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An Approximate Newton‐Like Coupling of Subsystems
Author(s) -
Menck J.
Publication year - 2002
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200202)82:2<101::aid-zamm101>3.0.co;2-o
Subject(s) - convergence (economics) , coupling (piping) , nonlinear system , computer science , newton's method , mathematics , type (biology) , local convergence , iterative method , matrix (chemical analysis) , complex system , mathematical optimization , algorithm , physics , engineering , artificial intelligence , mechanical engineering , ecology , materials science , quantum mechanics , economics , composite material , biology , economic growth
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.