Abstract
The discretization of linear integral equations for elliptic boundary value problems by the boundary element method yields linear systems of simultaneous equations with filled matrices. The structure of these matrices allows Fourier methods to be used to determine preconditioning matrices such that fast iterative solution of the linear system of algebraic equations is possible. The preconditioning method is applicable to Fredholm integral equations of the first kind with non-smooth convolutional principal part as well as to Fredholm integral equations of the second kind. Numerical examples are presented.
Zusammenfassung
Die Diskretisierung von linearen Integralgleichungen für elliptische Randwertaufgaben durch die Randelementmethode gibt lineare Gleichungssysteme mit gefüllten Matrizen. Die Struktur dieser Matrizen läßt Vorkonditionierung durch Fourier-Methoden zu, was schnelles iteratives Lösen des Gleichungssystems von algebraischen Gleichungen ermöglicht. Die Vorkonditionierungsmethode ist verwendbar für Fredholmsche Integralgleichungen erster Art mit unglattem Kern vom Faltungstyp, sowie für Fredholmsche Integralgleichungen zweiter Art. Numerische Beispiele werden präsentiert.
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Reichel, L. A method for preconditioning matrices arising from linear integral equations for elliptic boundary value problems. Computing 37, 125–136 (1986). https://doi.org/10.1007/BF02253186
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DOI: https://doi.org/10.1007/BF02253186