Swpts: an Efficient Parallel Thomas Split Algorithm for Tridiagonal Systems on Sunway Manycore Processors

Tridiagonal system solver is a basic kernel and has been well-supported in mainstream numerical libraries. The purpose of this paper is to devise an efficient parallel algorithm to solve a large-scale tridiagonal system. Based on the performance analysis of the classic Thomas algorithm and matrix splitting method, we propose a parallel Thomas split (PTS) algorithm. Compared with the matrix splitting method, the PTS algorithm can achieve an acceleration of 10.34 × . Furthermore, we propose a Sunway parallel Thomas split (swPTS) algorithm based on the sw26010pro manycore processor. In the swPTS algorithm, we propose a specific data partitioning scheme to implement MPI+Athread parallelism. In the reduced set of equations, a new reduction approach for the Sunway architecture is proposed. Experiments show that the parallel elimination stage of our swPTS algorithm achieves up to 38.31 × speedup over a PTS algorithm, and overall reaches 5.74 × speedup over a Thomas algorithm.