REDESIGNING THE SKYLINE SOLVER FOR PARALLEL/VECTOR SUPERCOMPUTERS
Charbel Farhat · International Journal of High Speed Computing · 1990
The traditional dot-product-based skyline symmetric solver is re-designed for implementation on parallel/vector supercomputers. A set of pivotal equations are reduced with the ijk/jki combined permutation. Resulting coefficients are buffered in parallel, then piped into an unrolled parallel/vector kji factorization scheme. The high performance of the resulting algorithm is demonstrated on the CRAY-2 (4 processors) and CRAY Y-MP (8 processors) with the solution of large-scale positive definite and semi-definite systems arising from the thermomechanical analysis of flexible aerospace structures. On an 8-processor system, speed-ups as high as 20 are achieved over the serial compiler-vectorized dot-product-based implementation. The proposed algorithm is also shown to compare favorably with recent alternative parallel/vector implementations of the skyline symmetric solver. However, not unlike most elimination methods, it leads to a low degree of parallelism and is suitable only for coarse grain multiprocessors.