Superlinear PCG algorithms: symmetric part preconditioning and boundary conditions
نویسنده
چکیده
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 discussion relies on suitably developed Hilbert space theory for linear operators.
منابع مشابه
Superlinear PCG methods for symmetric Toeplitz systems
In this paper we deal with the solution, by means of preconditioned conjugate gradient (PCG) methods, of n × n symmetric Toeplitz systems An(f)x = b with nonnegative generating function f . Here the function f is assumed to be continuous and strictly positive, or is assumed to have isolated zeros of even order. In the first case we use as preconditioner the natural and the optimal τ approximati...
متن کاملSuperlinear Pcg Methods for Symmetric Toeplitz Systems
In this paper we deal with the solution, by means of preconditioned conjugate gradient (PCG) methods, of n × n symmetric Toeplitz systems An(f)x = b with nonnegative generating function f . Here the function f is assumed to be continuous and strictly positive, or is assumed to have isolated zeros of even order. In the first case we use as preconditioner the natural and the optimal τ approximati...
متن کاملSymmetric part preconditioning of the CGM for Stokes type saddle-point systems
Saddle-point problems arise as mathematical models in various applications and have been a subject of intense investigation, e.g. [5, 11, 23, 26]. Besides the widespread Uzawa type methods, an efficient way of solving such problems is the preconditioned conjugate gradient method. In this paper we consider nonsymmetric formulations of saddle-point systems, following [12]. For nonsymmetric proble...
متن کاملSuperlinearly 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...
متن کاملMesh 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...
متن کامل