The Hierarchial Preconditioning On Unstructured Grids

摘要

We present the implementation of two hierarchically preconditioned methods for the fast solution of mesh equations that approximate 2D-elliptic boundary value problems on unstructured quasi uniform triangulations. Based on the fictitious space approach the original problem can be embed- ded into an auxiliary one, where both the hierarchical grid information and the preconditioner are well defined. We implemented the corresponding Yserentant preconditioned conjugate gradient method as well as the BPX-preconditioned cg-iteration having optimal computational costs. Several numerical examples demonstrate the efficiency of the artifically constructed hierarchical methods which can be of importance in industrial engienering, where often only the nodal coordinates and the element connectivity of the underlying (fine) fiscretization are available.