A generalized conjugate gradient, least square method
Numerische Mathematik
Preconditioning and boundary conditions
SIAM Journal on Numerical Analysis
Optimal equivalent preconditioners
SIAM Journal on Numerical Analysis
Iterative solution methods
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
MPI: The Complete Reference
Superlinearly convergent PCG algorithms for some nonsymmetric elliptic systems
Journal of Computational and Applied Mathematics
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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.