An adaptive model order reduction with Quasi‐Newton method for nonlinear dynamical problems
An adaptive model order reduction with Quasi‐Newton method for nonlinear dynamical problems
复制标题
非线性动力学问题的拟牛顿法自适应模型降阶
DOI：
10.1002/nme.5145
复制
发表时间：
2016
影响因子：
2.9
通讯作者：
P. Wriggers
中科院分区：
文献类型：
--
作者：
P. Nigro;M. Anndif;Y. Teixeira;P. Pimenta;P. Wriggers
模型降阶（莫尔）方法对于减少处理时间是非常有用的，即使在当今，当并行处理在任何个人计算机中都是可能的。这项工作描述了一种方法，结合适当的正交分解（POD）和里兹向量，以实现一个有效的伽辽金投影，在非线性求解（在线分析）的变化。该算法得到了一种新的自适应策略的支持，分析了非线性动力学问题的误差和收敛速度。该模型降阶得到了割线公式的帮助，该公式由Broyden-弗莱彻-Goldfarb-Shanno（BFGS）公式更新，以加速缩减空间的收敛，以及在需要校正缩减空间时的切向公式。此外，这项研究表明，这种自适应策略允许在低成本和小误差的简化模型的校正。版权所有© 2015约翰威利父子有限公司.
Model Order Reduction (MOR) methods are extremely useful to reduce processing time, even nowadays, when parallel processing is possible in any personal computer. This work describes a method that combines Proper Orthogonal Decomposition (POD) and Ritz vectors to achieve an efficient Galerkin projection, which changes during nonlinear solving (online analysis). It is supported by a new adaptive strategy, which analyzes the error and the convergence rate for nonlinear dynamical problems. This model order reduction is assisted by a secant formulation which is updated by the Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) formula to accelerate convergence in the reduced space, and a tangent formulation when correction of the reduced space is needed. Furthermore, this research shows that this adaptive strategy permits correction of the reduced model at low cost and small error. Copyright © 2015 John Wiley & Sons, Ltd.
DOI：
10.1016/j.cma.2010.10.009
发表时间：
2011-01-15
影响因子：
7.2
作者：
Kerfriden P;Gosselet P;Adhikari S;Bordas S
通讯作者：
Bordas S