  The parallel linear equations solver capable of effectively using 1000+
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 distributed memory computer cluster.
Through alternatively performing global equilibrium computation and local
relaxation, our proposed algorithm will reach the specific accuracy requirement
in a few of iterative steps. Moreover, each set/slave-processor majorly
communicate with its nearest neighbors, and the transferring data between
sets/slave-processors and master is always far below the set-neighbor
communication. The corresponding algorithm for implicit finite element analysis
has been implemented based on MPI library, and a super large 2-dimension square
system of triangle-lattice truss structure under random static loads is
simulated with over one billion degrees of freedom and up to 2001 processors on
"Exploration 100" cluster in Tsinghua University. The numerical experiments
demonstrate that this algorithm has excellent parallel efficiency and high
scalability, and it may have broad application in other implicit simulations.
