Strategies for parallelizing a Navier-Stokes code on the intel touchstone machines

The purpose of this paper is to predict the efficiency of the Navier-Stokes code NSS* which will run on an MIMD architecture parallel machine. Computations are performed using a three-dimensional overlapping structured multiblock grid. Each processor works with some of these blocks and exchanges data across the boundaries of the blocks. The efficiency of such a code depends on the number of grid points per processor, the amount of computation per grid point and the amount of communication per boundary point. In this paper we estimate these quantities for NSS* and present measurements of communication times for two parallel machines, the Intel Touchstone Delta machine and an Intel iPSC/860 machine, consisting of 520 and 64 Intel i860 processors respectively. The peak performance of the Delta machine is 32 Gflop. Secondly it is shown how, starting from a seven-block grid of about 5000 000 points for the Hermes space plane, a mesh of 512 equally sized blocks is constructed retaining the original topology. This example demonstrates that multiblock grids provide sufficient control over both the number and size of blocks. Therefore it will be possible to simulate realistic configurations on massively parallel systems with a specified number of processors while achieving good quality load balancing.     

Free material optimization via mathematical programming

This paper deals with a central question of structural optimization which is formulated as the problem of finding the stiffest structure which can be made when both the distribution of material as well as the material itself can be freely varied. We consider a general multi-load formulation and include the possibility of unilateral contact. The emphasis of the presentation is on numerical procedures for this type of problem, and we show that the problems after discretization can be rewritten as mathematical programming problems of special form. We propose iterative optimization algorithms based on penalty-barrier methods and interior-point methods and show a broad range of numerical examples that demonstrates the efficiency of our approach. Supported by the project 03ZO7BAY of BMBF (Germany) and the GIF-contract 10455-214.06/95.