The free-Lagrange method on the connection machine

Abstract

The three dimensional time-dependent free-Lagrange hydrodynamics code (X3D) has been implemented on the massively parallel Connection Machine CM2. This data parallel computer represents the state of the art in a single instruction multiple data (SIMD) processor with peak performance rates of 10 Gflops for well structured problems. While the performance on the CM2 of the free-Lagrange method (FLM) did not attain this remarkable peak rate, we did achieve Cray Y-MP performance levels. The implementation of the FLM with its unstructured grid and global connectivity matrix presents problems on all computer architectures, especially on the distributed memory CM2. The hydrodynamics portion of the code, which is written in a “long vector” style on the Y-MP and optimized for that machine, presented few problems when implemented on the CM2. However, to achieve the higher degree of parallelization required on the 64K processor CM2 over the 8 processor Y-MP, we had to take a different approach from the multitasked version on the Y-MP. We describe new data structures and algorithms that solve the problems of equation-of-state table lookup, parallelization of accumulation loops, and solution of large unstructured sparse linear systems. We also present timing results and comparisons with the Y-MP for various parts of the FLM and discuss CM2 techniques that are different from traditional techniques on multiple instruction multiple data (MIMD) machines. Almost all of the code is written in CM2 Fortran, a language that is under development; we have seen and expect improvements in performance as the compiler matures.