A Globally Convergent Newton-GMRES Subspace Method for Systems of Nonlinear Equations

Bellavia, Stefania; Morini, Benedetta

doi:10.1137/s1064827599363976

Cited by 73 publications

(74 citation statements)

References 20 publications

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“…Therefore, this procedure may be very time consuming even though the dimension is relatively small. In order to reduce the computational load, a strategy based on a Newton-Krylov method (implemented in "matrix free" way) has been considered [18,23]. Newton-Krylov methods are Newtontype methods, where a Krylov method is employed to approximate the arising linear systems (17).…”

Section: The Numerical Solution Of the Discrete Problemmentioning

confidence: 99%

An innovative wheel–rail contact model for multibody applications

Magheri

Malvezzi

Meli

et al. 2011

Wear

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a b s t r a c tIn this work an innovative elastic wheel-rail contact model is presented. The model considers the wheel and the rail as elastic deformable bodies and requires numerical solution of Navier's elasticity equation. The contact between wheel and rail has been described by means of suitable analytical contact conditions. The contact model was subsequently inserted into a multibody model of a benchmark railway vehicle (the Manchester Wagon) in order to obtain a complete model of the wagon. The complete model has been implemented in the Matlab/Simulink environment. Numerical simulations of the vehicle dynamics have been carried out on many different railway tracks with the aim of evaluating the performance of the model.The main objective of the authors is to achieve a better integration between the differential and multibody modeling. This kind of integration is almost absent in the literature (especially in the railway field) due to the computational cost and to the memory consumption. It is, however, very important as only differential modeling allows accurate analysis of the contact problem (in terms of contact forces, position and shape of the contact patch, stresses and strains), while multibody modeling is generally accepted as the current standard for studying railway dynamics.

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Section: The Numerical Solution Of the Discrete Problemmentioning

confidence: 99%

An innovative wheel–rail contact model for multibody applications

Magheri

Malvezzi

Meli

et al. 2011

Wear

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“…In such cases the use of other nonlinear solvers with guaranteed convergence should be considered at the beginning (see e.g. [3]). Also, we do not report data for the two-dimensional cases, since they show a similar pattern as the one-dimensional ones discussed here.…”

Section: Scalar Degenerate Equationmentioning

confidence: 99%

AMG preconditioning for nonlinear degenerate parabolic equations on nonuniform grids with application to monument degradation

Donatelli

Semplice

Serra‐Capizzano

2013

Applied Numerical Mathematics

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Motivated by the modelling of marble degradation by chemical pollutants, we consider the ap- proximation by implicit finite differences schemes of nonlinear degenerate parabolic equations in which sharp boundary layers naturally occur. The latter suggests to consider various types of nonuniform griddings, when defining suitable approximation schemes. The resulting large nonlinear systems are treated by Newton methods, while the locally Toeplitz linear systems aris- ing from the Jacobian have to be solved efficiently. To this end, we propose the use of AMG preconditioners and we study the related convergence issues, together with the associated spec- tral features. We present some numerical experiments supporting our theoretical results on the spectrum of the coefficient matrix of the linear systems, alongside others regarding the numerical simulations in the case of the specific model

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“…For nonlinear systems, some new iterative schemes have recently been presented that use in a systematic way the residual vectors as search directions [19,20]. These low-memory ideas become effective, and competitive with Newton-Krylov ( [3,9,10,18]) schemes for large-scale nonlinear systems, when the step lengths are chosen in a suitable way.…”

Section: Introductionmentioning

confidence: 99%