SEPARATION ANALYSIS, A TOOL FOR ANALYZING MULTIGRID ALGORITHMS

The separation of vectors by multigrid (MG) algorithms is applied to the study of convergence and to the prediction of the performance of MG algorithms. The separation operator for a two level cycle algorithm is derived. It is used to analyze the efficiency of the cycle when mixing of eigenvectors occurs. In particular cases the separation analysis reduces to Fourier type analysis. The separation operator of a two level cycle for a Sch"odinger eigenvalue problem, is derived and analyzed in a Fourier basis. Separation analysis gives information on how to chose relaxations and inter-level transfers. Separation analysis is a tool for analyzing and designing algorithms, and for optimizing their performance.