An Approximate Newton-Like Coupling of Subsystems
Jürgen Menck · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2002
Complex technical systems are often assembled from well-studied subsystems. Here, we elaborate on the obvious idea of coupling existing subsystem solvers to solve a coupled system. More specifically, we present a matrix-free iterative method that is inspired by a Newton type coupling of the subsystems but aims at efficiently controlled linear convergence. We prove its convergence and propose a control mechanism to optimize its efficiency. We illustrate the method's properties with the help of a numerical example. Note: (As yet) we only deal with the stationary case; mathematically speaking, we are looking for roots of systems of nonlinear equations.