Korneev, V.G. and Langer, U. and Xanthis, Leonidas (2003) *On fast domain decomposition solving procedures for hp-discretizations of 3-d elliptic problems.* Computational Methods in Applied Mathematics, 3 (4). pp. 536-559. ISSN 1609-4840

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Official URL: http://cmam.info/issues/?Vol=3&Num=4&ItID=82

## Abstract

A DD (domain decomposition) preconditioner of almost optimal in p arithmetical complexity is presented for the hierarchical hp-discretizations of 3-d second order elliptic equations. We adapt the wire basket substructuring technique to the hierarchical hp-discretization, obtain a fast preconditioner-solver for faces by K-interpolation technique and show that a secondary iterative process may be efficiently used for prolongations from faces. The fast solver for local Dirichlet problems on subdomains of decomposition is based on our earlier derived finite-difference like preconditioner for the internal stiffness matrices of p-finite elements and fast solution procedures for systems with this preconditioner, which appeared recently. The relative condition number, provided by the DD preconditioner under consideration, is $O((1+\log p)^{3.5})$ and its total arithmetic cost is $O((1+\log p)^{1.75}[(1+\log p)(1+\log(1+\log p))p^3 R+ p R^2])$, where $R$ is the number of finite elements. The term $p R^2$ is due to the solver for the wire basket subsystem. We outline, how the cost of this component may be reduced to $ O(p R)$. The presented DD algorithms are highly parallelizable.

Item Type: | Article |
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Research Community: | University of Westminster > Electronics and Computer Science, School of |

ID Code: | 537 |

Deposited On: | 26 Sep 2005 |

Last Modified: | 15 Oct 2009 14:56 |

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