract Nos. NAS1-17070 and NAS1-18107 while the author was in residence at ICASE, NASA Langley Research Center, Hampton, VA 23665-5225.
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References
A. Brandt, Multigrid Techniques: 1984 Guide With Applications to Fluid Dynamics. Monograph available as GMD-Studie No. 85, from GMD-FlT, Postfach 1240, D-5205, St. Augustin 1, W. Germany.
A. Brandt, Algebraic multigrid theory: the symmetric case. Preliminary Proceedings of International Multigrid Conference, Copper Mountain, Colorado, April 1983. Applied Math. Comp., to appear.
S. Ta'asan, Multigrid Methods for Highly Oscillatory Problems. Ph.D. Thesis, The Weizmann Institute of Science, Rehovot, Israel 1984.
K. Tanabe, Projection methods for solving a singular system of linear equations and its applications, Numer. Math., 17 (1971), pp. 203–214.
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© 1986 Springer-Verlag
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Brandt, A., Ta'asan, S. (1986). Multigrid method for nearly singular and slightly indefinite problems. In: Hackbusch, W., Trottenberg, U. (eds) Multigrid Methods II. Lecture Notes in Mathematics, vol 1228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072643
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DOI: https://doi.org/10.1007/BFb0072643
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