A parallel algorithm for systems of convection-diffusion equations

J. Karátson, Tamás Kurics, Ivan Lirkov

Research output: Conference contribution

4 Citations (Scopus)

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 languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages65-73
Number of pages9
Volume4310 LNCS
Publication statusPublished - 2007
Event6th International Conference on Numerical Methods and Applications, NMA 2006 - Borovets, Bulgaria
Duration: aug. 20 2006aug. 24 2006

Other

Other6th International Conference on Numerical Methods and Applications, NMA 2006
CountryBulgaria
CityBorovets
Period8/20/068/24/06

Fingerprint

Convection
Conjugate gradient method
Computer architecture
Convection-diffusion Equation
Message passing
Iterative methods
Parallel algorithms
Parallel Algorithms
Partial differential equations
Linear systems
Preconditioner
Computer Systems
Preconditioned Conjugate Gradient Method
Message Passing Interface
Computer Architecture
Superlinear Convergence
Parallel Architectures
Hermann Von Helmholtz
Iterative Solution
Finite Element Discretization

ASJC Scopus subject areas

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

Cite this

Karátson, J., Kurics, T., & Lirkov, I. (2007). A parallel algorithm for systems of convection-diffusion equations. In 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.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4310 LNCS 2007. p. 65-73.

Research output: Conference contribution

Karátson, J, Kurics, T & Lirkov, I 2007, A parallel algorithm for systems of convection-diffusion equations. in 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.
Karátson J, Kurics T, Lirkov I. A parallel algorithm for systems of convection-diffusion equations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4310 LNCS. 2007. p. 65-73
Karátson, J. ; Kurics, Tamás ; Lirkov, Ivan. / A parallel algorithm for systems of convection-diffusion equations. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4310 LNCS 2007. pp. 65-73
@inproceedings{50322f3224e2436faa93b70b958aa95f,
title = "A parallel algorithm for systems of convection-diffusion equations",
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.",
author = "J. Kar{\'a}tson and Tam{\'a}s Kurics and Ivan Lirkov",
year = "2007",
language = "English",
isbn = "3540709401",
volume = "4310 LNCS",
pages = "65--73",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}

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

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 -