### 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 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 65-73 |

Number of pages | 9 |

Volume | 4310 LNCS |

Publication status | Published - 2007 |

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

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 4310 LNCS, pp. 65-73)

**A parallel algorithm for systems of convection-diffusion equations.** / Karátson, J.; Kurics, Tamás; Lirkov, Ivan.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 4310 LNCS, pp. 65-73, 6th International Conference on Numerical Methods and Applications, NMA 2006, Borovets, Bulgaria, 8/20/06.

}

TY - GEN

T1 - A parallel algorithm for systems of convection-diffusion equations

AU - Karátson, J.

AU - Kurics, Tamás

AU - Lirkov, Ivan

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=35448979021&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35448979021&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:35448979021

SN - 3540709401

SN - 9783540709404

VL - 4310 LNCS

SP - 65

EP - 73

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -