A mesh independent superlinear algorithm for some nonlinear nonsymmetric elliptic systems

Superlinearly convergent PCG algorithms for some nonsymmetric elliptic systems

The conjugate gradient method is a widespread way of solving nonsymmetric linear algebraic systems, in particular for large systems arising from discretized elliptic problems. A celebrated property of the CGM is superlinear convergence, see the book [2] where a comprehensive summary is given on the convergence of the CGM. For discretized elliptic problems, the CGM is mostly used with suitable p...

Mesh Independent Superlinear PCG Rates Via Compact-Equivalent Operators

The subject of the paper is the mesh independent convergence of the preconditioned conjugate gradient method for nonsymmetric elliptic problems. The approach of equivalent operators is involved, in which one uses the discretization of another suitable elliptic operator as preconditioning matrix. By introducing the notion of compact-equivalent operators, it is proved that for a wide class of ell...

Superlinear PCG algorithms: symmetric part preconditioning and boundary conditions

The superlinear convergence of the preconditioned CGM is studied for nonsymmetric elliptic problems (convection-diffusion equations) with mixed boundary conditions. A mesh independent rate of superlinear convergence is given when symmetric part preconditioning is applied to the FEM discretizations of the BVP. This is the extension of a similar result of the author for Dirichlet problems. The di...

Mesh independent superlinear convergence of some iterative methods for elliptic problems

Domain Decomposition Algorithms for Indeenite Elliptic Problems

Iterative methods for linear systems of algebraic equations arising from the nite element discretization of nonsymmetric and indeenite elliptic problems are considered. Methods previously known to work well for positive deenite, symmetric problems are extended to certain nonsymmetric problems, which can also have some eigenvalues in the left half plane. We rst consider an additive Schwarz metho...