On a New SSOR-Like Method with Four Parameters for the Augmented Systems

Wang, Hui-Di; Huang, Zhengda

doi:10.4208/eajam.190716.081116a

Cited by 4 publications

(3 citation statements)

References 44 publications

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“…Many different SSOR-like methods are available for augmented systems, as well. Wang and Huang [24] introduced a four-parameter method, Louka and Missirlis [25] introduced a five-parameter extrapolated form of SSOR, and Najafi and Edalatpanah [26] introduced an improved version of the modified SSOR method for large sparse augmented systems, proposed earlier by Darvishi and Hessari [27]. Another improved SSOR method intended for the solution of augmented systems was proposed by Salkuyeh et al [28].…”

Section: Introductionmentioning

confidence: 99%

Improving Performance of Simplified Computational Fluid Dynamics Models via Symmetric Successive Overrelaxation

Turek

2019

Energies

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The ability to model fluid flow and heat transfer in process equipment (e.g., shell-and-tube heat exchangers) is often critical. What is more, many different geometric variants may need to be evaluated during the design process. Although this can be done using detailed computational fluid dynamics (CFD) models, the time needed to evaluate a single variant can easily reach tens of hours on powerful computing hardware. Simplified CFD models providing solutions in much shorter time frames may, therefore, be employed instead. Still, even these models can prove to be too slow or not robust enough when used in optimization algorithms. Effort is thus devoted to further improving their performance by applying the symmetric successive overrelaxation (SSOR) preconditioning technique in which, in contrast to, e.g., incomplete lower–upper factorization (ILU), the respective preconditioning matrix can always be constructed. Because the efficacy of SSOR is influenced by the selection of forward and backward relaxation factors, whose direct calculation is prohibitively expensive, their combinations are experimentally investigated using several representative meshes. Performance is then compared in terms of the single-core computational time needed to reach a converged steady-state solution, and recommendations are made regarding relaxation factor combinations generally suitable for the discussed purpose. It is shown that SSOR can be used as a suitable fallback preconditioner for the fast-performing, but numerically sensitive, incomplete lower–upper factorization.

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Section: Introductionmentioning

confidence: 99%

Improving Performance of Simplified Computational Fluid Dynamics Models via Symmetric Successive Overrelaxation

Turek

2019

Energies

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“…For example, Bai et al presented the GSOR 29 for augmented linear systems and SSOR-like precondition for non-Hermitian positive definite matrices 30 , Zhang and Liang proposed the GSSOR and MUSOR for saddlepoint problem 20,28 . Recently, Wang et al studied a new SSOR-like method with four parameters for the augmented systems, analysed the convergence of the method and obtained the optimal convergence factor under some suitable conditions 25 .…”

Section: Introductionmentioning

confidence: 99%

“…for solving the linear system (1), where x = (u T , v T ) ∈ 2n , and ω is a positive scalar. Inspired by these jobs 19,20,25,28 , we establish the modified SSOR (MSSOR) iterative…”

Section: Introductionmentioning

confidence: 99%

A modified SSOR iterative method for a class of block two-by-two linear systems

Xie¹,

Ma²

2019

ScienceAsia

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An interesting phenomenon when it comes to solving a class of complex linear systems is that the modified symmetric successive overrelaxation (MSSOR) method with two parameters seems to enjoy the fine convergence performance over symmetric successive overrelaxation (SSOR) which is recently proposed by Liang 19 and Bai 30. Owing to the flexible selection of the parameters, the MSSOR method possesses the valuable role to solve some large scale linear systems including the complex situation. Meanwhile, we also establish an accelerated MSSOR (AMSSOR) which can offer a meaningful improvement on MSSOR method. This has been illustrated experimentally and shown theoretically in this study. Our results may provide an analytical justification for popularity of SSOR and its accelerated version as efficient solvers for some linear systems.

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Some generalizations of the new SOR-like method for solving symmetric saddle-point problems

Wen

Guan

2018

J Inequal Appl

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Saddle-point problems arise in many areas of scientific computing and engineering applications. Research on the efficient numerical methods of these problems has become a hot topic in recent years. In this paper, we propose some generalizations of the new SOR-like method based on the original method. Convergence of these methods is discussed under suitable restrictions on iteration parameters. Numerical experiments are given to show that these methods are effective and efficient.

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On a New SSOR-Like Method with Four Parameters for the Augmented Systems

Cited by 4 publications

References 44 publications

Improving Performance of Simplified Computational Fluid Dynamics Models via Symmetric Successive Overrelaxation

Improving Performance of Simplified Computational Fluid Dynamics Models via Symmetric Successive Overrelaxation

A modified SSOR iterative method for a class of block two-by-two linear systems

Some generalizations of the new SOR-like method for solving symmetric saddle-point problems

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