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Defect corrected averaging for parabolic PDEs
Author(s) -
Naumann Andreas,
Wensch Jörg
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310247
Subject(s) - parabolic partial differential equation , krylov subspace , partial differential equation , oscillation (cell signaling) , subspace topology , operator (biology) , mathematical analysis , mathematics , method of averaging , physics , linear system , chemistry , nonlinear system , biochemistry , repressor , quantum mechanics , transcription factor , gene
We consider parabolic partial differential equations with highly oscillatory source terms. The timescale of the problem is assumed to be much larger than the timescale of the oscillation. Resolution of the smallest timescale constitutes a strong restriction on the stepsize of time integration method. Averaging techniques like stroboscopic averaging have been developed to overcome this restriction. In case of parabolic equations these techniques are of limited advantage. We have developed defect corrected averaging techniques that allow timesteps taylored to the timescale of diffusion. They are based on Krylov subspace iterations for the abstract solution operator of the system. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)