Multi-preconditioned Gmres
نویسندگان
چکیده
Standard Krylov subspace methods only allow the user to choose a single preconditioner, although in many situations there may be a number of possibilities. Here we describe an extension of GMRES, multi-preconditioned GMRES, which allows the use of more than one preconditioner. We give some theoretical results, propose a practical algorithm, and present numerical results from problems in domain decomposition and PDE-constrained optimization. These numerical experiments illustrate the applicability and potential of the multi-preconditioned approach.
منابع مشابه
Preconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation
Introduction Fractional differential equations (FDEs) have attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme may be a good approach, particularly, the schemes in numerical linear algebra for solving ...
متن کاملFourier Analysis of GMRES(m) Preconditioned by Multigrid
This paper deals with convergence estimates of GMRES(m) [Saad and Schultz, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856–869] preconditioned by multigrid [Brandt, Math. Comp., 31 (1977), pp. 333–390], [Hackbusch, Multi-Grid Methods and Applications, Springer, Berlin, 1985]. Fourier analysis is a well-known and useful tool in the multigrid community for the prediction of two-grid convergence ...
متن کاملUsing the preconditioned Generalized Minimum RESidual (GMRES) method to solve the sea-ice momentum equation
[1] We introduce the preconditioned generalized minimum residual (GMRES) method, along with an outer loop (OL) iteration to solve the sea-ice momentum equation. The preconditioned GMRES method is the linear solver. GMRES together with the OL is used to solve the nonlinear momentum equation. The GMRES method has low storage requirements, and it is computationally efficient and parallelizable. It...
متن کاملPreconditioned Global FOM and GMRES Methods for Solving Lyapunov Matrix Equations
This paper presents, a preconditioned version of global FOM and GMRES methods for solving Lyapunov matrix equations AX + XA = −BTB. These preconditioned methods are based on the global full orthogonalization and generalized minimal residual methods. For constructing effective preconditioners, we will use ADI spiliting of above lyapunov matrix equations. Numerical experiments show that the solut...
متن کاملSolving large systems arising from fractional models by preconditioned methods
This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned gen...
متن کامل