Scalable Hierarchical Parallel Algorithm for the Solution of Super Large Scale Sparse Linear Equations

Abstract

The parallel linear equations solver capable of effectively using 1000+ processors becomes the bottleneck of largescale implicit engineering simulations. In this paper, we present a new hierarchical parallel masterslavestructural iterative algorithm for the solution of super largescale 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/slaveprocessor majorly communicates with its nearest neighbors, and the transferring data between sets/slaveprocessors and the masterprocessor is always far below the communication between neighboring sets/slaveprocessors. The corresponding algorithm for implicit finite element analysis has been implemented based on the MPI library, and a super large 2dimension square system of trianglelattice truss structure under randomly distributed loadings is simulated with over 1 أ— 109 degrees of freedom (DOF) on up to 2001 processors of the “Exploration 100â€‌ cluster in Tsinghua University. The numerical experiments demonstrate that this algorithm has excellent parallel efficiency and high scalability, and it may have broad applications in other implicit simulations.