DRAM(h):A Parallel Computation Model for High Performance Numerical Computing
Yun Zhang · Chinese Journal of Computers · 2003
In this paper, a new parallel computation model DRAM( h ), which has h-level memory hierarchies, was proposed. With this new model, we performed memory complexity analysis on different implementation forms of two classical parallel numerical linear algebra algorithms, i.e., four forms of parallel lower triangular solver(PTRS) and six forms of parallel LU factorization without column pivoting(PLU). Under DRAM(h) model, we find out that the different implementation forms of the same algorithm can have different memory complexity though they have almost the same time and space complexity under traditional RAM model. Finally, we validate our analytical results with experimental results on three parallel computing platforms, i.e., HITACHI SR2201, DAWNING3000 and 128 node LSEC Linux Cluster. In most cases, our model’s analytical results match well with experimental results, which indicates the effectiveness of our new model on clarifying the different memory access pattern of various forms of the same algorithm. Some mismatches can be well explained through slightly modification on model analysis assumptions according to platform memory hierarchy features.