Structural index reduction algorithms for differential algebraic equations via fixed-point iteration
For researchers working on numerical simulation of differential algebraic equations, this provides an incremental improvement in scalability for large-scale systems.
The paper analyzes the complexity of Pryce's fixed-point iteration for structural index reduction of DAEs and proposes a block version for large-scale systems with block upper triangular structure, including complexity analysis.
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.