## The Use Of Pointwise Interpolation In Domain Decomposition Methods With Non-Nested Meshes (1995)

Venue: | SIAM J. Sci. Comput |

Citations: | 23 - 3 self |

### BibTeX

@ARTICLE{Cai95theuse,

author = {Xiao-chuan Cai},

title = {The Use Of Pointwise Interpolation In Domain Decomposition Methods With Non-Nested Meshes},

journal = {SIAM J. Sci. Comput},

year = {1995},

volume = {16},

pages = {250--256}

}

### OpenURL

### Abstract

. In this paper, we develop a new technique, and a corresponding theory, for Schwarz type overlapping domain decomposition methods for solving large sparse linear systems which arise from finite element discretization of elliptic partial differential equations. The theory provides an optimal convergence of an additive Schwarz algorithm that is constructed with a non-nested coarse space, and a not necessarily shape regular subdomain partitioning. The theory is also applicable to the graph partitioning algorithms recently developed, [5, 15], for problems defined on unstructured meshes. Key words. unstructured grids, non-nested meshes, domain decomposition, iterative method. AMS(MOS) subject classifications. 65F10, 65N30. 1. Introduction. Considerable interest has developed in Schwarz type overlapping domain decomposition methods for the numerical solution of partial differential equations; see for examples [2, 3, 4, 6, 7, 12, 13, 18] and the references therein. This class of methods o...

### Citations

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Citation Context ...10, 65N30. 1. Introduction. Considerable interest has developed in Schwarz type overlapping domain decomposition methods for the numerical solution of partial differential equations; see for examples =-=[2, 3, 4, 6, 7, 12, 13, 18]-=- and the references therein. This class of methods offers a great deal of parallelism and is very promising for modern parallel computers. The success of the methods depends heavily on the existence o... |

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Citation Context ...10, 65N30. 1. Introduction. Considerable interest has developed in Schwarz type overlapping domain decomposition methods for the numerical solution of partial differential equations; see for examples =-=[2, 3, 4, 6, 7, 12, 13, 18]-=- and the references therein. This class of methods offers a great deal of parallelism and is very promising for modern parallel computers. The success of the methods depends heavily on the existence o... |

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Citation Context ...10, 65N30. 1. Introduction. Considerable interest has developed in Schwarz type overlapping domain decomposition methods for the numerical solution of partial differential equations; see for examples =-=[2, 3, 4, 6, 7, 12, 13, 18]-=- and the references therein. This class of methods offers a great deal of parallelism and is very promising for modern parallel computers. The success of the methods depends heavily on the existence o... |

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Citation Context ...er recent developments along this line can be found in [9, 10, 11, 19, 20]. Some theory and experiments with the pointwise interpolation in the context of non-nested multigrid methods can be found in =-=[1, 8, 16, 17]-=-, and references therein. In [14], Dryja and Widlund developed a general theory for Schwarz type algorithms which has a convergence rate characterized by the quantity (1 + H=ffi), where H measures SIA... |

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Citation Context ... that is constructed with a non-nested coarse space, and a not necessarily shape regular subdomain partitioning. The theory is also applicable to the graph partitioning algorithms recently developed, =-=[5, 15]-=-, for problems defined on unstructured meshes. Key words. unstructured grids, non-nested meshes, domain decomposition, iterative method. AMS(MOS) subject classifications. 65F10, 65N30. 1. Introduction... |

53 | A comparison of some domain decomposition and ilu preconditioned iterative methods for nonsymmetric elliptic problems. Numerical Linear Algebra with Applications
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Citation Context ...pplications. For technical reasons, we assume that the coarse mesh is quasi-uniform, however, no such assumption is needed for the fine mesh. Other recent developments along this line can be found in =-=[9, 10, 11, 19, 20]-=-. Some theory and experiments with the pointwise interpolation in the context of non-nested multigrid methods can be found in [1, 8, 16, 17], and references therein. In [14], Dryja and Widlund develop... |

48 | Domain decomposition algorithms for indefinite elliptic problems
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Citation Context ... that is constructed with a non-nested coarse space, and a not necessarily shape regular subdomain partitioning. The theory is also applicable to the graph partitioning algorithms recently developed, =-=[5, 15]-=-, for problems defined on unstructured meshes. Key words. unstructured grids, non-nested meshes, domain decomposition, iterative method. AMS(MOS) subject classifications. 65F10, 65N30. 1. Introduction... |

27 | Additive Schwarz domain decomposition methods for elliptic problems on unstructured meshes
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Citation Context ...pplications. For technical reasons, we assume that the coarse mesh is quasi-uniform, however, no such assumption is needed for the fine mesh. Other recent developments along this line can be found in =-=[9, 10, 11, 19, 20]-=-. Some theory and experiments with the pointwise interpolation in the context of non-nested multigrid methods can be found in [1, 8, 16, 17], and references therein. In [14], Dryja and Widlund develop... |

24 |
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Citation Context ...er recent developments along this line can be found in [9, 10, 11, 19, 20]. Some theory and experiments with the pointwise interpolation in the context of non-nested multigrid methods can be found in =-=[1, 8, 16, 17]-=-, and references therein. In [14], Dryja and Widlund developed a general theory for Schwarz type algorithms which has a convergence rate characterized by the quantity (1 + H=ffi), where H measures SIA... |

20 |
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Citation Context ...er recent developments along this line can be found in [9, 10, 11, 19, 20]. Some theory and experiments with the pointwise interpolation in the context of non-nested multigrid methods can be found in =-=[1, 8, 16, 17]-=-, and references therein. In [14], Dryja and Widlund developed a general theory for Schwarz type algorithms which has a convergence rate characterized by the quantity (1 + H=ffi), where H measures SIA... |

17 |
decomposition algorithms with small overlap
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Citation Context ...be found in [9, 10, 11, 19, 20]. Some theory and experiments with the pointwise interpolation in the context of non-nested multigrid methods can be found in [1, 8, 16, 17], and references therein. In =-=[14]-=-, Dryja and Widlund developed a general theory for Schwarz type algorithms which has a convergence rate characterized by the quantity (1 + H=ffi), where H measures SIAM J. Sci. Comput., 16, 1995, to a... |

13 |
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12 | Parallel implicit methods for aerodynamics
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8 | Domain decomposition algorithms for inde nite elliptic problems - Cai, Widlund - 1992 |

8 | Towards a uni ed theory of domain decomposition algorithms for elliptic problems - Dryja, Widlund - 1990 |

2 |
Domain Decomposition: Algorithms, Implementations and a Little Theory
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