scholarly journals An efficient method for constructing an ILU preconditioner for solving large sparse nonsymmetric linear systems by the GMRES method

2003 ◽  
Vol 45 (10-11) ◽  
pp. 1757-1772 ◽  
Author(s):  
R.C Mittal ◽  
A.H Al-Kurdi
Keyword(s):  
Linear Systems ◽  
Efficient Method ◽  
Gmres Method ◽  
Nonsymmetric Linear Systems

scholarly journals Residual-Based Simpler Block GMRES for Nonsymmetric Linear Systems with Multiple Right-Hand Sides

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Qinghua Wu ◽  
Liang Bao ◽  
Yiqin Lin
Keyword(s):  
Linear Systems ◽  
Linear Dependence ◽  
Numerical Experiments ◽  
Gmres Method ◽  
Algebraic Equations ◽  
Rank Deficiency ◽  
Nonsymmetric Linear Systems ◽  
Right Hand ◽  
Linear Algebraic Equations ◽  
Block Arnoldi

We propose in this paper a residual-based simpler block GMRES method for solving a system of linear algebraic equations with multiple right-hand sides. We show that this method is mathematically equivalent to the block GMRES method and thus equivalent to the simpler block GMRES method. Moreover, it is shown that the residual-based method is numerically more stable than the simpler block GMRES method. Based on the deflation strategy proposed by Calandra et al. (2013), we derive a deflation strategy to detect the possible linear dependence of the residuals and a near rank deficiency occurring in the block Arnoldi procedure. Numerical experiments are conducted to illustrate the performance of the new method.

The Linear System Solver of Programs Named CORTH and KYLIN2

2017 ◽  
Author(s):  
Pingzhou Ming ◽  
Junjie Pan ◽  
Xiaolan Tu ◽  
Dong Liu ◽  
Hongxing Yu
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Nuclear Power ◽  
Experimental Results ◽  
Gmres Method ◽  
Thermal Hydraulics ◽  
Lattice Calculation ◽  
Minimal Residual

Sub-channel thermal-hydraulics program named CORTH and assembly lattice calculation program named KYLIN2 have been developed in Nuclear Power Institute of China (NPIC). For the sake of promoting the computing efficiency of these programs and achieving the better description on fined parameters of reactor, the programs’ structure and details are interpreted. Then the characteristics of linear systems of these programs are analyzed. Based on the Generalized Minimal Residual (GMRES) method, different parallel schemes and implementations are considered. The experimental results show that calculation efficiencies of them are improved greatly compared with the serial situation.

scholarly journals AN OVERVIEW OF MGMRES AND LAN/MGMRES METHODS FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS

2000 ◽  
Vol 4 (3) ◽  
pp. 385-396 ◽  
Author(s):  
David R. Kincaid ◽  
David M. Young ◽  
Jen-Yuan Chen
Keyword(s):  
Linear Systems ◽  
Nonsymmetric Linear Systems

Preconditioning Techniques for Nonsymmetric Linear Systems in the Computation of Incompressible Flows

2009 ◽  
Vol 76 (2) ◽  
Author(s):  
Murat Manguoglu ◽  
Ahmed H. Sameh ◽  
Faisal Saied ◽  
Tayfun E. Tezduyar ◽  
Sunil Sathe
Keyword(s):  
Linear Systems ◽  
Krylov Subspace ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Handling Time ◽  
Navier Stokes ◽  
Preconditioning Techniques ◽  
Navier Stokes Equations ◽  
Nonsymmetric Linear Systems ◽  
Steady State Solutions

In this paper we present effective preconditioning techniques for solving the nonsymmetric systems that arise from the discretization of the Navier–Stokes equations. These linear systems are solved using either Krylov subspace methods or the Richardson scheme. We demonstrate the effectiveness of our techniques in handling time-accurate as well as steady-state solutions. We also compare our solvers with those published previously.

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