Scientific progress in the Par-EXPDE-project. Here we present the scientific progress of the Par-EXPDE project, the primary goal of which is to provide an efficient library for the numerical computation of PDEs on the Hitachi SR8000. It is intended that this library will significantly reduce the implementation effort required by users for the development of parallel adaptive multigrid methods on arbitrary 3D-domains by providing them with a high level interface that closely resembles mathematical language. This high level user interface is accomplished through the use of a special programming technique called expression templates that effectively hides the complexity of the underlying data structures while still allowing for an efficient implementation of computationally intensive codes. The low level data structures themselves use a technique of patchwise regular refinement of unstructured grid elements to allow for more aggressive compiler optimization and the use of stencil based smoothers that are better able to exploit the memory hierarchy and pseudo vectorization capabilities of the SR8000. Geometry and visualization capabilities are provided by the GRIDLIB project.