The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform

Kengo Nakajima - One of the best experts on this subject based on the ideXlab platform.

  • parallel Multigrid Method on multicore manycore clusters
    IEEE International Conference on High Performance Computing Data and Analytics, 2020
    Co-Authors: Kengo Nakajima
    Abstract:

    Parallel Multigrid Method is expected to be a useful algorithm in exascale era because of its scalability. It is widely known that overhead of coarse grid solver in parallel Multigrid Method is significant, if the number of MPI processes is O(104) or larger. The author proposed the hCGA for avoiding such overhead. Recently, the AM-hCGA, further optimized version of the hCGA, was proposed by the author, and its performance was evaluated on the Oakforest-PACS system (OFP) with IHK/McKernel at JCAHPC using up to 2,048 nodes of Intel Xeon Phi (Knights Landing). In the present work, developed Method is also implemented to the Oakbridge-CX system (OBCX) at the University of Tokyo using up to 1,024 nodes (2,048 sockets) of Intel Xeon Platinum 8280 (Cascade Lake). Performance in weak and strong scaling are evaluated for application on 3D groundwater flow through heterogeneous porous media (pGW3D-FVM). The hCGA and the AM-hCGA provide excellent performance on both of OFP and OBCX with larger number of nodes. Especially, it achieved excellent performance in strong scaling on OBCX.

  • Optimization of serial and parallel communications for parallel geometric Multigrid Method
    2014 20th IEEE International Conference on Parallel and Distributed Systems (ICPADS), 2014
    Co-Authors: Kengo Nakajima
    Abstract:

    The parallel Multigrid Method is expected to play an important role in large-scale scientific computing on post-peta/exa-scale supercomputer systems, and it also includes serial and parallel communication processes which are generally expensive. In the present work, new format for sparse matrix storage based on sliced Ellpack-Itpack (ELL) format is proposed for optimization of serial communication in data transfer through memories, and hierarchical coarse grid aggregation (hCGA) is introduced for optimization of parallel communication by message passing. The proposed Methods are implemented for pGW3D-FVM, a parallel code for 3D groundwater flow simulations using the Multigrid Method, and the robustness and performance of the code was evaluated on up to 4,096 nodes (65,536 cores) of the Fujistu FX10 supercomputer system at the University of Tokyo. The parallel Multigrid solver using the sliced ELL format provided performance improvement in both weak scaling (25%-31%) and strong scaling (9%-22%) compared to the code using the original ELL format. Moreover, hCGA provided excellent performance improvement in both weak scaling (1.61 times) and strong scaling (6.27 times) for flat MPI parallel programming model.

  • large scale simulations of 3d groundwater flow using parallel geometric Multigrid Method
    Procedia Computer Science, 2013
    Co-Authors: Kengo Nakajima
    Abstract:

    The Multigrid Method used with OpenMP/MPI hybrid parallel programming models is expected to play an important role in large-scale scientific computing on post-peta/exa-scale supercomputer systems. In the present work, the effect of sparse matrix storage formats on the performance of parallel geometric Multigrid solvers was evaluated, and a new data structure for the Ellpack-Itpack (ELL) format is proposed. The proposed Method is implemented for pGW3D-FVM, a parallel code for 3D groundwater flow simulations using the Multigrid Method, and the robustness and performance of the code was evaluated on up to 4,096 nodes (65,536 cores) of the Fujistu FX10 supercomputer system at the University of Tokyo. The parallel Multigrid solver using the ELL format with coarse grid aggregation provided excellent performance improvement in both weak scaling (13%–35%) and strong scaling (40%–70%) compared to the original code using the CRS format.

  • openmp mpi hybrid parallel Multigrid Method on fujitsu fx10 supercomputer system
    International Conference on Cluster Computing, 2012
    Co-Authors: Kengo Nakajima
    Abstract:

    The Multigrid Method used with OpenMP/MPI hybrid parallel programming models is expected to play an important role in large-scale scientific computing on post-peta/exa scale supercomputer systems. In the present work, gcoarse grid aggregationh is proposed for robust convergence of Multigrid solvers with large numbers of MPI processes. The robustness and performance of the proposed Method has been evaluated using up to 4,096 nodes (65,536 cores) of the Fujistu FX10 supercomputer system. The results of the proposed Method have proved to be excellent, especially for strong scaling computation.

  • OpenMP/MPI Hybrid Parallel Multigrid Method on Fujitsu FX10 Supercomputer System
    2012 IEEE International Conference on Cluster Computing Workshops, 2012
    Co-Authors: Kengo Nakajima
    Abstract:

    The Multigrid Method used with OpenMP/MPI hybrid parallel programming models is expected to play an important role in large-scale scientific computing on post-peta/exa scale supercomputer systems. In the present work, gcoarse grid aggregationh is proposed for robust convergence of Multigrid solvers with large numbers of MPI processes. The robustness and performance of the proposed Method has been evaluated using up to 4,096 nodes (65,536 cores) of the Fujistu FX10 supercomputer system. The results of the proposed Method have proved to be excellent, especially for strong scaling computation.

Jun Zhang - One of the best experts on this subject based on the ideXlab platform.

  • Nonlinear Multigrid Method for solving the LLT model
    Applied Mathematics and Computation, 2020
    Co-Authors: Jun Zhang, Yu-fei Yang
    Abstract:

    Our goal in this paper is to study a nonlinear Multigrid Method for solving the LLT model. In order to improve the convergence rate of the proposed Multigrid Method, an improved dual iteration is proposed as its smoother. Furthermore, we give the local Fourier analysis (LFAs) of the Chambolle's dual iterations and a modified smoother for solving the LLT model, respectively. Numerical results illustrate the efficiency of the proposed Method and indicate that such a Multigrid Method is more suitable to deal with large-sized images.

  • a transformation free hoc scheme and Multigrid Method for solving the 3d poisson equation on nonuniform grids
    Journal of Computational Physics, 2013
    Co-Authors: Yongbin Ge, Jun Zhang
    Abstract:

    A high-order compact (HOC) difference scheme is proposed to solve the three-dimensional (3D) Poisson equation on nonuniform orthogonal Cartesian grids involving no coordinate transformation from the physical space to the computational space. Theoretically, the proposed scheme has third to fourth-order accuracy; its fourth-order accuracy is achieved under uniform grid settings. Then, a Multigrid Method is developed to solve the linear system arising from this HOC difference scheme and the corresponding Multigrid restriction and interpolation operators are constructed using the volume law. Numerical experiments are conducted to show the computed accuracy of the HOC scheme and the computational efficiency of the Multigrid Method.

  • sixth order compact scheme combined with Multigrid Method and extrapolation technique for 2d poisson equation
    Journal of Computational Physics, 2009
    Co-Authors: Yin Wang, Jun Zhang
    Abstract:

    We develop a sixth order finite difference discretization strategy to solve the two dimensional Poisson equation, which is based on the fourth order compact discretization, Multigrid Method, Richardson extrapolation technique, and an operator based interpolation scheme. We use Multigrid V-Cycle procedure to build our multiscale Multigrid algorithm, which is similar to the full Multigrid Method (FMG). The Multigrid computation yields fourth order accurate solution on both the fine grid and the coarse grid. A sixth order accurate coarse grid solution is computed by using the Richardson extrapolation technique. Then we apply our operator based interpolation scheme to compute sixth order accurate solution on the fine grid. Numerical experiments are conducted to show the solution accuracy and the computational efficiency of our new Method, compared to Sun-Zhang's sixth order Richardson extrapolation compact (REC) discretization strategy using Alternating Direction Implicit (ADI) Method and the standard fourth order compact difference (FOC) scheme using a Multigrid Method.

Yongbin Ge - One of the best experts on this subject based on the ideXlab platform.

Yin Wang - One of the best experts on this subject based on the ideXlab platform.

  • sixth order compact scheme combined with Multigrid Method and extrapolation technique for 2d poisson equation
    Journal of Computational Physics, 2009
    Co-Authors: Yin Wang, Jun Zhang
    Abstract:

    We develop a sixth order finite difference discretization strategy to solve the two dimensional Poisson equation, which is based on the fourth order compact discretization, Multigrid Method, Richardson extrapolation technique, and an operator based interpolation scheme. We use Multigrid V-Cycle procedure to build our multiscale Multigrid algorithm, which is similar to the full Multigrid Method (FMG). The Multigrid computation yields fourth order accurate solution on both the fine grid and the coarse grid. A sixth order accurate coarse grid solution is computed by using the Richardson extrapolation technique. Then we apply our operator based interpolation scheme to compute sixth order accurate solution on the fine grid. Numerical experiments are conducted to show the solution accuracy and the computational efficiency of our new Method, compared to Sun-Zhang's sixth order Richardson extrapolation compact (REC) discretization strategy using Alternating Direction Implicit (ADI) Method and the standard fourth order compact difference (FOC) scheme using a Multigrid Method.

Wolfgang A Wall - One of the best experts on this subject based on the ideXlab platform.