Parallel iterative solution of the Hermite Collocation equations on GPUs II

Hermite Collocation is a high order finite element method for Boundary Value Problems modelling applications in several fields of science and engineering. Application of this integration free numerical solver for the solution of linear BVPs results in a large and sparse general system of algebraic equations, suggesting the usage of an efficient iterative solver especially for realistic simulations. In part I of this work an efficient parallel algorithm of the Schur complement method coupled with Bi-Conjugate Gradient Stabilized (BiCGSTAB) iterative solver has been designed for multicore computing architectures with a Graphics Processing Unit (GPU). In the present work the proposed algorithm has been extended for high performance computing environments consisting of multiprocessor machines with multiple GPUs. Since this is a distributed GPU and shared CPU memory parallel architecture, a hybrid memory treatment is needed for the development of the parallel algorithm. The realization of the algorithm took place on a multiprocessor machine HP SL390 with Tesla M2070 GPUs using the OpenMP and OpenACC standards. Execution time measurements reveal the efficiency of the parallel implementation