• 论文 •

### 基于线性代数的大规模快速量纲分析算法及其在爆炸与冲击工程研究中的应用

1. 1. 西北核技术研究院, 西安 710024;
2. 北京大学数学科学学院, 北京 100871;
3. 北京理工大学 爆炸科学与技术国家重点实验室, 北京 100081
• 收稿日期:2018-05-23 出版日期:2020-05-15 发布日期:2020-05-15

Zhong Wei, Tian Zhou, Shou Liefeng. A LARGE-SCALE AND FAST DIMENSIONAL ANALYSIS METHOD BASED ON LINEAR ALGEBRA AND ITS APPLICATIONS IN THE FIELD OF EXPLOSION AND IMPACT ENGINEERING[J]. Mathematica Numerica Sinica, 2020, 42(2): 170-195.

### A LARGE-SCALE AND FAST DIMENSIONAL ANALYSIS METHOD BASED ON LINEAR ALGEBRA AND ITS APPLICATIONS IN THE FIELD OF EXPLOSION AND IMPACT ENGINEERING

Zhong Wei1,2, Tian Zhou1, Shou Liefeng1,3

1. 1. Northwest Institute of Nuclear Technology, Xi'an 710024, China;
2. School of Mathematical Sciences, Peking University, Beijing 100871, China;
3. State Key Lab of Explosion and Safety Science, Beijing Institute of Technology, Beijing 100081, China
• Received:2018-05-23 Online:2020-05-15 Published:2020-05-15

Dimensional analysis is a very important theoretical analysis tool in scientific studies and engineering applications. It has a history of more than 100 years since the Π theorem was first put forward by E. Buckingham, and has gradually formed mature basic theories and methods. Meanwhile, dimensional analysis has made remarkable achievements in various fields, and it will still be widely used in these fields. However, with in-depth study, the problems the researchers need to face have become much more complicated and detailed, and more attentions are paid to the so-called minor factors abandoned in the traditional dimensional analysis. Therefore, more and more physical quantities are involved, which make the traditional dimensional analysis very cumbersome, even extremely difficult to solve. In this paper, from the point of view of linear algebra, the dimensional analysis has been converted into linear space problem, and then, the key process of the dimensional analysis has been finished through matrix operation. The basic theorems of linear algebra problem corresponding to dimensional analysis have been proposed, and on the basis of these theorems, a programmed dimensional analysis algorithm has been built. The algorithm transforms the original complex dimesional analysis problem into a matrix operation problem, which can be solved quickly and conveniently by any computer algebra system. Finally, with years of personal experience in the field of explosion and impact engineering research, the author has provided several examples to show the detailed operation method and illustrate the advantage of the present method.

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