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Acceleration methods for the convergence of vector sequences applied to multi‐physics problems
Author(s) -
Erbts Patrick,
Düster Alexander
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410248
Subject(s) - convergence (economics) , sequence (biology) , acceleration , coupling (piping) , limit (mathematics) , computer science , matching (statistics) , stability (learning theory) , range (aeronautics) , polygon mesh , mathematical optimization , algorithm , process (computing) , mathematics , theoretical computer science , physics , engineering , machine learning , mechanical engineering , mathematical analysis , statistics , genetics , computer graphics (images) , classical mechanics , aerospace engineering , economics , biology , economic growth , operating system
Partitioned solution approaches are well‐known strategies to solve coupled problems and have demonstrated their applicability in a wide range of multi‐physical simulations. Applying a partitioned approach opens up numerous possibilities, such as connecting different solvers or combining non‐matching meshes and time‐step sizes. On the other hand such a procedure has the drawback of only conditional stability, leading to poor convergence rates or ‐ as a worst case scenario ‐ to divergent behavior. In this contribution, we will give an interpretation of the iterative coupling process as a sequence of vectors converging to an unknown limit, which indeed represents a solution to the coupled problem. In order to improve computational efficiency, there are several practicable methods to accelerate the convergence of vector sequences. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)