Accuracy Measures and Fourier Analysis for the Full Multigrid Algorithm

Abstract

The full multigrid (FMG) algorithm is often claimed to achieve so-called discretization-level accuracy. In this paper, this notion is formalized by defining a worst-case relative accuracy measure, denoted $E_{FMG}^{\ell}$, which compares the total error of the $\ell$-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 $E_{FMG}^{\ell}$, and the resulting estimates are confirmed by numerical tests.