On Three-Grid Fourier Analysis for Multigrid

作者: Roman Wienands , Cornelis W. Oosterlee

DOI: 10.1137/S106482750037367X

关键词:

摘要: In this paper, we present three-grid Fourier analysis for multigrid methods. Due to the recursive structure of a iteration, can be deduced from well-known two-grid analysis. The coarse grid correction part algorithms more accurately evaluated with We apply several scalar equations and discretizations an emphasis on problems difficulty like upwind convection diffusion equation. main focus lies possible improvements by carefully chosen Galerkin operators and/or additional acceleration restarted GMRES, GMRES($m$). Numerical test calculations validate theoretical predictions.

参考文章(25)
Petr Vanek, Jan Mandel, Marian Brezina, Algebraic Multigrid on Unstructured Meshes University of Colorado at Denver. ,(1994)
Piet Hemker, Fourier analysis of gridfunctions, prolongations and restrictions Stichting Mathematisch Centrum. Numerieke Wiskunde. pp. 1- 34 ,(1980)
Pieter Wesseling (Dr. Ir.), An Introduction to Multigrid Methods ,(1992)
C.W. Oosterlee, F.J. Gaspar, T. Washio, R. Wienands, Multigrid Line Smoothers for Higher Order Upwind Discretizations of Convection-Dominated Problems Journal of Computational Physics. ,vol. 139, pp. 274- 307 ,(1998) , 10.1006/JCPH.1997.5854
C. W. Oosterlee, T. Washio, Krylov Subspace Acceleration of Nonlinear Multigrid with Application to Recirculating Flows SIAM Journal on Scientific Computing. ,vol. 21, pp. 1670- 1690 ,(1999) , 10.1137/S1064827598338093
Achi Brandt, Rigorous quantitative analysis of multigrid, I: constant coefficients two-level cycle with L 2 -norm SIAM Journal on Numerical Analysis. ,vol. 31, pp. 1695- 1730 ,(1994) , 10.1137/0731087
Irad Yavneh, Analysis of a Fourth-Order Compact Scheme for Convection-Diffusion Journal of Computational Physics. ,vol. 133, pp. 361- 364 ,(1997) , 10.1006/JCPH.1997.5659
B. Fischer, A. Ramage, D.J. Silvester, A.J. Wathen, On parameter choice and iterative convergence for stabilised discretisations of advection–diffusion problems Computer Methods in Applied Mechanics and Engineering. ,vol. 179, pp. 179- 195 ,(1999) , 10.1016/S0045-7825(99)00037-7