Results 1  10
of
598,673
A Numerical Study of Globalizations of NewtonGMRES Methods
, 2003
"... Newton’s method is at the core of many algorithms used for solving nonlinear equations. A globalized Newton method is an implementation of Newton’s method augmented with “globalization procedures ” intended to enhance the likelihood of convergence to a solution from an arbitrary initial guess. A Ne ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
robust and efficient algorithms for solving nonlinear equations. The aim of this project is to describe the development of some globalized NewtonGMRES methods and to compare their performances on a few benchmark fluid flow problems. i Acknowledgments I was first introduced to the topic of Numerical
Some convergence results for the NewtonGMRES algorithm
, 1993
"... : In this paper, we consider both local and global convergence of the Newton algorithm to solve nonlinear problems when GMRES is used to invert the Jacobian at each Newton iteration. Under weak assumptions, we give a sufficient condition for an inexact solution of GMRES to be a descent direction in ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
: In this paper, we consider both local and global convergence of the Newton algorithm to solve nonlinear problems when GMRES is used to invert the Jacobian at each Newton iteration. Under weak assumptions, we give a sufficient condition for an inexact solution of GMRES to be a descent direction
Some convergence results for the NewtonGMRES algorithm
, 1993
"... : In this paper, we consider both local and global convergence of the Newton algorithm to solve nonlinear problems when GMRES is used to invert the Jacobian at each Newton iteration. Under weak assumptions, we give a sufficient condition for an inexact solution of GMRES to be a descent direction in ..."
Abstract
 Add to MetaCart
: In this paper, we consider both local and global convergence of the Newton algorithm to solve nonlinear problems when GMRES is used to invert the Jacobian at each Newton iteration. Under weak assumptions, we give a sufficient condition for an inexact solution of GMRES to be a descent direction
On backtracking failure in NewtonGMRES methods with a demonstration for the NavierStokes equations
 J. of Comp. Phy
"... In an earlier study of inexact Newton methods, we pointed out that certain counterintuitive behavior may occur when applying residual backtracking to the Navier– Stokes equations with heat and mass transport. Specifically, it was observed that a Newton–GMRES method globalized by backtracking (linese ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
In an earlier study of inexact Newton methods, we pointed out that certain counterintuitive behavior may occur when applying residual backtracking to the Navier– Stokes equations with heat and mass transport. Specifically, it was observed that a Newton–GMRES method globalized by backtracking
An Efficient NewtonGMRES Solver for Aerodynamic Computations
 Proceedings of the 13th AIAA CFD Conference, Snowmass
, 1997
"... An efficient inexactNewtonKrylov algorithm is presented for the computation of steady aerodynamic flows. The algorithm uses preconditioned, restarted GMRES in matrixfree form to solve the linear system arising at each Newton iteration. The preconditioner is formed using an ILU(2) factorization of ..."
Abstract

Cited by 13 (4 self)
 Add to MetaCart
An efficient inexactNewtonKrylov algorithm is presented for the computation of steady aerodynamic flows. The algorithm uses preconditioned, restarted GMRES in matrixfree form to solve the linear system arising at each Newton iteration. The preconditioner is formed using an ILU(2) factorization
NewtonGMRES preconditioning for discontinuous Galerkin discretizations of the NavierStokes equations
 SIAM J. Sci. Comput
, 2008
"... Abstract. We study preconditioners for the iterative solution of the linear systems arising in the implicit time integration of the compressible NavierStokes equations. The spatial discretization is carried out using a Discontinuous Galerkin method with fourth order polynomial interpolations on tri ..."
Abstract

Cited by 39 (11 self)
 Add to MetaCart
on triangular elements. The time integration is based on backward difference formulas resulting in a nonlinear system of equations which is solved at each timestep. This is accomplished using Newton’s method. The resulting linear systems are solved using a preconditioned GMRES iterative algorithm. We consider
A NewtonGMRES Method for the Parallel NavierStokes Equations
, 1995
"... this paper is about the convergence properties of the NavierStokes code for different preconditioners used on parallel architectures ..."
Abstract
 Add to MetaCart
this paper is about the convergence properties of the NavierStokes code for different preconditioners used on parallel architectures
A NewtonGMRES Method for the Parallel NavierStokes Equations
"... CFD is becoming increasingly sophisticated: grids define highly complex geometries, and flows are solved involving very different length and time scales. The solution of the NavierStokes equations must be performed on parallel systems, both for reasons of overall computing power and cost effectiven ..."
Abstract
 Add to MetaCart
CFD is becoming increasingly sophisticated: grids define highly complex geometries, and flows are solved involving very different length and time scales. The solution of the NavierStokes equations must be performed on parallel systems, both for reasons of overall computing power and cost
Results 1  10
of
598,673