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Stability Analysis of Decoupled Solution Strategies for Coupled Multi‐field Problems – A General Framework
Author(s) -
Zinatbakhsh Seyedmohammad,
Markert Bernd,
Ehlers Wolfgang
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210168
Subject(s) - stability (learning theory) , solver , partial differential equation , computer science , field (mathematics) , scheme (mathematics) , mathematical optimization , integrator , mathematics , mathematical analysis , machine learning , pure mathematics , computer network , bandwidth (computing)
A coupled partial differential equation (PDE) system, stemming from the mathematical modelling of a coupled phenomenon, is usually solved numerically following a monolithic or a decoupled solution method. In spite of the potential unconditional stability offered by monolithic solvers, their usage for solving complex problems sometimes proves cumbersome. This has motivated the development of various partitioned and staggered solution strategies, generally known as decoupled solution schemes. To this end, the problem is broken down into several isolated yet communicating sub‐problems that are independently advanced in time, possibly by different integrators. Nevertheless, using a decoupled solver introduces additional errors to the system and, therefore, may jeopardise the stability of the solution [1]. Consequently, to scrutinise the stability of the solution scheme becomes a pertinent step in proposing decoupled solution strategies. Here, we endeavour to present a practical stability analysis algorithm, which can readily be used to reveal the stability condition of numerical solvers. To illustrate its capabilities, the algorithm is then utilised for the stability analysis of solution schemes applied to multi variate coupled PDE systems resulting from the mathematical modelling of surface‐ and volume‐coupled multi‐field problems. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)