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An Optimal p ‐Refinement Strategy for Dynamic Iteration of Ordinary and Differential Algebraic Equations
Author(s) -
Schöps Sebastian,
Bartel Andreas,
Günther Michael
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310262
Subject(s) - convergence (economics) , recursion (computer science) , mathematics , approximation error , coupling (piping) , algebraic number , rate of convergence , ordinary differential equation , reduction (mathematics) , computer science , mathematical optimization , differential equation , algorithm , mathematical analysis , mechanical engineering , computer network , channel (broadcasting) , geometry , engineering , economic growth , economics
Multiphysical simulation tasks are often numerically solved by dynamic iteration schemes. Usually, this demands the efficient and stable coupling of existing simulation software for the contributing physical subdomains or subsystem. Since the coupling is weakened by such a simulation strategy, iteration is needed to enhance the quality of the numerical approximation. By the means of error recursions, one obtains estimates for the approximation order and the reduction of error per iteration (convergence rate). It is know that the first iterations can be coarsely sampled (in time), but the last iterations need to be refined ( h ‐refinement) to obtain the accuracy gain of latter iterations (‘sweeps’). In this work we discuss an optimal choice of the approximation order p used in the time integration with respect to the iteration ‘sweep’ count. It is deduced from the analytical error recursion and yields a p ‐refinement strategy. Numerical experiments show that our estimates are sharp and give a precise prediction of the correct convergence. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)