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(ℓ) compared to the MPA, which is mainly consistent with the results of our analysis.
Highlights
The recent decades encountered a tremendous progress in the field of multi-disciplinary simulation tools for continuous time discrete variable systems
We focus on structural index reduction method to directly calculate the global canonical offsets of large-scale differential algebraic equations (DAEs) with any high order, which are critical for its efficient solution scheme by combing the Pantelides’ method with Pryce’s Σ-method
In order to determine the crucial canonical offsets for structural analysis in DAEs system using fixed-point iteration algorithm (FPIA) [10], we introduce some necessary definitions, firstly
Summary
The recent decades encountered a tremendous progress in the field of multi-disciplinary simulation tools for continuous time discrete variable systems. In [12,13], Pryce and Nediakov et al generalized the structural analysis method to the DAE systems with coarse or fine block-triangular form (BTF), and showed that the difference between the global offsets of signature matrix Σ and the local offsets of each diagonal sub-block in Σ with fine BTF is a constant They compute the fine BTF for system’s numerical scheme via valid global offset vectors or the local offsets of each separated coarse block. We focus on structural index reduction method to directly calculate the global canonical offsets of large-scale DAEs with any high order, which are critical for its efficient solution scheme by combing the Pantelides’ method with Pryce’s Σ-method.
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