Parallel iterative solvers for finite-element methods using an OpenMP/MPI hybrid programming model on the Earth Simulator

An efficient parallel iterative method for finite-element method has been developed for symmetric multiprocessor (SMP) cluster architectures with vector processors such as the Earth Simulator. The method is based on a three-level hybrid parallel programming model, including message passing for inter-SMP node communication, loop directives by OpenMP for intra-SMP node parallelization and vectorization for each processing element (PE). Simple 3D linear elastic problems with more than 2.2 × 109 DOF have been solved using 3 × 3 block ICCG(0) method with additive Schwarz domain decomposition and PDJDS/CM-RCM reordering on 176 nodes of the Earth Simulator, achieving performance of 3.80 TFLOPS. Furthermore, effect of color number in reordering has been evaluated on various types of computers.