Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 28 October 2020 / Approved: 29 October 2020 / Online: 29 October 2020 (14:34:38 CET)

A peer-reviewed article of this Preprint also exists.

Tang, J.; Rao, Y. A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations. Mathematics 2020, 8, 2057. Tang, J.; Rao, Y. A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations. Mathematics 2020, 8, 2057.

Journal reference: Mathematics 2020, 8, 2057
DOI: 10.3390/math8112057

Abstract

A new generation of universal tools and languages for modeling and simulation multi-physical domain applications emerged and became widely accepted, which generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAEs systems with large dimension, high index or block structures, we first propose a modified Pantelides’ algorithm (MPA) for any high order DAEs based on its Σ matrix, which is similar to Pryce’s Σ method. By introducing a vital parameter vector, a modified Pantelides’ algorithm with parameter 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 numerical experiments show that the time complexity of BPA can be reduced by at least O(ℓ) compared to the MPA, which is mainly consistent with the results of our analysis.

Subject Areas

differential algebraic equations; index reduction; block triangular forms

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