Parallel solution of triangular systems in direct numerical simulation

To improve the parallel computational efficiency of triangular equations, a new parallel algorithm was proposed in large scale direct numerical simulation (DNS). The algorithm was based on Wang's splitting algorithm, and the triangular equations were divided by equalily policy. Non-blocking message passive mode was utilized instead of blocking mode, and the new calculated value was stored in the former space. Two triangular equation systems with different matrix size were realized on the Linux clusters, then the calculation time and acceleration ratio were studied under different nodes and matrix scales. Results show that the algorithm has high parallel efficiency with high overlapping ratio between communication and computation, minimizes calculation steps and memory requirement. Under the current 100 M networks, the consumption time is reduced by the algorithm when matrix scale is larger than 1×105 , and the acceleration ratio increases with increasing matrix size. The proposed algorithm is suitable for large scale triangular matrix parallel computation.