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Multigrid preconditioning for time‐periodic Navier–Stokes problems
Author(s) -
Hupp Daniel,
Obrist Dominik,
Arbenz Peter
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510287
Subject(s) - preconditioner , multigrid method , generalized minimal residual method , nonlinear system , mathematics , fourier transform , block (permutation group theory) , discrete fourier transform (general) , linear system , fourier series , focus (optics) , fast fourier transform , fourier analysis , mathematical analysis , algorithm , partial differential equation , fractional fourier transform , physics , geometry , optics , quantum mechanics
We propose to solve time‐periodic Navier–Stokes problems by a discrete Fourier transform in time. Truncating the Fourier series yields a nonlinear system of equations for the unknown Fourier coefficients. Its solution by Picard iteration requires to solve a sequence of linear systems of equations. The focus of this work is on an efficient method to solve these linear systems. We employ GMRES, complemented by an optimal block triangular preconditioner. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)