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

• Main Authors: Juan Tang, Yongsheng Rao
• Format: Article
• Language: English
• Published: MDPI AG 2020-11-01
• Series: Mathematics
• Subjects: differential algebraic equations; index reduction; block triangular forms
• Online Access: https://www.mdpi.com/2227-7390/8/11/2057

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 <inline-formula><math display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><mi>ℓ</mi><mo>)</mo></mrow></semantics></math></inline-formula> compared to the MPA, which is mainly consistent with the results of our analysis.