The hierarchial preconditioning on unstructured grids
Two hierarchical preconditioned methods for the approximation of 2D-elliptic equations on unstructured quasi uniform triangulations are presented. Based on the fictitious space approach the original problem can be embedded into an auxiliary one, where both the hierarchical grid information and the preconditioner are well defined. The corresponding preconditioned conjugate gradient methods of \textit{H. Yserentant} [Numer. Math. 49, 379-412 (1986; Zbl 0608.65065)] and of \textit{J. H. Bramble, J. E. Pasciak} and \textit{J. Xu} [Math. Comput. 55, No. 191, 1-22 (1990; Zbl 0703.65076)] are implemented and have optimal computational costs.
scientific article; zbMATH DE number 1269977