Stopping Criterion in Iterative Solution Methods for Reynolds Equations

Wang, Nenzi; Chang, Shun‐Fu; Huang, Hsin‐Hua

doi:10.1080/10402001003753358

Cited by 17 publications

(7 citation statements)

References 26 publications

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“…According to Wang et al (2010), a reasonable stopping criterion of iterative methods for solving Reynolds equation is to terminate the iterative procedure when the L 2 norm of residual, true(Δx2 ∑i=0n∑j=0ntrue(Δtruep¯i,jtrue)2true)12, in iterative computation is smaller than the truncation error ( C Δ x ¯ r ) of the difference method used. Thus, the iterative procedure in this study is terminated when the stopping criterion [equation (4)] is met.…”

Section: Stopping Criterion Of Iterative Methodsmentioning

confidence: 99%

“…However, a system of linear equations obtained from a discretized partial differential equation, such as various type of compressible-fluid Reynolds equations, in tribological studies is usually solved by iterative methods (Wang et al , 2011). The use of iterative methods versus direct matrix operations (methods based on Gaussian elimination algorithm) can have the following advantages: much less memory storage requirement; easy to implement in parallel computing with very good speed-up performance (Wang and Chen, 2004; Wang and Tsai, 2006; Wang et al ., 2012); can handle a bearing model with recesses directly, as in modeling hydrostatic bearings; can be faster in execution if the convergence criterion is properly set (Wang et al ., 2010); and in some simulations where the Reynolds boundary condition is needed, can be met without additional treatment. …”

Section: Introductionmentioning

confidence: 99%

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A cross-platform parallel programming model for fluid-film lubrication optimization

Wang

Chen

2018

ILT

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Purpose A cross-platform paradigm (computing model), which combines the graphical user interface of MATLAB and parallel Fortran programming, for fluid-film lubrication analysis is proposed. The purpose of this paper is to take the advantages of effective multithreaded computing of OpenMP and MATLAB’s user-friendly interface and real-time display capability. Design/methodology/approach A validation of computing performance of MATLAB and Fortran coding for solving two simple sliders by iterative solution methods is conducted. The online display of the particles’ search process is incorporated in the MATLAB coding, and the execution of the air foil bearing optimum design is conducted by using OpenMP multithreaded computing in the background. The optimization analysis is conducted by particle swarm optimization method for an air foil bearing design. Findings It is found that the MATLAB programs require prolonged execution times than those by using Fortran computing in iterative methods. The execution time of the air foil bearing optimum design is significantly minimized by using the OpenMP computing. As a result, the cross-platform paradigm can provide a useful graphical user interface. And very little code rewritting of the original numerical models is required, which is usually optimized for either serial or parallel computing. Research limitations/implications Iterative methods are commonly applied in fluid-film lubrication analyses. In this study, iterative methods are used as the solution methods, which may not be an effective way to compute in the MATLAB’s setting. Originality/value In this study, a cross-platform paradigm consisting of a standalone MATLAB and Fortran codes is proposed. The approach combines the best of the two paradigms and each coding can be modified or maintained independently for different applications.

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Section: Stopping Criterion Of Iterative Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A cross-platform parallel programming model for fluid-film lubrication optimization

Wang

Chen

2018

ILT

View full text Add to dashboard Cite

show abstract

“…The stopping criterion used in the iterative methods is based on a truncation error analysis, which can terminate the iteration with predefined solution accuracy. 17 In this study, the gridwork used is 378 3 126. And the matching stopping criterion is shown in equation ( 4), in which d is the modification of solution in the consecutive iterations.…”

Section: Lubrication Modelsmentioning

confidence: 99%

“…16 A stopping criterion for iterative solution methods, which is based on a truncation error analysis of Taylor series expansion, in lubrication analysis was presented. 17 The iterative methods used to validate the stopping criterion were SOR, PCG, and successive-under-relaxation for solving compressible-and incompressible-fluid Reynolds equations. The study shows that a proper stopping criterion for iterative methods can prevent excessive computations with satisfactory results.…”

Section: Introductionmentioning

confidence: 99%

Fluid-film lubrication computing with many-core processors and graphics processing units

Wang

Chen

2018

Advances in Mechanical Engineering

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The advancement of modern processors with many-core and large-cache may have little computational advantages if only serial computing is employed. In this study, several parallel computing approaches, using devices with multiple or many processor cores, and graphics processing units are applied and compared to illustrate the potential applications in fluid-film lubrication study. Two Reynolds equations and an air bearing optimum design are solved using three parallel computing paradigms, OpenMP, Compute Unified Device Architecture, and OpenACC, on standalone shared-memory computers. The newly developed processors with many-integrated-core are also using OpenMP to release the computing potential. The results show that the OpenACC computing can have a better performance than the OpenMP computing for the discretized Reynolds equation with a large gridwork. This is mainly due to larger sizes of available cache in the tested graphics processing units. The bearing design can benefit most when the system with many-integrated-core processor is being used. This is due to the many-integrated-core system can perform computation in the optimization-algorithm-level and using the many processor cores effectively. A proper combination of parallel computing devices and programming models can complement efficient numerical methods or optimization algorithms to accelerate many tribological simulations or engineering designs.

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“…Moreover, the successive over-relaxation method is applied to solve the film pressure. In this process, the relaxation factor used for the pressure iteration can affect the numerical stability, which was researched by Wang et al (2010). According to their results, the optimal relaxation factor opt is given below:…”

Section: Numerical Schemementioning

confidence: 99%

Numerical and experimental investigation on influence of compound dimple on tribological performances for rough parallel surfaces

Meng

Cheng

Zou

2017

ILT

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Purpose This study aims to explore the superiority of the compound dimple (e.g. the rectangular-rectangular dimple) and compare its tribological performance for rough parallel surfaces with those of the traditional one-layer dimple (simple dimple). Design/methodology/approach A mixed-lubrication model for a rough textured surface is established and solved using the finite difference method for film pressure and contact pressure. To accelerate the evaluation of surface deformation, the efficient Continuous convolution fast Fourier transform algorithm is applied. The effects of the compound dimple on the tribological performance for the rough parallel surfaces is numerically investigated. And these effects are compared with those of the simple dimple. Furthermore, a reciprocating friction test is conducted to verify the superiority of the compound dimple. Findings The compound dimple exhibits better tribological performances in comparison with the traditional simple dimple, that is, a larger load-carrying capacity and a smaller friction coefficient. To achieve the best tribological performances for the rough parallel surfaces, the depth ratio of the lower pore to the total pore of the compound dimple and the dimple interval should be reasonably chosen. For the surface with compound dimples, there exists an optimal surface roughness to simultaneously maximize the load-carrying capacity and minimize the friction coefficient. The smaller friction coefficient of the surface with compound dimples is verified by the reciprocating friction test. Originality/value The compound dimple is proposed and the superiority of this novel surface texture is confirmed. This study is expected to provide a new texturing method to improve the tribological performances of the traditional simple dimple.

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Stopping Criterion in Iterative Solution Methods for Reynolds Equations

Cited by 17 publications

References 26 publications

A cross-platform parallel programming model for fluid-film lubrication optimization

A cross-platform parallel programming model for fluid-film lubrication optimization

Fluid-film lubrication computing with many-core processors and graphics processing units

Numerical and experimental investigation on influence of compound dimple on tribological performances for rough parallel surfaces

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