Practical Fourier analysis for multigrid methods
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منابع مشابه
Practical Aspects of Theoretical Bounds for Algebraic Multigrid Performance
Algebraic multigrid methods continue to grow in robustness as effective solvers for the large and sparse linear systems of equations that arise in many applications. Unlike geometric multigrid approaches, however, the theoretical analysis of algebraic multigrid is less predictive of true performance. Multigrid convergence factors naturally depend on the properties of the relaxation, interpolati...
متن کاملTheoretical bounds for algebraic multigrid performance: review and analysis
Algebraic multigrid methods continue to grow in robustness as effective solvers for the large and sparse linear systems of equations that arise in many applications. Unlike geometric multigrid approaches, however, the theoretical analysis of algebraic multigrid is less predictive of true performance. Multigrid convergence factors naturally depend on the properties of the relaxation, interpolati...
متن کاملOn Three-Grid Fourier Analysis for Multigrid
In this paper, we present three-grid Fourier analysis for multigrid methods. Due to the recursive structure of a multigrid iteration, this analysis can be deduced from the well-known two-grid Fourier analysis. The coarse grid correction part of multigrid algorithms can be more accurately evaluated with the three-grid analysis. We apply the analysis to several scalar equations and discretization...
متن کاملFourier Analysis of Multigrid Methods for General Systems of Pdes
Most iteration methods for solving boundary value problems can be viewed as approximations of a time-dependent differential equation. In this paper we show that the multigrid method has the effect of increasing the timestep for the smooth part of the solution leading back to an increase of the convergence rate. For the nonsmooth part the convergence is an effect of damping. Fourier analysis is ...
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We are interested in the design of efficient geometric multigrid methods on hierarchical triangular grids for problems in two dimensions. Fourier analysis is a well-known useful tool in multigrid for the prediction of two-grid convergence rates which has been used mainly for rectangular–grids. This analysis can be extended straightforwardly to triangular grids by using an appropriate expression...
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ورودعنوان ژورنال:
- Math. Comput.
دوره 76 شماره
صفحات -
تاریخ انتشار 2007