Operator Splitting on Vector Processors

摘要

The basic idea behind operator splitting for two-dimensional time-dependent parabolic partial differential equations is to break the problem down to that of solving two one-dimensional problems. If one uses a vectorized Gauss Elimination to solve these 1-D problems, then one is faced with transposing several matrices in between the two solution processes. Parallel Gauss Elimination is compared with cyclic reduction, which requires no transposes. Actual STAR timings differ markedly from theoretical ones. A compiler allowing users to assign variables to registers eliminates this discrepancy. 2 tables. (ERA citation 02:057825)