Superlinear Convergence of a Preconditioned Iterative Method for the Convection-diffusion Equation
نویسندگان
چکیده
The convergence features of a preconditioned algorithm for the convection-diffusion equation based on its diffusion part are considered. An analysis of the distribution of the eigenvalues of the preconditioned matrix and of the fundamental parameters of convergence are provided, showing the existence of a proper cluster of eigenvalues and the superlinear behavior of preconditioned iterations. The structure of the cluster is not influenced by the discretization but the number of outliers increases at most proportionally to ν as the viscosity parameter ν is increased. The overall cost of the algorithm is O(n), where n is the size of the underlying matrices.
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