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Erschienen in:
2007 | OriginalPaper | Buchkapitel
A Parallel Algorithm for Systems of Convection-Diffusion Equations
verfasst von : János Karátson, Tamás Kurics, Ivan Lirkov
Erschienen in: Numerical Methods and Applications
Verlag: Springer Berlin Heidelberg
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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.