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

Friday, January 23rd, 1998

Some software and algorithmic concepts of FEAST

One current trend in software development for PDE's, and here especially for Finite Element approaches, goes clearly towards object-oriented techniques and adaptive methods in any sense. Hereby the employed data and solver structures, and particularly the `matrix structures', are often in contradiction to modern hardware platforms. As a result, the observed computational efficiency is far from the expected Peak rates of almost 1 GFlop nowadays, and the 'real life' gap is even further increasing. High performance calculations can be reached only by explicitly exploiting 'caching in' and 'pipelining' in combination with long sequentially stored arrays (BLAS, LAPACK) which seem to be 'easier' for simple Finite Difference approaches, but how to perform similar techniques for much more sophisticated Finite Element codes?

These discrepancies often lead to unreasonable calculation times for `real world' problems, e.g. CFD calculations in 3D, as can be seen from recent benchmarks for commercial as well as research codes. Hence, strategies for efficiency enhancement are necessary, not only from the mathematical (algorithms, discretizations) but also from the software side of view.

To realize some of these aims our new finite element package (project name: FEAST --- Finite Element Analysis & Solution Tools) is under development at the Institute for Applied Mathematics of the University of Heidelberg. This package is based on following concepts:

• hierarchical data and solver structure, but also hierarchical `matrix structure'
• frequent use of machine optimized low level linear algebra routines (BLAS, ESSL, etc.)
• solution strategy ScaRC as 'new' generalization of multigrid and domain decomposition techniques
• all typical Finite Element facilities included

The result shall be a flexible software package with special emphasis on ('eierlegende Wollmilchsau'):

• (closer to) peak performance on modern processors
• typical multigrid behaviour (efficiency/robustness)
• parallelization directly included
• open for different adaptivity concepts
• low storage requirements
• application to many `real life' problems possible

In contrast to many other approaches which often aim to develop preferrably software for research or education topics, our approach clearly is designed for high performance applications with industrial background, especially in CFD.
Consequently, our main emphasis lies on the aspects 'efficiency' and 'robustness' and less on topics as `easy implementable' or `most modern programming language'.

Therefore, Fortran77/90 is used. This makes it possible to adopt many reliable parts of the predecessor packages FEAT2D, FEAT3D and FEATFLOW. Further on high performance computers very efficient Fortran compilers are available and transparent access to the data structures is possible. The pre- and postprocessing, which has to be based on (commercial) professional tools, is handled by Java-based program parts under Netscape. Configuring a high performance computer as a FEAST server the user can do the calculation by a FEAST client.

In the lecture we give examples for `real' computational efficiency results of typical numerical tools which motivate why we introduce our hierarchical data, solver and matrix structures. To understand these better, we explain the corresponding solution technique ScaRC ("Scalable Recursive Clustering") which is essential for the software package FEAST. We show how typical multigrid rates, even on very complex meshes, can be achieved, on parallel as well as sequential computers, with a very high computational efficiency.