Preconditioned iterative linear solvers for unstructured grids on the Earth simulator

Efficient parallel preconditioned iterative linear solvers for unstructured grid have been developed for symmetric multiprocessor (SMP) cluster architectures with vector processors such as the Earth simulator. Three types of preconditioning methods (ICCG, multigrid and selective-blocking for contact problems) have been developed and performance has been demonstrated on the Earth simulator using flat-MPI and hybrid parallel programming models, where each of three preconditioning methods corresponds to typical finite-element type applications in solid earth simulation developed in GeoFEM project. Simple 3D linear elastic problems with more than 2.2× 10⁹ (DOF have been solved using 3×3 block ICCG(O) method and PDJDS/CM-RCM reordering on 176 nodes of the Earth simulator, achieving performance of 3.80 TFLOPS. Multicolor and RCM ordering provide excellent parallel and vector performance of the three preconditioned methods on the Earth simulator.