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Weak coupling in function space: a unifying coupling approach for multiscale simulations
Author(s) -
Fackeldey Konstantin,
Krause Rolf
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700834
Subject(s) - discretization , coupling (piping) , transfer operator , phase space , molecular dynamics , statistical physics , space (punctuation) , degrees of freedom (physics and chemistry) , function space , partition function (quantum field theory) , operator (biology) , transfer function , scale (ratio) , sobolev space , function (biology) , physics , computer science , mathematics , mathematical analysis , chemistry , thermodynamics , quantum mechanics , mechanical engineering , engineering , biochemistry , electrical engineering , repressor , evolutionary biology , biology , transcription factor , gene , operating system
In multiscale simulations, often on the micro‐ and the macro scale different discretization are used in order to capture the different behavior of the materials under consideration on the respective scales. Using, e.g., molecular dynamics (MD) on the micro scale and finite elements (FE) in the macro scale, values in the phase space ℝ d (MD) have to be correlated with the values from the FE‐simulation in the Sobolev space H 1 . Here, we present a new coupling approach which gives rise to a stabilizing new scale transfer operator. Our construction allows moreover for a unifying theoretical description of already existing coupling methods. The key idea is to construct the transfer operator by assigning a partition of unity to the molecular degrees of freedom, thus giving rise to a fully function space based treatment. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)