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.
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parallel Multigrid Method on multicore manycore clusters
IEEE International Conference on High Performance Computing Data and Analytics, 2020Co-Authors: Kengo NakajimaAbstract: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.
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Optimization of serial and parallel communications for parallel geometric Multigrid Method
2014 20th IEEE International Conference on Parallel and Distributed Systems (ICPADS), 2014Co-Authors: Kengo NakajimaAbstract: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.
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large scale simulations of 3d groundwater flow using parallel geometric Multigrid Method
Procedia Computer Science, 2013Co-Authors: Kengo NakajimaAbstract: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.
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openmp mpi hybrid parallel Multigrid Method on fujitsu fx10 supercomputer system
International Conference on Cluster Computing, 2012Co-Authors: Kengo NakajimaAbstract: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.
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OpenMP/MPI Hybrid Parallel Multigrid Method on Fujitsu FX10 Supercomputer System
2012 IEEE International Conference on Cluster Computing Workshops, 2012Co-Authors: Kengo NakajimaAbstract: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.
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Nonlinear Multigrid Method for solving the LLT model
Applied Mathematics and Computation, 2020Co-Authors: Jun Zhang, Yu-fei YangAbstract: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.
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a transformation free hoc scheme and Multigrid Method for solving the 3d poisson equation on nonuniform grids
Journal of Computational Physics, 2013Co-Authors: Yongbin Ge, Jun ZhangAbstract: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.
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sixth order compact scheme combined with Multigrid Method and extrapolation technique for 2d poisson equation
Journal of Computational Physics, 2009Co-Authors: Yin Wang, Jun ZhangAbstract: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.
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a transformation free hoc scheme and Multigrid Method for solving the 3d poisson equation on nonuniform grids
Journal of Computational Physics, 2013Co-Authors: Yongbin Ge, Jun ZhangAbstract: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.
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A High Order Compact Difference Scheme and Multigrid Method for Solving the 3D Convection Diffusion Equation on Non-uniform Grids
2012 Fourth International Conference on Computational and Information Sciences, 2012Co-Authors: Yongbin GeAbstract:A high order compact (HOC) difference scheme is proposed to solve the 3D convection diffusion equation on non-uniform Cartesian grids involving no transformation from the physical space to the computational space. A Multigrid Method based on this HOC scheme is developed to solve the linear system arising from the difference equation. Numerical experiments about a boundary layer problem are conducted to show the computed accuracy of the HOC scheme and the computational efficiency of the Multigrid Method.
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Multigrid Method based on the transformation free hoc scheme on nonuniform grids for 2d convection diffusion problems
Journal of Computational Physics, 2011Co-Authors: Yongbin GeAbstract:In this paper, a Multigrid Method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for steady convection-diffusion on non-uniform grids, Int. J. Numer. Methods Fluids 44 (2004) 33-53], is proposed to solve the two-dimensional (2D) convection diffusion equation. The HOC scheme is not involved in any grid transformation to map the nonuniform grids to uniform grids, consequently, the Multigrid Method is brand-new for solving the discrete system arising from the difference equation on nonuniform grids. The corresponding Multigrid projection and interpolation operators are constructed by the area ratio. Some boundary layer and local singularity problems are used to demonstrate the superiority of the present Method. Numerical results show that the Multigrid Method with the HOC scheme on nonuniform grids almost gets as equally efficient convergence rate as on uniform grids and the computed solution on nonuniform grids retains fourth order accuracy while on uniform grids just gets very poor solution for very steep boundary layer or high local singularity problems. The present Method is also applied to solve the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation and the numerical solutions of the lid-driven cavity flow problem are obtained and compared with solutions available in the literature.
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Multigrid Method and fourth order compact difference discretization scheme with unequal meshsizes for 3d poisson equation
Journal of Computational Physics, 2010Co-Authors: Yongbin GeAbstract:A fourth-order compact difference discretization scheme with unequal meshsizes in different coordinate directions is employed to solve a three-dimensional (3D) Poisson equation on a cubic domain. Two multgrid Methods are developed to solve the resulting sparse linear systems. One is to use the full-coarsening Multigrid Method with plane Gauss-Seidel relaxation, which uses line Gauss-Seidel relaxation to compute each planewise solution. The other is to construct a partial semi-coarsening Multigrid Method with the traditional point or plane Gauss-Seidel relaxations. Numerical experiments are conducted to test the computed accuracy of the fourth-order compact difference scheme and the computational efficiency of the Multigrid Methods with the fourth-order compact difference scheme.
Yin Wang - One of the best experts on this subject based on the ideXlab platform.
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sixth order compact scheme combined with Multigrid Method and extrapolation technique for 2d poisson equation
Journal of Computational Physics, 2009Co-Authors: Yin Wang, Jun ZhangAbstract: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.
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an algebraic variational multiscale Multigrid Method for large eddy simulation of turbulent flow
Computer Methods in Applied Mechanics and Engineering, 2010Co-Authors: Volker Gravemeier, Martin Kronbichler, Wolfgang A WallAbstract:An algebraic variational multiscale–Multigrid Method for large eddy simulation of turbulent flow