Krylov Subspace Solvers and Preconditioners
نویسندگان
چکیده
منابع مشابه
New Krylov-subspace Solvers for Hermitian Positive Definite Matrices with Indefinite Preconditioners
Incomplete LDL∗ factorizations sometimes produce an inde nite preconditioner even when the input matrix is Hermitian positive de nite. The two most popular iterative solvers for Hermitian systems, MINRES and CG, cannot use such preconditioners; they require a positive de nite preconditioner. We present two new Krylov-subspace solvers, a variant of MINRES and a variant of CG, both of which can b...
متن کاملPredictor-Corrector Preconditioners for Newton-Krylov Solvers in Fluid Problems
We propose an alternative implementation of preconditioning techniques for the solution of non-linear problems. Within the framework of Newton-Krylov methods, preconditioning techniques are needed to improve the performance of the solvers. We propose a different implementation approach to re-utilize existing semiimplicit methods to precondition fully implicit non-linear schemes. We propose a pr...
متن کاملKrylov-Subspace Preconditioners for Discontinuous Galerkin Finite Element Methods
Standard (conforming) finite element approximations of convection-dominated convectiondiffusion problems often exhibit poor stability properties that manifest themselves as nonphysical oscillations polluting the numerical solution. Various techniques have been proposed for the stabilisation of finite element methods (FEMs) for convection-diffusion problems, such as the popular streamline upwind...
متن کاملOn Short Recurrences in Optimal Krylov Subspace Solvers:
To solve large sparse linear systems of equations computational fast methods are preferable above methods such as GMRES. By exploiting structure of the involved matrix one can in certain cases use short recurrences to create an optimal Krylov subspace method. In this report we explain some of the theory regarding short-recurrence methods for solving linear systems. A central object in this theo...
متن کاملNonlinear Krylov-Secant Solvers∗
This report describes a new family of Newton-Krylov methods for solving nonlinear systems of equations arising from the solution of Richards’ equation and in fully implicit formulations in air-water systems. The basic approach is to perform secant (Broyden) updates restricted to the Krylov subspace generated by the GMRES iterative solver. This approach is introduced as Krylov-secant methods. On...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ESAIM: Proceedings and Surveys
سال: 2018
ISSN: 2267-3059
DOI: 10.1051/proc/201863001