A Scalable Parallel Partition Tridiagonal Solver for Many-Core and Low B/F Processors

Tridiagonal systems are among the most fundamental computations in science, engineering, and mathematics, and one solver used in such systems is Tree Partitioning Reduction (TPR), which is a divide-and-conquer method that solves large-scale linear equations by dividing them and then computing the parts in parallel within different local memory threads. Herein, we propose an improved TPR algorithm that has a parallel cyclic reduction flavor, with which we reduced the number of algorithm steps by approximately half while simultaneously increasing arithmetic intensity and cache reusability. A performance evaluation conducted on an Intel Skylake-SP microprocessor showed a high hit ratio for the L1 cache and that our solver was as much as 31 times faster on 32 threads for 262144 equations. In the case of a Nvidia Tesla P100 GPU, our method processed 10 MRow/s more than TPR and cuSPARSE.