We construct and study overlapping Schwarz preconditioners for the iterative solution of elliptic problems discretized with spectral elements based on Fekete nodes (TSEM). These are a generalization to non-tensorial elements of the classical Gauss-Lobatto-Legendre hexahedral spectral elements (QSEM). Even if the resulting discrete problem is more ill-conditioned than in the classical QSEM case, the resulting preconditioned algorithm using generous overlap is optimal and scalable, since its convergence rate is bounded by a constant independent of the number of elements, subdomains and polynomial degree employed.
Overlapping Schwarz preconditioners for Fekete spectral elements / R. Pasquetti, L.F. Pavarino, F. Rapetti, E. Zampieri (LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING). - In: Domain decomposition methods in science and engineering XVI / [a cura di] O.B. Widlund, D.E. Keyes. - Berlin : Springer Verlag, 2007. - ISBN 9783540344681. - pp. 715-722 (( Intervento presentato al 16. convegno Domain Decomposition Methods in Science and Engineering [10.1007/978-3-540-34469-8_89].
Overlapping Schwarz preconditioners for Fekete spectral elements
L.F. PavarinoSecondo
;E. ZampieriUltimo
2007
Abstract
We construct and study overlapping Schwarz preconditioners for the iterative solution of elliptic problems discretized with spectral elements based on Fekete nodes (TSEM). These are a generalization to non-tensorial elements of the classical Gauss-Lobatto-Legendre hexahedral spectral elements (QSEM). Even if the resulting discrete problem is more ill-conditioned than in the classical QSEM case, the resulting preconditioned algorithm using generous overlap is optimal and scalable, since its convergence rate is bounded by a constant independent of the number of elements, subdomains and polynomial degree employed.File | Dimensione | Formato | |
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