Accuracy Measures and Fourier Analysis for the Full Multigrid Algorithm
نویسندگان
چکیده
The full multigrid (FMG) algorithm is often claimed to achieve so-called discretizationlevel accuracy. In this paper, this notion is formalized by defining a worst-case relative accuracy measure, denoted E` FMG, which compares the total error of the `-level FMG solution against the inherent discretization error. This measure can be used for tuning algorithmic components so as to obtain discretization-level accuracy. A Fourier analysis is developed for estimating E` FMG, and the resulting estimates are confirmed by numerical tests.
منابع مشابه
Fast and High Accuracy Multigrid Solution of the Three Dimensional Poisson Equation
We employ a fourth-order compact finite difference scheme (FOS) with the multigrid algorithm to solve the three dimensional Poisson equation. We test the influence of different orderings of the grid space and different grid-transfer operators on the convergence and efficiency of our high accuracy algorithm. Fourier smoothing analysis is conducted to show that FOS has a smaller smoothing factor ...
متن کاملFourier Analysis of Multigrid Methods on Hexagonal Grids
This paper applies local Fourier analysis to multigrid methods on hexagonal grids. Using oblique coordinates to express the grids and a dual basis for the Fourier modes, the analysis proceeds essentially the same as for rectangular grids. The framework for oneand two-grid analyses is given and then applied to analyze the performance of multigrid methods for the Poisson problem on a hexagonal gr...
متن کاملp-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier–Stokes equations
We present a p-multigrid solution algorithm for a high-order discontinuous Galerkin finite element discretization of the compressible Navier–Stokes equations. The algorithm employs an element line Jacobi smoother in which lines of elements are formed using coupling based on a p = 0 discretization of the scalar convection–diffusion equation. Fourier analysis of the two-level p-multigrid algorith...
متن کاملA Compact Multigrid Solver for Convection-Diffusion Equations
diffusion equations using a nine-point compact difference scheme. implementation with multigrid, and carry out a Fourier We test the efficiency of the algorithm with various smoothers and smoothing analysis of the Gauss–Seidel operator. In Secintergrid transfer operators. The algorithm displays a grid-indepention 3 we present numerical experiments that demonstrate dent convergence rate and prod...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Scientific Computing
دوره 32 شماره
صفحات -
تاریخ انتشار 2010