## Abstract

The vertex space algorithm of Smith is a domain decomposition method for two dimensional elliptic problems based on non-overlapping subregions, in which the reduced Schur complement system on the interface is solved using a generalized block Jacobi type preconditioner, with the blocks corresponding to the vertex space, edges and a coarse grid. In this paper, we describe several variants of this algorithm derived from using two kinds of approximations for the edge and vertex space sub-blocks, one based on Fourier approximation, and another based on an algebraic probing technique in which sparse approximations to these sub-blocks are computed. Our motivation is to improve efficiency of the algorithm without sacrificing the optimal convergence rate. Numerical and theoretical results on the performance of these algorithms are presented.

Original language | English (US) |
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Title of host publication | Domain Decomposition Methods for Partial Differential Equations |

Publisher | Publ by Soc for Industrial & Applied Mathematics Publ |

Pages | 236-249 |

Number of pages | 14 |

ISBN (Print) | 0898712882 |

State | Published - Dec 1 1992 |

Externally published | Yes |

Event | Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations - Norfolk, VA, USA Duration: May 6 1991 → May 8 1991 |

### Conference

Conference | Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations |
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City | Norfolk, VA, USA |

Period | 05/6/91 → 05/8/91 |

## ASJC Scopus subject areas

- Engineering(all)