A fast nonlinear conjugate gradient based method for 3D concentrated frictional contact problems

J. Zhao; E.A.H. Vollebregt; C.W. Oosterlee

doi:10.1016/j.jcp.2015.02.016

A fast nonlinear conjugate gradient based method for 3D concentrated frictional contact problems

J. Zhao, E.A.H. Vollebregt, C.W. Oosterlee

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Research output: Contribution to journal › Article › Academic › peer-review

Abstract

This paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from 3D concentrated frictional shift and rolling contact problems with dry Coulomb friction. The solver combines an active set strategy with a nonlinear conjugate gradient method. One novelty is to consider the tractions of each slip element in a polar coordinate system, using azimuth angles as variables instead of conventional traction variables. The new variables are scaled by the diagonal of the underlying Jacobian. The fast Fourier transform (FFT) technique accelerates all matrix–vector products encountered, exploiting the matrix' Toeplitz structure. Numerical tests demonstrate a significant reduction of the computational time compared to existing solvers for concentrated contact problems.

Original language	English
Pages (from-to)	86-100
Journal	Journal of Computational Physics
Volume	288
DOIs	https://doi.org/10.1016/j.jcp.2015.02.016
Publication status	Published - 2015
Externally published	Yes

Keywords

Frictional contact problem
Azimuth angle variables
Active set strategy
Nonlinear conjugate gradient
Preconditioner
Fast
Fourier transform

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10.1016/j.jcp.2015.02.016

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title = "A fast nonlinear conjugate gradient based method for 3D concentrated frictional contact problems",

abstract = "This paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from 3D concentrated frictional shift and rolling contact problems with dry Coulomb friction. The solver combines an active set strategy with a nonlinear conjugate gradient method. One novelty is to consider the tractions of each slip element in a polar coordinate system, using azimuth angles as variables instead of conventional traction variables. The new variables are scaled by the diagonal of the underlying Jacobian. The fast Fourier transform (FFT) technique accelerates all matrix–vector products encountered, exploiting the matrix' Toeplitz structure. Numerical tests demonstrate a significant reduction of the computational time compared to existing solvers for concentrated contact problems.",

keywords = "Frictional contact problem, Azimuth angle variables, Active set strategy, Nonlinear conjugate gradient, Preconditioner, Fast, Fourier transform",

author = "J. Zhao and E.A.H. Vollebregt and C.W. Oosterlee",

year = "2015",

doi = "10.1016/j.jcp.2015.02.016",

language = "English",

volume = "288",

pages = "86--100",

journal = "Journal of Computational Physics",

issn = "0021-9991",

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T1 - A fast nonlinear conjugate gradient based method for 3D concentrated frictional contact problems

AU - Zhao, J.

AU - Vollebregt, E.A.H.

AU - Oosterlee, C.W.

PY - 2015

Y1 - 2015

N2 - This paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from 3D concentrated frictional shift and rolling contact problems with dry Coulomb friction. The solver combines an active set strategy with a nonlinear conjugate gradient method. One novelty is to consider the tractions of each slip element in a polar coordinate system, using azimuth angles as variables instead of conventional traction variables. The new variables are scaled by the diagonal of the underlying Jacobian. The fast Fourier transform (FFT) technique accelerates all matrix–vector products encountered, exploiting the matrix' Toeplitz structure. Numerical tests demonstrate a significant reduction of the computational time compared to existing solvers for concentrated contact problems.

AB - This paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from 3D concentrated frictional shift and rolling contact problems with dry Coulomb friction. The solver combines an active set strategy with a nonlinear conjugate gradient method. One novelty is to consider the tractions of each slip element in a polar coordinate system, using azimuth angles as variables instead of conventional traction variables. The new variables are scaled by the diagonal of the underlying Jacobian. The fast Fourier transform (FFT) technique accelerates all matrix–vector products encountered, exploiting the matrix' Toeplitz structure. Numerical tests demonstrate a significant reduction of the computational time compared to existing solvers for concentrated contact problems.

KW - Frictional contact problem

KW - Azimuth angle variables

KW - Active set strategy

KW - Nonlinear conjugate gradient

KW - Preconditioner

KW - Fast

KW - Fourier transform

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U2 - 10.1016/j.jcp.2015.02.016

DO - 10.1016/j.jcp.2015.02.016

M3 - Article

SN - 0021-9991

VL - 288

SP - 86

EP - 100

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

A fast nonlinear conjugate gradient based method for 3D concentrated frictional contact problems

Abstract

Keywords

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