Abstract
An algebraic multigrid method is developed which can be used as a preconditioner for the solution of linear systems of equations with postitive definite matrices. The method is directed to equations which arise from the discretization of elliptic equations of second order, but only the matrix is the source for the information used by the algorithm. One has only to know whether the matrix stems from a 2-dimensional or 3-dimensional problem and whether the elliptic equations are scalar equations or belong to a system.
Zusammenfassung
Es wird ein algebraisches Mehrgitterverfahren vorgestellt, das zur Vorkonditionierung von positiv definiten Matrizen geeignet ist. Es wurde entworfen für Gleichungssysteme, die aus der Diskretisierung von elliptischen Differentialgleichungen stammen. Alle Information wird aus der Matrix herausgezogen. Man braucht nur zu wissen, ob ein zwei- oder dreidimensionales Problem und ob eine skalare Gleichung oder ein System zugrunde liegt.
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Braess, D. Towards algebraic multigrid for elliptic problems of second order. Computing 55, 379–393 (1995). https://doi.org/10.1007/BF02238488
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DOI: https://doi.org/10.1007/BF02238488