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Preconditioned defect corrected averaging for parabolic PDEs
Author(s) -
Klöppel Michael,
Naumann Andreas,
Wensch Jörg
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410415
Subject(s) - integrator , operator (biology) , scale (ratio) , stroboscope , oscillation (cell signaling) , mathematics , linear system , parabolic partial differential equation , mathematical analysis , partial differential equation , computer science , physics , computer network , biochemistry , chemistry , genetics , bandwidth (computing) , repressor , quantum mechanics , biology , transcription factor , optics , gene
Abstract Modelling physical systems with fast moving components leads to PDEs with highly oscillatory sources. Often, the time scale of the oscillation is much below the scale of the interesting variables. Time integrators must follow the scale of the fast motion, leading to long simulation times. For mechanical systems, methods like heterogeneous multiscaling and stroboscopic averaging are quite satisfactory. In case of semidiscretized PDEs, their advantage is limited. Here, we derive a smooth source term which generates a solution that coincides with the solution of the oscillatory system in stroboscopic points. The derivation involves the solution of a linear system with the solution operator of the PDE being the linear operator. Several preconditioners are developed and compared for those systems. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)