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On the spectrum of the iteration operator associated to the finite element preconditioning of Chebyshev collocation calculations

par Francken, Philippe ;Deville, Michel;Mund, Ernest
Référence Computer methods in applied mechanics and engineering, 80, 1-3, page (295-304)
Publication Publié, 1990-06

Article révisé par les pairs

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Résumé :

An analytical investigation is performed of the spectrum of the iteration operator associated to the finite element preconditioning of Chebyshev collocation calculations, on a one-dimensional Dirichlet model problem. Use is made of the techniques developed by Haldenwang et al. for the finite difference preconditioning of the same problem. In the latter case the eigenvalues may be obtained as the diagonal elements of an upper-triangular matrix. This is not possible with finite element preconditioning, where the corresponding operator splits into two parts, one of which only is upper-triangular. Discarding the non-triangular part of the operator (which vanishes asymptotically for large values of N, partition size), this procedure yields an approximate expression of the eigenvalues in good agreement with the properties given earlier by Deville and Mund. © 1990.