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Analysis of Chebyshev Relaxation in Multigrid Methods for Nonlinear Parabolic Differential Equations
Author(s) -
van der Houwen P. J.,
Sommeijer B. P.
Publication year - 1983
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19830630307
Subject(s) - multigrid method , relaxation (psychology) , discretization , mathematics , nonlinear system , chebyshev filter , runge–kutta methods , mathematical analysis , partial differential equation , gauss–seidel method , grid , chebyshev iteration , iterative method , differential equation , mathematical optimization , physics , geometry , psychology , social psychology , quantum mechanics
The main purpose of this paper is the analysis of the behaviour of (nonlinear) Chebyshev relaxation in multigrid methods for solving the implicit relations obtained when an implicit linear multistep method is applied to the space‐discretized parabolic differential equation. The relaxation parameters are tuned to those frequencies in the iteration error which one wants to damp on the successive grids. The coarsest grid problem, being related to the semi‐discrete parabolic equation on the coarsest grid, is solved by a stabilized Runge‐Kutta method. Numerical experiments and comparison with Gauss‐Seidel relaxation are reported.