摘要
针对减基法快速分析固体结构时容易出现的奇异问题,提出了一种改进的减基法.该方法通过将参数域样本点对应的响应基进行奇异性判别和处理,删除响应基中线性相关程度高的向量,并把新得到的基进行约化的QR分解,使原系统通过Galerkin映射向矩阵Q的列向量基所张成的空间进行投影,从而提高了固体结构快速计算的精度及可靠性.数值算例验证了其有效性.
A method was proposed to improve the singularity condition of the reduced basis method in the rapid analysis of solid structures.This method examines and deals with the response basis which corresponds to the sample points in the parameter domain,and eliminates the highly linearly dependent vectors.Subsequently,the newly obtained basis is conducted by reduced QR factorization,and Galerkin projection is then performed onto the space spanned by the column vectors of the matrix Q.Therefore,the proposed method can enhance the computational accuracy and reliability.The numerical example has demonstrated this result.
出处
《湖南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2011年第2期30-34,共5页
Journal of Hunan University:Natural Sciences
基金
国家973计划资助项目(2010CB832705)
国家杰出青年基金资助项目(10725208)
国家自然科学基金资助项目(10802028)
关键词
减基法
奇异性
约化的QR分解
可靠性
reduced basis method
singularity condition
reduced QR factorization
reliability
