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

Juan Tang and Yongsheng Rao
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Juan Tang: School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China
Yongsheng Rao: School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China

Mathematics, 2020, vol. 8, issue 11, 1-15

Abstract: 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.

Keywords: differential algebraic equations; index reduction; block triangular forms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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