On the Robustness of ILU Smoothing

摘要: In the present paper, a detailed analysis of multigrid method with an ILU smoother applied to singularly perturbed problem is given. Based on simple anisotropic model problem, variant usual incomplete LU factorization introduced, which especially suited as robust smoother. For this and proof robustness Furthermore, some contradictions between smoothing rates predicted by local Fourier practically observed convergence factors are explained (see [W. Hackbusch, Multi-grid Methods Applications, Springer-Verlag, Berlin, Heidelberg, 1985; R. Kettler, “Analysis comparison relaxation schemes in multi-grid preconditioned conjugate gradient methods,” Methods, Lecture Notes Math. 960, 1982; C. A. Thole, Beitrage zur Fourieranalyse von Mehrgitterver fahren, Diplomarbeit, Universitat Bonn, 1983]. The theoretical results confirmed numerical tests.