### Abstract

The numerical solution of systems of convection-diffusion equations is considered. The problem is described by a system of second order partial differential equations (PDEs). This system is discretized by Courant-elements. The preconditioned conjugate gradient method is used for the iterative solution of the large-scale linear algebraic systems arising after the finite element discretization of the problem. Discrete Helmholtz preconditioners are applied to obtain a mesh independent superlinear convergence of the iterative method. A parallel algorithm is derived for the proposed preconditioner. A portable parallel code using Message Passing Interface (MPI) is developed. Numerical tests well illustrate the performance of the proposed method on a parallel computer architecture.

Original language | English |
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Title of host publication | Numerical Methods and Applications - 6th International Conference, NMA 2006, Revised Papers |

Pages | 65-73 |

Number of pages | 9 |

Publication status | Published - Oct 29 2007 |

Event | 6th International Conference on Numerical Methods and Applications, NMA 2006 - Borovets, Bulgaria Duration: Aug 20 2006 → Aug 24 2006 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4310 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 6th International Conference on Numerical Methods and Applications, NMA 2006 |
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Country | Bulgaria |

City | Borovets |

Period | 8/20/06 → 8/24/06 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Numerical Methods and Applications - 6th International Conference, NMA 2006, Revised Papers*(pp. 65-73). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4310 LNCS).