Classical and cascadic multigrid a methodical comparison
Abstract: "Using the full multigrid method without any coarse grid correction steps but with an a posteriori control of the number of smoothing iterations was shown by Bornemann and Deuflhard [2] to be an optimal iteration method with respect to the energy norm. They named this new kind of mult...
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik
1996
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| Schriftenreihe: | Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin
1996,25 |
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| Zusammenfassung: | Abstract: "Using the full multigrid method without any coarse grid correction steps but with an a posteriori control of the number of smoothing iterations was shown by Bornemann and Deuflhard [2] to be an optimal iteration method with respect to the energy norm. They named this new kind of multigrid iteration the cascadic multigrid method. However, numerical examples with linear finite elements raised serious doubts whether the cascadic multigrid method can be made optimal with respect to the L²-norm. In this paper we prove that the cascadic multigrid method cannot be optimal for linear finite elements and show that the case might be different for higher order elements. We present a careful analysis of the two grid variant of the cascadic multigrid method providing a setting where one can understand the methodical difference between the cascadic multigrid method and the classical multigrid V-cycle almost immediately. As a rule of thumb we get that whenever the cascadic multigrid works the classical multigrid will work too but not vice versa." |
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| Beschreibung: | 10 S. |