Structural index reduction algorithms for differential algebraic equations via fixed-point iteration

TL;DR

This paper introduces a parameterized fixed-point iteration method for reducing the structural index of large-scale differential algebraic equations, improving efficiency and applicability to block-structured systems.

Contribution

It proposes a novel fixed-point iteration algorithm with parameters, along with complexity analysis, for structural index reduction of DAEs, especially for large-scale block-structured systems.

Findings

The proposed method is applicable to large-scale DAEs with block upper triangular structure.

Complexity analysis of the fixed-point iteration algorithm is provided.

The method enhances the efficiency of index reduction for structured DAEs.

Abstract

Motivated by Pryce's structural index reduction method for differential algebraic equations (DAEs), we show the complexity of the fixed-point iteration algorithm and propose a fixed-point iteration method with parameters. It leads to a block fixed-point iteration method which can be applied to large-scale DAEs with block upper triangular structure. Moreover, its complexity analysis is also given in this paper.