多重网格法全局和局部傅里叶分析

he aim of this master thesis is to apply Fourier analysis and local Fourier analysis (LFA) to calculate the exact convergence factor of two-grid methods for the solution of linear algebraic systems arising in different applications. We first consider the one-dimensional Poisson problem. Both Fourier analysis and LFA are used to derive two-grid convergence factors. Differences between these two analysis tools are illustrated. Then we study a saddle-point problem stemming from an optimal control problem. The smoothing factor for the optimal control problem is derived by Fourier analysis for a special preconditioner. Moreover, the robustness of the preconditioner is shown by the numerical experiment.