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2005 Fiscal Year Final Research Report Summary

Unstructured Multi-Grid method and the efficient implementation technique on parallel machines

Research Project

Project/Area Number 15607005
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 計算科学
Research InstitutionUniversity of Tokyo

Principal Investigator

OYANAGI Yoshio  The University of Tokyo, Graduate School of Information Science and Technology, Professor, 大学院・情報理工学系研究科, 教授 (60011673)

Co-Investigator(Kenkyū-buntansha) SUDA Reiji  The University of Tokyo, Graduate School of Information Science and Technology, Associate Professor, 大学院・情報理工学系研究科, 助教授 (40251392)
NISHIDA Akira  The University of Tokyo, Graduate School of Information Science and Technology, Research Associate, 大学院・情報理工学系研究科, 助手 (60302808)
Project Period (FY) 2003 – 2005
KeywordsLinear Equation / Multi-Grid method / Conjugate Gradient Method / Preconditioning / Parallelization / Vectorization / Load balance / Network
Research Abstract

Efficient preconditioning for Conjugate Gradient method requires parallelization and good acceleration of convergence. These two things are often incompatible. Thus, the authors proposed the Multi-Grid preconditioning, which satisfies both of two things, and have demonstrated the efficiency of the method.
In this study, we considered the problems with unstructured grids and with a big anisotropy. SA-AMG method, which is one of the multi-grid methods, calculates the smaller matrix and reaches the convergence efficiently utilizing that smaller matrix. But the SA-AMG method's efficiency deteriorates for anisotropic problems. The authors have shown that the smaller matrix creation method based on domain border information enables the method efficient convergence.
We also studied the vectorization of the SA-AMG method for the implementation technique. Three matrix multiplications occupy the most calculation cost. For vectorization of this part, we tested various combinations of sparse matrix … More data structures and demonstrated the method based on the JDS and the CRS data structures is the most efficient for 3-Dimentional elastic problems. For another related study of the implementation technique, the authors created the re-distribution and re-ordering library for distributed sparse matrix. This library offers the frame work of the dynamic re-distribution and re-ordering, and enables those things easily.
For other study of basic parallel implementation technique, the authors have studied the redistribution scheduling problem for finite sized multi-master divisible load problem. By identification of some parameters the authors showed that the simulation duplicates the behavior of the real system. We have also studied data distribution problem of the parallel molecular dynamics, and researched the best data distribution method in the case that the communication band-width and latency between computer nodes are not uniform. It is a challenge for the future to apply these basic techniques for parallel implementation of multi-grid method on various computer platforms. Less

  • Research Products

    (33 results)

All 2005 2004 2003

All Journal Article (33 results)

  • [Journal Article] Evaluation of Parallel Aggregate Creation Orders : Smoothed Aggregation Algebraic Multigrid Method2005

    • Author(s)
      A.Fujii, A.Nishida, Y.Oyanagi
    • Journal Title

      IFIP International Federation for Information Processing 172

      Pages: 99-122

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Parallel Matrix Distribution Library for Sparse Matrix Solvers2005

    • Author(s)
      A.Fujii, R.Suda, A.Nishida
    • Journal Title

      Proceedings of The 8th International Conference on High Performance Computing in Asia Pacific Region (HPC Asia 2005)

      Pages: 213-219

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Multi-master divisible loadの漸近最適スケジューリングの実機への実装2005

    • Author(s)
      富さやか, 須田礼仁
    • Journal Title

      社団法人情報処理学会研究報告 HPC 103(7) IPSJ SIG Technical lReport

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Multi-master divisible loadモデルに対する漸近最適スケジューリングの評価2005

    • Author(s)
      富さやか, 須田礼仁
    • Journal Title

      社団法人情報処理学会研究報告HPC HPC 102(9) IPSJ SIG Technical lReport 2005(57)

      Pages: 51-62

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] 2次元列ベース分割によるヘテロ型クラスタのためのLU分解2005

    • Author(s)
      三森 慶卓, 須田 礼仁
    • Journal Title

      社団法人情報処理学会研究報告 HPC 103(22) IPSJ SIG Technical lReport

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] ヘテロ型クラスタのための2次元列ベース分割における通信スケジューリングと分割の最適化2005

    • Author(s)
      三森 慶卓, 須田 礼仁
    • Journal Title

      社団法人情報処理学会研究報告 HPC 102(10) IPSJ SIG Technical lReport

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Network-aware Data Mapping on Parallel Molecular Dynamics2005

    • Author(s)
      Y.Hourai, A.Nishida, Y.Oyanagi
    • Journal Title

      Proc. Of 11^<th> International Conference on Parallel and Distributed Systems (ICPAD2005)

      Pages: 126-132

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] The Multi-Grid Preconditioned Conjugate Gradient Method2005

    • Author(s)
      Y.Oyanagi
    • Journal Title

      2005 International Conference on Scientific Computing and Differential Equations (SciCADE2005)

      Pages: 6

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] AMG Preconditioned Conjugate Gradient Type Methods for Nonsymmetric Eigenproblems2005

    • Author(s)
      西田 晃
    • Journal Title

      Twelfth Copper Mountain Conference on Multigrid Methods

      Pages: 30

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Evaluation of Parallel Aggregate Creation Orders : Smoothed Aggregation Algebraic Multigrid Method2005

    • Author(s)
      A.Fujii, A.Nishida, Y.Oyanagi
    • Journal Title

      IFIP International Federation for Information Processing (Springer) Vol.172

      Pages: 99-122

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Asymptotically optimum scheduling of multi-master divisible load problems evaluated on actual machines2005

    • Author(s)
      S.Tomi, R.Suda
    • Journal Title

      IPSJ SIG Technical Report HPC 103(7)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Evaluation of asymptotically optimum scheduling algorithms for multi-master divisible load model2005

    • Author(s)
      S.Tomi, R.Suda
    • Journal Title

      IPSJ SIG Technical Report HPC 102(9)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] LU Decomposition for Heterogeneous Clusters Using Two-Dimensional Column-Based Data Distributional Column-Based Data Distribution2005

    • Author(s)
      Y.Mimori, R.Suda
    • Journal Title

      IPSJ SIG Technical Report HPC 103(22)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Scheduling of Communication and Optimization of Data Distribution on Two-Dimensional Column-Based Distribution for Heterogeneous Clusters2005

    • Author(s)
      Y.Mimori, R.Suda
    • Journal Title

      IPSJ SIG Technical Report HPC 102(10)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Network-aware Data Mapping on Parallel Molecular Dynamics2005

    • Author(s)
      Y.Hourai, A.Nishida, Y.Oyanagi
    • Journal Title

      Proceedings Of 11th International Conference on Parallel and Distributed Systems (ICPAD2005)

      Pages: 126-132

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] The Multi-Grid Preconditioned Conjugate Gradient Method2005

    • Author(s)
      Y.Oyanagi
    • Journal Title

      International Conference on Scientific Computing and Differential Equations (SciCADE2005)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] AMG Preconditioned Conjugate Gradient Type Methods for Nonsymmetric Eigenproblems2005

    • Author(s)
      A.Nishida
    • Journal Title

      Twelfth Copper Mountain Conference on Multigrid Methods April

      Pages: 3-8

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Vectorized Algebraic Multigrid Algorithm for Unstructured Finite Element Problems.2004

    • Author(s)
      A.Fujii, A.Nishida, Y.Oyanagi.
    • Journal Title

      Proceedings of 6th International Meeting on High Performance Computing for Computational Science (VECPAR2004), Poster Presentation, June 28-30, Valencia.

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] The Evaluation of The Aggregate Creation Orders : Smoothed Aggregation Algebraic MultiGrid Method.2004

    • Author(s)
      A.Fujii, A.Nishida, Y.Oyanagi.
    • Journal Title

      Proceedings of International Symposium on High Performance Computational Science and Engineering (HPCSE-04) (CDROM)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Optimal Broadcast Scheduling on Tree-structured Networks2004

    • Author(s)
      Y.Hourai, A.Nishida, Y.Oyanagi
    • Journal Title

      IPSJ Transactions on Advanced Computing Systems Vol. 44, No. SIG3

      Pages: 100-108

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] 非線形最適化問題としての固有値解法 : 最適化手法の適用と評価2004

    • Author(s)
      西田 晃
    • Journal Title

      2004年日本応用数理学会年会予稿集

      Pages: 220-221

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] 大規模固有値問題への並列AMG前処理付共役勾配法の適用と評価2004

    • Author(s)
      西田 晃
    • Journal Title

      情報処理学会研究報告 2004(20)

      Pages: 205-210

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] 非対称固有値問題への並列AMG前処理付共役勾配法の適用と評価2004

    • Author(s)
      西田 晃
    • Journal Title

      情報処理学会研究報告 2004(81)

      Pages: 85-90

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Vectorized Algebraic Multigrid Algorithm for Unstructured Finite Element Problems2004

    • Author(s)
      A.Fujii, A.Nishida, Y.Oyanagi
    • Journal Title

      Proceedings of 6th International Meeting on High Performance Computing for Computational Science (VECPAR2004), Poster Presentation, June (Valencia)

      Pages: 28-30

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] The Evaluation of The Aggregate Creation Orders : Smoothed Aggregation Algebraic MultiGrid Method2004

    • Author(s)
      A.Fujii, A.Nishida, Y.Oyanagi
    • Journal Title

      Proceedings of International Symposium on High Performance Computational Science and Engineering (HPCSE-04) (CDROM)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Eigenvalue Problems as Nonlinear Optimization : Application and Evaluation of Optimization Methodologies2004

    • Author(s)
      A.Nishda
    • Journal Title

      Proceedings of the 2004 annual conference of the Japan Society for Industrial Applied Mathematics

      Pages: 220-221

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Performance Evaluation of Parallel AMG Preconditioned Conjugate Gradient Methods for Large Scale Eigenproblems2004

    • Author(s)
      A.Nishda
    • Journal Title

      IPSJ SIG Notes 2004(20)

      Pages: 205-210

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Parallel AMG Preconditioned Conjugate Residual Methods for Nonsymmetric Eigenproblems and its Evaluation2004

    • Author(s)
      A.Nishda
    • Journal Title

      IPSJ SIG Notes (in Japanese) 2004(81)

      Pages: 85-90

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Optimal Broadcast Scheduling on Tree-structured Networks2004

    • Author(s)
      Y.Hourai, A.Nishida, Y.Oyanagi
    • Journal Title

      IPSJ Transactions on Advanced Computing and Systems. Vol.44, No.SIG3

      Pages: 100-108

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Smoothed Aggregation MG法の異方性問題への対応と評価2003

    • Author(s)
      A.Fujii, A.Nishida, Y.Oyanagi.
    • Journal Title

      先進的計算基盤システムシンポジウム(SACSIS2003),

      Pages: 137-144

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] 大規模固有値問題への前処理付共役勾配法の適用と評価2003

    • Author(s)
      西田 晃
    • Journal Title

      2003年日本応用数理学会年会予稿集

      Pages: 326-327

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Improvement evaluation of Smoothed Aggregation MG for anisotropic problems2003

    • Author(s)
      A.Fujii, A.Nishida, Y.Oyanagi
    • Journal Title

      Proceedings of Symposium on Advanced Computing Systems Infrastructures

      Pages: 137-144

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A Short Survey of Applications and Evaluations of Preconditioned Conjugate Gradient Method for Large Scale Eigenvalue Problems2003

    • Author(s)
      A.Nishida
    • Journal Title

      Proceedings of the 2003 annual conference of the Japan Society for Industrial Applied Mathematics

      Pages: 326-327

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2007-12-13  

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