| 一种新的减基法中的采样方法及误差估计 |
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| 引用本文： | 张正,韩旭,姜潮.一种新的减基法中的采样方法及误差估计[J].计算力学学报,2011,28(5):798-802,812. |
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| 作者姓名： | 张正 韩旭 姜潮 |
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| 作者单位： | 湖南大学 汽车车身先进设计与制造国家重点实验室,长沙 410082;湖南大学 汽车车身先进设计与制造国家重点实验室,长沙 410082;湖南大学 汽车车身先进设计与制造国家重点实验室,长沙 410082 |
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| 基金项目： | 国家杰出青年基金(10725208);高等学校博士点学科专项科研基金(20070532021)资助项目. |
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| 摘 要： | 针对减基法中求解精度受减基空间完备性影响的问题，提出了一种基于向量空间逼近原理的采样方法及相应的误差估计。该方法使每一步采样得到的特征向量与之前已得到的特征向量所张成的向量空间角度最大，从而保证了每步采样所对应的特征向量都具有最弱相关性，进而使最终得到的特征向量基空间更具完备性。并且由该方法产生了一种先验特征值误差界，...
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| 关 键 词： | 减基法 动力学 采样法 特征值误差 瞬态响应 |
| 收稿时间： | 5/8/2009 12:00:00 AM |
| 修稿时间： | 2010/10/28 0:00:00 |
A novel sampling method with error estiomation for the reduced basis method |
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| ZHANG Zheng,HAN Xu and JIANG Chao.A novel sampling method with error estiomation for the reduced basis method[J].Chinese Journal of Computational Mechanics,2011,28(5):798-802,812. |
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| Authors: | ZHANG Zheng HAN Xu and JIANG Chao |
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| Institution: | State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China;State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China;State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China |
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| Abstract: | The vector-space approximation sampling method is proposed here for the reduced basis method in which the precision of solution is influenced by completeness of basis space. The method can enable the corresponding eigenvector obtained in every step to have the biggest angle with the space constructed by early sampling eigenvectors, and then it makes the constructed eigenvector basis space have the weakest correlation and thus be more complete. Furthermore, this method can bring on a prior eigenvalue error bound which can ensure the eigenvalue errors produced by the reduced basis methods to be limited in the previously set scopes. The numerical example demonstrates the validity of the proposed sampling method. |
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| Keywords: | reduced basis method dynamics sampling method eigenvalue error transient response |
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