Efficient index reduction algorithm for large scale systems of differential algebraic equations

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• 作者：Xiaolin Qin ; ^a ; ^b ; ^{qinxl@casit.ac.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{qinxl2001@163.com" class="auth_mail" title="E-mail the corresponding author} ; Juan Tang^a ; ^{tangjuan0822@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Yong Feng^a ; Bernhard Bachmann^c ; Peter Fritzson^b
• 关键词：Differential algebraic equations ; Sparsity ; Shortest augmenting path ; Block triangular forms ; Structural analysis
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：20 March 2016
• 年：2016
• 卷：277
• 期：Complete
• 页码：10-22
• 全文大小：1147 K

文摘

In many mathematical models of physical phenomenons and engineering fields, such as electrical circuits or mechanical multibody systems, which generate the differential algebraic equations (DAEs) systems naturally. In general, the feature of DAEs is a sparse large scale system of fully nonlinear and high index. To make use of its sparsity, this paper provides a simple and efficient algorithm for index reduction of large scale DAEs system. We exploit the shortest augmenting path algorithm for finding maximum value transversal (MVT) as well as block triangular forms (BTFs). We also present the extended signature matrix method with the block fixed point iteration and its complexity results. Furthermore, a range of nontrivial problems are demonstrated by our algorithm.