Matrix computations (3rd ed.)
Multigrid
Superlinear Convergence of Conjugate Gradients
SIAM Journal on Numerical Analysis
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Superlinear Preconditioners for Finite Differences Linear Systems
SIAM Journal on Matrix Analysis and Applications
A Preconditioner for Generalized Saddle Point Problems
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
On the Asymptotic Spectrum of Finite Element Matrix Sequences
SIAM Journal on Numerical Analysis
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A two-step preconditioned iterative method based on the Hermitian and skew-Hermitian splitting is applied to the solution of nonsymmetric linear systems arising from the finite element approximation of diffusion-dominated convection-diffusion equations. The theoretical spectral analysis focuses on the case of matrix sequences related to finite element approximations on uniform structured meshes, by referring to spectral tools derived from Toeplitz theory. In such a setting, if the problem is coercive and the diffusive and convective coefficients are regular enough, then the proposed preconditioned matrix sequence shows a strong clustering at unity, i.e., a superlinear preconditioning sequence is obtained. Under the same assumptions, the optimality of the preconditioned Hermitian and skew-Hermitian splitting (PHSS) method is proved, and some numerical experiments confirm the theoretical results. Tests on unstructured meshes are also presented, showing the same convergence behavior.