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Jacobian-free newton-krylov subspace method with wavelet-based preconditioner for analysis of transient elastohydrodynamic lubrication problems with surface asperities

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Applied Mathematics and Mechanics(English Edition) 2020年第6期41卷 881-898页

作者： N.M.BUJURKE M.H.KANTLI Department of Mathematics Karnatak UniversityDharwad 580003India Department of Mathematics Biluru Gurubasava Mahaswamiji Institute of TechnologyMudhol 587313India

This paper presents an investigation into the effect of surface asperities on the over-rolling of bearing surfaces in transient elastohydrodynamic lubrication(EHL) line contact. The governing equations are discretized by the finite difference method. The resulting nonlinear system of algebraic equations is solved by the Jacobian-free newtongeneralized minimal residual(GMRES) from the krylov subspace method(KSM). The acceleration of the GMRES iteration is accomplished by a wavelet-based *** profiles of the lubricant pressure and film thickness are obtained at each time step when the indented surface moves through the contact region. The prediction of pressure as a function of time provides an insight into the understanding of fatigue life of *** analysis confirms the need for the time-dependent approach of EHL problems with surface asperities. This method requires less storage and yields an accurate solution with much coarser grids. It is stable, efficient, allows a larger time step, and covers a wide range of parameters of interest.

关键词： transient elastohydrodynamic lubrication(EHL) surface roughness bearing newton-krylov method generalized minimal residual(GMRES) wavelet preconditioner

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The newton-krylov-Lanczons method

The Newton-Krylov-Lanczons method

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2016年航空科学与技术全国博士生学术论坛

作者： Yan Xiao Sun Qin School of Aeronautics Northwestern Polytechnical University

The Generalized Minimal RESidual method（GMRES） is widely used in newton-krylov（NK） methods. It is an Arnoldi-based method with Gram-Schmidt orthogonalization process where two matrices have to be formed and stored for solving newton correction equations. It will be a high demand for memory and calculated quantity because each vector generated by the GramSchmidt method has to use all information of vectors previous and moreover it will be horrendous for storage and operations in large-scale cases. While the Lanczos orthogonalization method needs just two vectors’ information previous and forms a tridiagonal matrix which can be stored in only two vectors. Hence, the Lanczos orthogonalization method costs fewer oprations to orthogonalize the krylov subspace with almost half memory and saves lots of time compared to the Gram-Schmidt method.

关键词： newton-krylov method Lanczos’ method save storage save operations

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