A Hybrid Parallel Tridiagonal Solver on Multi-core Architectures

Abstract

An optimized parallel algorithm is proposed to solve the problem occurred in the process of complicated backward substitution of cyclic reduction during solving tridiagonal linear systems. Adopting a hybrid parallel model, this algorithm combines the cyclic reduction method and the partition method. This hybrid algorithm has simple backward substitution on parallel computers comparing with the cyclic reduction method. In this paper, the operation count and execution time are obtained to evaluate and make comparison for these methods. On the basis of results of these measured parameters, the hybrid algorithm using the hybrid approach with a multi-threading implementation achieves better efficiency than the other parallel methods, i.e., the cyclic reduction and the partition methods. Among them, the cyclic reduction method is previously found to be the fastest algorithm in many ways for solutions. In particular, the approach involved in this paper has the least scalar operation count and the shortest execution time on multi-core computer when the size of an equation is large enough. The hybrid parallel algorithm improves the performance of the cyclic reduction and partition methods by 30% and 20% respectively.