Collection of abstracts 14th GAMM-Seminar Kiel on Concepts of Numerical Software January 23rd to 25th, 1998.

Sunday, January 25th, 1998

Reusable software components for sequential and distributed solution of PDE problems

Algorithms are the central entities in scientific computing. Therefore it is a prime concern to develop reusable software components implementing algorithms as the basic building blocks for complex applications dealing with the numerical treatment of PDE's. In order to be widely applicable, the implementation of an algorithm has to be generic, i.e. independent of the specific form of data representation. One way to achieve this is to separate data and algorithms and to formulate the latter in terms of an abstract view to the data. Then one can exploit modern compiler technology to perform automatic specialization into efficient code.

In the presentation we focus on the interaction between grids and geometric kernels on the one hand and numerical, combinatorial and visualization algorithms on the other hand. It is demonstrated how separation of the functionality of grids and geometries into several layers can enhance the reusability of the corresponding software modules, introduce a taxonomy for these components and help in understanding and describing their relationship to the algorithms using them. These aspects prove essential for the development of truly general implementations of algorithms.

A parallel implementation the algorithms under consideration can be eased substantially when we rely on data structures hiding most of the complexity of topological data distribution. We demonstrate how to extend the abstract notion mentioned above so as to incorporate distributed grids and dependent data, allowing to reuse large parts of sequential code without changes.

In order to show the potential of the outlined concepts, we present both implementations of specific tasks as well as full grown applications from computational fluid dynamics. In particular, it is shown that different numerical methods such as Finite Volume and FEM discretizations can be built on a common basis.