3-D finite element transport models by upwind preconditioned conjugate gradients

1989 ◽  
Vol 12 (2) ◽  
pp. 54-58 ◽  
Author(s):  
G. Pini ◽  
G. Gambolati ◽  
G. Galeati
Keyword(s):  
Finite Element ◽  
Conjugate Gradients ◽  
Transport Models ◽  
Preconditioned Conjugate Gradients ◽  
Element Transport

The effect of ordering on preconditioned conjugate gradients

1989 ◽  
Vol 29 (4) ◽  
pp. 635-657 ◽  
Author(s):  
Iain S. Duff ◽  
Gérard A. Meurant
Keyword(s):  
Conjugate Gradients ◽  
Preconditioned Conjugate Gradients

Deflated preconditioned conjugate gradients applied to a Petrov-Galerkin generalized least squares finite element formulation for incompressible flows with heat transfer

2015 ◽  
Vol 25 (2) ◽  
pp. 272-298
Author(s):  
Rosilene A. Kraft ◽  
Alvaro L. G. A. Coutinho
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Least Squares ◽  
Incompressible Flows ◽  
Viscous Flows ◽  
Generalized Least Squares ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Content Type ◽  
Preconditioned Conjugate Gradients

Purpose – The purpose of this paper is to show benefits of deflated preconditioned conjugate gradients (CG) in the solution of transient, incompressible, viscous flows coupled with heat transfer. Design/methodology/approach – This paper presents the implementation of deflated preconditioned CG as the iterative driver for the system of linearized equations for viscous, incompressible flows and heat transfer simulations. The De Sampaio-Coutinho particular form of the Petrov-Galerkin Generalized Least Squares finite element formulation is used in the discretization of the governing equations, leading to symmetric positive definite matrices, allowing the use of the CG solver. Findings – The use of deflation techniques improves the spectral condition number. The authors show in a number of problems of coupled viscous flow and heat transfer that convergence is achieved with a lower number of iterations and smaller time. Originality/value – This work addressed for the first time the use of deflated CG for the solution of transient analysis of free/forced convection in viscous flows coupled with heat transfer.

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