Scalable Hierarchical Parallel Algorithm for the Solution of Super Large-Scale Sparse Linear Equations
Ran Xu, Bin Liu, Yuan Dong · 2014
The parallel linear equations solver capable of effectively using 1000þ processors becomes the bottleneck of large-scale implicit engineering simulations. In this paper, we present a new hierarchical parallel master-slave-structural iterative algorithm for the solution of super large-scale sparse linear equations in a distributed memory computer cluster. Through alternatively performing global equilibrium computation and local relaxation, the specific accuracy requirement can be met in a few iterations. Moreover, each set/slave-processor majorly communicates with its nearest neighbors, and the transferring data between sets/slave-processors and the master-processor is always far below the communi-cation between neighboring sets/slave-processors. The corresponding algorithm for implicit finite element analysis has been implemented based on the MPI library, and a super large 2-dimension square system of triangle-lattice truss structure under randomly distributed loadings is simulated with over 1 109 degrees of freedom (DOF) on up to 2001 processors of the “Exploration 100 ” cluster in Tsinghua University. The numerical experiments dem-onstrate that this algorithm has excellent parallel efficiency and high scalability, and it may have broad applications in other implicit simulations. [DOI: 10.1115/1.4023481]