Numeric models use a collection of triangular facets called elements connected over a domain in what is referred to as a mesh or unstructured grid as the computational basis for calculations. The density of elements in a mesh affects the numeric stability of a model when performing computations. Furthermore, these meshes can be difficult and time consuming to create. This thesis describes an automated process of creating meshes which utilizes local truncation analysis to generate a spatially varied size function. An advancing frontal mesh generation algorithm uses this function to optimize node placement and density. Further analysis to better understand appropriate applications of this technique is also presented. The toolbox was able to create efficient meshes with relatively little user input. The final mesh spacing honored the guidelines from the truncation error analysis and resulted in appropriate mesh density. It was also shown that the process could be applied to several shelf based meshes.

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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.

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.