On the validity of the local Fourier analysis
This work provides a theoretical foundation for applying LFA to a broader range of problems, benefiting researchers and practitioners using geometric multigrid methods.
The authors prove that local Fourier analysis (LFA) yields exact convergence factors for geometric multigrid methods on a wider class of problems beyond rectangular domains with periodic boundary conditions, extending the theoretical validity of LFA.
Local Fourier analysis (LFA) is a useful tool in predicting the convergence factors of geometric multigrid methods (GMG). As is well known, on rectangular domains with periodic boundary conditions this analysis gives the exact convergence factors of such methods. In this work, using the Fourier method, we extend these results by proving that such analysis yields the exact convergence factors for a wider class of problems.