Continuing the previous work in the preprint 97-11 done for the 2D-approach in this paper we describe the Yserentant preconditioned conjugate gradient method as well as the BPX-preconditioned cg-iteration fastly solving 3D-elliptic boundary value problems on unstructured quasi uniform grids. These artificially constructed hierarchical methods have optimal computational costs. In the case of the sequential computing several numerical examples demonstrate their efficiency not depending on the finite element types used for the discretiziation of the original potential problem. Moreover, implementing the methods in parallel first results are given.

In this paper we present 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 embedded into an auxiliary one, where both the hierarchical grid information and the preconditioner by decomposing functions on it 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 artificially constructed hierarchical methods which can be of importance in the industrial engineering, where often only the nodal coordinates and the element connectivity of the underlying (fine) discretization are available.

Continuing the previous work in the preprint 97-11 done for the 2D-approach in this paper we describe the Yserentant preconditioned conjugate gradient method as well as the BPX-preconditioned cg-iteration fastly solving 3D-elliptic boundary value problems on unstructured quasi uniform grids. These artificially constructed hierarchical methods have optimal computational costs. In the case of the sequential computing several numerical examples demonstrate their efficiency not depending on the finite element types used for the discretiziation of the original potential problem. Moreover, implementing the methods in parallel first results are given.

In this paper we present 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 embedded into an auxiliary one, where both the hierarchical grid information and the preconditioner by decomposing functions on it 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 artificially constructed hierarchical methods which can be of importance in the industrial engineering, where often only the nodal coordinates and the element connectivity of the underlying (fine) discretization are available.