Explicit preconditioned iterative methods for solving large unsymmetric finite element systems

A class of Generalized Approximate Inverse Matrix (GAIM) techniques, based on the concept of LU-sparse factorization procedures, is introduced for computing explicitly approximate inverses of large sparse unsymmetric matrices of irregular structure, without inverting the decomposition factors. Explicit preconditioned iterative methods, in conjunction with modified forms of the GAIM techniques, are presented for solving numerically initial/boundary value problems on multiprocessor systems. Application of the new methods on linear boundary-value problems is discussed and numerical results are given.ZusammenfassungEs wird eine Methode zur Approximation der verallgemeinerten inversen Matrix (GAIM) diskutiert, die auf dem Konzept der schwachbesetzten LU-Faktorisierung basiert und explizite Inverse großer schwachbesetzter unsymmetrischer Matrizen auf irregulären Strukturen approximiert, ohne die Zerlegungsfaktoren zu invertieren. In Verbindung mit Modifikationen der GAIM-Technik werden explizite Präkonditionierungsmethoden zur numerischen Lösung von Anfangsrandwertproblemen auf Multiprozessorsystemen vorgestellt. Anwendungen der neuen Methoden auf lineare Randwertaufgaben werden diskutiert und numerische Resultate präsentiert.

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