Extending Broyden's method to interaction problems

Abstract

The solution of problems involving the interaction of different systems is a domain of ongoing research, although often a good solver already exists for each system separately. In this paper we draw our ideas from one of the best known all-round quasi-Newton methods: Broyden's rank-one update, which we extend to algorithms using 2 approximate Jacobians. A comparison is made with the iterative substructuring method and Aitken's acceleration method. It is shown that a Broyden method using only a single approximate Jacobian performs best.