Abstract
Generalized extended to the limit sparse factorization procedures in algorithmic form are derived yielding direct and iterative methods for the solution of unsymmetric finite element or finite difference systems of irregular structure. The proposed approximate factorization procedures are chosen as the basis to yield systems on which Chebyshev methods are implicitly applied. Application of the methods on a two dimensional linear boundary-value problem is discussed and numerical results are given.
Zusammenfassung
Es werden verallgemeinerte Faktorisierungsprozeduren für dünnbesetzte Matrizen hergeleitet, die auf direkte und iterative Verfahren zur Lösung von unsymmetrischen Gleichungssystemen unregelmäßiger Struktur führen, wie sie bei Finiten Elementen oder Differenzenverfahren auftreten. Die vorgeschlagenen näherungsweisen Faktorisierungsprozeduren werden zur Gewinnung von Systemen verwendet, auf die dann Chebyshev-Methoden implizit angewandt werden. Die Anwendung des Vorgehens auf ein zweidimensionales lineares Randwertproblem wird diskutiert, numerische Ergebnisse werden angegeben.
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Lipitakis, E.A. Generalized extended to the limit sparse factorization techniques for solving unsymmetric finite element systems. Computing 32, 255–270 (1984). https://doi.org/10.1007/BF02243576
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DOI: https://doi.org/10.1007/BF02243576