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Spectral methods with sparse matrices. (English) Zbl 0661.65120

Für die Helmholtz-Gleichung wird ein spektrales Verfahren vorgestellt, das zu einer dünn besetzten System-Matrix führt. Im Koeffizientenraum ergibt sich eine symmetrische Neun-Punkt-Formel. Die Kondition verhält sich wie \(O(N^ 2)\) (N: maximaler Polynomgrad). Das spektrale System kann mit Mehrgittermethoden (Linien-Relaxation, Galerkin Grobgitteroperator) effizient gelöst werden.
Reviewer: W.Heinrichs

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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