Effective numerical algorithms for the solution of algebraic systems arising in spectral methods
type: Item
instance of: scholarly article
title: Effective numerical algorithms for the solution of algebraic systems arising in spectral methods
zbMATH Open document ID: 0754.65031
DOI: 10.1016/0168-9274(92)90033-A
published in: Applied Numerical Mathematics
publication date: 1993-01-16T00:00:00Z
review text: The authors first present the weak formulation of the spectral collocation method for elliptic boundary value problems on a rectangular domain with Dirichlet and Neumann conditions. If Legendre nodes and weights are used it is shown that the weak formulation naturally leads to symmetric matrices, whereas the more popular approach by the pointwise strong formulation yields unsymmetric spectral matrices. Next the solution of the algebraic systems with symmetric and unsymmetric spectral matrices is considered and especially the aspects of preconditioning and vectorization are discussed. The effects and results are outlined for several examples, and comparisons are made between the methods of Richardson, CGS, BI-CGSTAB and GMRES obtained on four different supercomputers. Finally, the multidomain approach is considered in which the given domain is splitted into subregions, where the spectral method is combined with an iteration with respect to interface conditions.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65Y10
zbMATH DE Number: 89534
zbMATH Keywords: domain decomposition
zbMATH Keywords: Richarson method
zbMATH Keywords: CGS method
zbMATH Keywords: BI-CGSTAB method
zbMATH Keywords: GMRES method
zbMATH Keywords: CRAY X/MP-EA
zbMATH Keywords: CRAY Y-MP 8/432
zbMATH Keywords: IBM 3090/200S VF
zbMATH Keywords: NCUBE2
zbMATH Keywords: spectral collocation method
zbMATH Keywords: unsymmetric spectral matrices
zbMATH Keywords: preconditioning
zbMATH Keywords: vectorization
zbMATH Keywords: comparisons
zbMATH Keywords: iteration
author: Claudio Carlenzoli
author: Paola Gervasio
describes a project that uses: CGS
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 89534