Abstract
In this paper we discuss a hierarchical relaxation method for solving a system of equations. The method proceeds by adjoining to a given system of equations whose solution is sought, an auxiliary hierarchy of systems. The relaxation procedure consists of a judicious mixing of relaxation steps in the different members of the hierarchy. When the choice of the hierarchy and the mixing of relaxation steps are appropriate, the entire procedure provides an acceleration of the relaxation process toward a determination of the solution of the original system. The procedure lends itself to parallel implementation, even in an asynchronous mode. We discuss these aspects of hierarchical relaxation as well.
Zusammenfassung
In dieser Arbeit präsentieren wir eine hierarchische Relaxationsmethode zur Lösung eines Gleichungssystems. Die Methode geht so vor, daß einem gegebenen Gleichungssystem, dessen Lösung gesucht wird, eine Hilfshierarchie von Systemen zugefügt wird. Die Relaxationsmethode besteht in einer ausgefeilten Mischung von Relaxationsschritten in den verschiedenen Mitgliedern der Hierarchie. Wenn die Wahl der Hierarchie und die Mischung der Relaxationsschritte geeignet sind, liefert die ganze Prozedur eine beschleunigung des Relaxationsprozesses zur Bestimmung einer Lösung des ursprünglichen Systems. Die Prozedur ist auch für parallele, sogar asynchrone Implementierung geeignet. Auch diese Aspekte der hierarchischen Relaxation werden diskutiert.
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Miranker, W.L. Hierarchical relaxation. Computing 23, 267–285 (1979). https://doi.org/10.1007/BF02252132
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DOI: https://doi.org/10.1007/BF02252132