Efficient algorithm for computing large scale systems of differential algebraic equations

TL;DR

This paper introduces an efficient algorithm for solving large-scale sparse differential algebraic equations by leveraging maximum value transversal and block triangular forms, improving computational performance.

Contribution

It presents a novel algorithm combining shortest augmenting path and extended signature matrix methods for large-scale DAEs, enhancing efficiency and scalability.

Findings

Successfully applied to complex real-world problems

Achieved significant reduction in computational complexity

Demonstrated effectiveness on large-scale systems

Abstract

In many mathematical models of physical phenomenons and engineering fields, such as electrical circuits or mechanical multibody systems, which generate the differential algebraic equations (DAEs) systems naturally. In general, the feature of DAEs is a sparse large scale system of fully nonlinear and high index. To make use of its sparsity, this paper provides a simple and efficient algorithm for computing the large scale DAEs system. We exploit the shortest augmenting path algorithm for finding maximum value transversal (MVT) as well as block triangular forms (BTF). We also present the extended signature matrix method with the block fixed point iteration and its complexity results. Furthermore, a range of nontrivial problems are demonstrated by our algorithm.