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Preconditioning by approximations of the Gram matrix for convection–diffusion equations

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  • Juncu, Gh.
  • Popa, C.

Abstract

The paper analyses the numerical performance of preconditioning with Gram matrix approximations for the solution of a convection–diffusion equation. The convection–diffusion equation is discretized on a rectangular grid by standard finite element methods with piecewise linear test and trial functions. The discrete linear system is solved by two different conjugate gradient algorithms: CGS and GMRES. The preconditioning with Gram matrix approximations consists of replacing the solving of the equation with the preconditioner by a few iterations of an appropriate iterative scheme. Two iterative algorithms are tested: incomplete Cholesky and multigrid. Numerical experiments indicate that these preconditioners are efficient at relatively small values of the Reynolds number.

Suggested Citation

  • Juncu, Gh. & Popa, C., 1998. "Preconditioning by approximations of the Gram matrix for convection–diffusion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(2), pages 225-233.
    • Handle: RePEc:eee:matcom:v:48:y:1998:i:2:p:225-233
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    Cited by:

    1. Juncu, Gh. & Popa, C., 2002. "Preconditioning by Gram matrix approximation for diffusion–convection–reaction equations with discontinuous coefficients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 60(6), pages 487-506.
    2. Juncu, Gheorghe & Popa, Constantin, 2000. "Numerical experiments with preconditioning by gram matrix approximation for non-linear elliptic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 52(1), pages 53-71.

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