Parallelization of Preconditioned MRTR Method Combined with Block-multicolor Ordering Supported by Level Structure Arising in RCM Ordering

摘要

The performance of preconditioned Minimized Residual method based on the Three-term Recurrence formula of the CG-type (MRTR) using multicolor (MC) ordering has been demonstrated on various symmetric linear systems derived from 3-D FEM. The elapsed time using MC is longer than that using block preconditioner with RCM ordering because the cache hit deteriorate owing to increase in bandwidth. To realize further reduction of elapsed time, the block-multicolor (BMC) ordering based on level structure arising in RCM ordering is proposed. The validity of proposed method is shown in comparison to conventional block preconditioner combined with the traditional orderings.