The effect of intergrid operators on multigrid convergence

摘要

We study the effect of interpolation and restriction operators on the convergence of multigrid algorithms for solving linear PDEs. Using a modal analysis of a subclass of these systems, we determine how two groups of the modal components of the error are filtered and mixed at each step in the algorithm. We then show that the convergence rate of the algorithm depends on both the properties of the interpolation and restriction operators and the characteristics of the system. The analysis opens the problem of optimization of these operators. By different choices of operators we show a trade-off between the optimization of the convergence rate and the optimization of the number of computations required per iteration.