Block preconditioned conjugate gradient method for extraction of natural vibration frequencies in structural analysis

机译：块预处理共轭梯度法提取结构分析中的固有振动频率

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摘要

The block preconditioned conjugate gradient method for extraction of eigenfrequencies and eigenmodes is presented for finite element software in structural analysis. The proposed approach is focused on multi-core desktops and laptops and allows us to effectively analyze large design models, when classical methods based on the factoring of stiffness matrix, significantly reduce performance by intensive use of disk memory. The main attention is paid to proper construction of preconditioning, application of shift technique and creation of the block algorithm allowing the improvement of computing stability and multithreaded parallelization.

机译：针对结构分析中的有限元软件，提出了用于提取特征频率和特征模态的块预处理共轭梯度法。所提出的方法着重于多核台式机和笔记本电脑，当基于刚度矩阵分解的经典方法通过大量使用磁盘内存显着降低性能时，我们可以有效地分析大型设计模型。主要注意力集中在适当的预处理结构，移位技术的应用以及块算法的创建上，从而可以提高计算稳定性和多线程并行化。

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《Federated Conference on Computer Science and Information Systems》|2015年|655-662|共8页
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Fialko Sergiy; Zeglen Filip; Kosciuszko Tadeusz;
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eigenvalues and eigenfunctions; elastic constants; finite element analysis; laptop computers; matrix algebra; multi-threading; structural engineering computing; block preconditioned conjugate gradient method; disk memory; eigenfrequency; eigenmode; finite element software; laptop; multicore desktop; multithreaded parallelization; natural vibration frequency; stiffness matrix; structural analysis; Analytical models; Convergence; Electronic mail; Finite element analysis; Gradient methods; Software; Vibrations;

机译：特征值和特征函数;弹性常数;有限元分析;笔记本计算机;矩阵代数;多线程;结构工程计算;块预处理共轭梯度法;磁盘存储器;本征频率;本征模;有限元软件;笔记本;多核台式机;多线程并行化;自然振动频率;刚度矩阵;结构分析;分析模型;收敛;电子邮件;有限元分析;梯度法;软件;振动;

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专利

1. Block subspace projection preconditioned conjugate gradient method in modal structural analysis [J] . Fialko Sergiy, Karpilovskyi Viktor Computers & mathematics with applications . 2020,第12期

机译：块子空间投影预由缀合物梯度法在模态结构分析中
2. Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method [J] . Knyazev AV. SIAM Journal on Scientific Computing . 2001,第2期

机译：走向最优预处理特征求解器：局部最优块预处理共轭梯度法
3. THE RESTRICTIVELY PRECONDITIONED CONJUGATE GRADIENT METHODS ON NORMAL RESIDUAL FOR BLOCK TWO-BY-TWO LINEAR SYSTEMS [J] . Junfeng Yin, Zhongzhi Bai Journal of Computational Mathematics . 2008,第2期

机译：两两两线性系统正常残值的约束预处理共轭梯度法
4. Block preconditioned conjugate gradient method for extraction of natural vibration frequencies in structural analysis [C] . Fialko Sergiy, Zeglen Filip, Kosciuszko Tadeusz Federated Conference on Computer Science and Information Systems . 2015

机译：结构分析中自然振动频率提取的预由缀合物梯度方法
5. The SSOR preconditioned conjugate gradient method on parallel computers [D] . Vaughan, Courtenay Thomas 1989

机译：并行计算机上的SSOR预条件共轭梯度法
6. Computational strategies for the preconditioned conjugate gradient method applied to ssSNPBLUP with an application to a multivariate maternal model [O] . Jeremie Vandenplas, Herwin Eding, Maarten Bosmans, 2020

机译：应用于ssSNPBLUP的预处理共轭梯度法的计算策略及其在多元母体模型中的应用
7. Toward The Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method [O] . Andrew V. Knyazev 2000

机译：最优预条件特征解算器：局部最优块预处理共轭梯度法

Block preconditioned conjugate gradient method for extraction of natural vibration frequencies in structural analysis

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