MULTILEVEL FILTERING PRECONDITIONERS: EXTENSIONS TO MORE GENERAL ELLIPTIC PROBLEMS*

Abstract. The concept of multilevel filtering (MF) preconditioning applied to second-order selfadjoint elliptic problems is briefly reviewed. It is then shown how to effectively apply this concept to other elliptic problems such as the second-order anisotropic problem, biharmonic equation, equa-tions on locally refined grids and interface operators arising from domain decomposition methods. Numerical results are given to show the effectiveness of the MF preconditioners on these problems. Key words, multilevel preconditioners, elliptic problems, conjugate gradient method, domain decomposition AMS(MOS) subject classifications. 65F10, 65N3