Analysis of a semi–Toeplitz preconditioner for a convection-diffusion problem∗
نویسندگان
چکیده
We have defined and analyzed a semi-Toeplitz preconditioner for timedependent and steady-state convection-diffusion problems. The preconditioner exhibits very good theoretical convergence properties. The analysis is corroborated by numerical experiments.
منابع مشابه
Semi-Toeplitz Preconditioning for Linearized Boundary Layer Problems
We have defined and analyzed a semi-Toeplitz preconditioner for timedependent and steady-state convection-diffusion problems. Analytic expressions for the eigenvalues of the preconditioned systems are obtained. An asymptotic analysis shows that the eigenvalue spectrum of the timedependent problem is reduced to two eigenvalues when the number of grid points go to infinity. The numerical experime...
متن کاملA new model of (I+S)-type preconditioner for system of linear equations
In this paper, we design a new model of preconditioner for systems of linear equations. The convergence properties of the proposed methods have been analyzed and compared with the classical methods. Numerical experiments of convection-diffusion equations show a good im- provement on the convergence, and show that the convergence rates of proposed methods are superior to the other modified itera...
متن کاملPreconditioned HSS Method for Finite Element Approximations of Convection-Diffusion Equations
A two-step preconditioned iterative method based on the Hermitian/Skew-Hermitian splitting is applied to the solution of nonsymmetric linear systems arising from the Finite Element approximation of convection-diffusion equations. The theoretical spectral analysis focuses on the case of matrix sequences related to FE approximations on uniform structured meshes, by referring to spectral tools der...
متن کاملPreconditioning Techniques for Diagonal-times-Toeplitz Matrices in Fractional Diffusion Equations
The fractional diffusion equation is discretized by an implicit finite difference scheme with the shifted Grünwald formula, which is unconditionally stable. The coefficient matrix of the discretized linear system is equal to the sum of a scaled identity matrix and two diagonal-times-Toeplitz matrices. Standard circulant preconditioners may not work for such Toeplitz-like linear systems. The mai...
متن کاملKronecker product approximation preconditioners for convection-diffusion model problems
We consider the iterative solution of linear systems arising from four convection–diffusion model problems: scalar convection–diffusion problem, Stokes problem, Oseen problem and Navier–Stokes problem. We design preconditioners for these model problems that are based on Kronecker product approximations (KPAs). For this we first identify explicit Kronecker product structure of the coefficient ma...
متن کامل