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On the General Solution of Coupled Problems: Comparison of Monolithic and Partitioning Approaches
Author(s) -
Zinatbakhsh Seyedmohammad,
Markert Bernd,
Ehlers Wolfgang
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010190
Subject(s) - boundary value problem , decoupling (probability) , partial differential equation , mathematics , computer science , stability (learning theory) , operator (biology) , mathematical optimization , mathematical analysis , biochemistry , chemistry , repressor , control engineering , machine learning , transcription factor , engineering , gene
Coupled systems arise whenever there is a dynamic interaction between two or more functionally distinct components. The mathematical model for such a phenomenon consists of a system of coupled partial differential equations (PDE) in space and time, that has to be solved, either analytically or numerically, in order to describe or predict the response of the system under specific conditions. In spite of the natural accuracy of the analytical methods, they are less favourable due to their disability to treat more complex problems. Instead, different numerical schemes have been developed during the last decades, which are specialised to solve various coupled problems. These methods can be divided into two main categories, namely, monolithic and partitioned approaches. The main goal of this work is to study the general ideas behind monolithic and partitioned solution schemes for the pure differentially coupled systems. In the next step, the coupled problem of linear thermoelasticity is considered as benchmark example and the isothermal and isentropic operator‐splitting schemes as two typical decoupling methods for this problem are presented. A canonical initial boundary‐value problem has also been solved monolithically as well as by using the a.m. operator‐splitting schemes and using the acquired results, the efficiency and stability of the methods are compared. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)