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A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations

by 1,2,* and 1,2
1
School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China
2
Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(11), 2057; https://doi.org/10.3390/math8112057
Received: 27 October 2020 / Revised: 14 November 2020 / Accepted: 15 November 2020 / Published: 18 November 2020
(This article belongs to the Section Mathematics and Computer Science)
A new generation of universal tools and languages for modeling and simulation multi-physical domain applications has emerged and became widely accepted; they generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAE systems with large dimensions, high index or block structures, we first propose a modified Pantelides’ algorithm (MPA) for any high order DAEs based on the Σ matrix, which is similar to Pryce’s Σ method. By introducing a vital parameter vector, a modified Pantelides’ algorithm with parameters has been presented. It leads to a block Pantelides’ algorithm (BPA) naturally which can immediately compute the crucial canonical offsets for whole (coupled) systems with block-triangular form. We illustrate these algorithms by some examples, and preliminary numerical experiments show that the time complexity of BPA can be reduced by at least O() compared to the MPA, which is mainly consistent with the results of our analysis. View Full-Text
Keywords: differential algebraic equations; index reduction; block triangular forms differential algebraic equations; index reduction; block triangular forms
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MDPI and ACS Style

Tang, J.; Rao, Y. A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations. Mathematics 2020, 8, 2057. https://doi.org/10.3390/math8112057

AMA Style

Tang J, Rao Y. A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations. Mathematics. 2020; 8(11):2057. https://doi.org/10.3390/math8112057

Chicago/Turabian Style

Tang, Juan, and Yongsheng Rao. 2020. "A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations" Mathematics 8, no. 11: 2057. https://doi.org/10.3390/math8112057

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