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High performance linear solver for advanced computational electromagnetics

Research Project

Project/Area Number 19H04122
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Review Section Basic Section 60100:Computational science-related
Research InstitutionHokkaido University

Principal Investigator

IWASHITA TAKESHI  北海道大学, 情報基盤センター, 教授 (30324685)

Co-Investigator(Kenkyū-buntansha) 塙 敏博  東京大学, 情報基盤センター, 教授 (30308283)
伊田 明弘  国立研究開発法人海洋研究開発機構, 付加価値情報創生部門(地球情報基盤センター), 副主任研究員 (80742121)
美舩 健  京都大学, 工学研究科, 講師 (20362460)
高橋 康人  同志社大学, 理工学部, 教授 (90434290)
深谷 猛  北海道大学, 情報基盤センター, 助教 (30633846)
Project Period (FY) 2019-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥16,510,000 (Direct Cost: ¥12,700,000、Indirect Cost: ¥3,810,000)
Fiscal Year 2021: ¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
Fiscal Year 2020: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2019: ¥5,980,000 (Direct Cost: ¥4,600,000、Indirect Cost: ¥1,380,000)
Keywords高性能計算 / 計算電磁気学 / 線形反復法 / 混合精度演算 / 時間並列処理 / H行列 / 計算科学 / 並列処理 / 電磁場解析 / 非定常解析 / 非線形解析 / 階層型行列 / 有限要素法
Outline of Research at the Start

本研究では,計算電磁気学の深化に必要となる高性能な線形ソルバについて,計算機科学的側面と数理的側面の両面から,研究開発する.計算機科学的側面では,① 次世代計算機上の電磁場解析向けソルバ技術として,(a) 時空間並列処理技術の高度化 (b) 線形反復ソルバにおけるSIMD命令,アクセラレータ活用技術の開発 (c) 低精度演算の活用による線形ソルバ,階層型行列法の高性能化 に取り組む.また,数理的側面では,電磁場解析において未解決問題となっている,② 線形反復法の収束性悪化問題への対策 について研究開発する.最終的に,研究成果を電磁場解析に導入し,計算電磁気学の深化を導く

Outline of Final Research Achievements

In this study, we studied the acceleration of the linear solver to make the electromagnetic field analysis based on the finite element and the boundary element methods more efficiently. Research was conducted from both the computer science and the mathematical approaches. From the computer science side, we studied the parallel in time technique, the preconditioning techniques in which SIMD instructions or accelerators are effectively used. We also studied the mixed precision computing in the context of iterative linear solvers. From the mathematical side, we focused on the situation in which a sequence of linear systems was solved. We proposed a technique based on error vector sampling and confirmed its effectiveness. In these studies, we attained many research results which were reported in journals and conferences.

Academic Significance and Societal Importance of the Research Achievements

現代社会では,社会のあらゆる場面で電気機器や電子デバイスが重要な役割を果たしている.このような機器・デバイスの設計には,電磁場解析が用いられ,それを高速化することは,機器設計の効率化に寄与する.本研究では,SIMD演算や混合精度演算の利用といった計算機科学的アプローチと誤差修正法や減次法といった数理・解法的アプローチの両面から研究を行い,電磁場解析の高速化に貢献する線形ソルバの高速化技術を開発した.

Report

(4 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • Research Products

    (34 results)

All 2022 2021 2020 2019

All Journal Article (5 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 5 results,  Open Access: 3 results) Presentation (29 results) (of which Int'l Joint Research: 12 results)

  • [Journal Article] Comparison of Parallel-in-Space-and-Time Finite-Element Methods for Magnetic Field Analysis of Electric Machines2021

    • Author(s)
      Yasuhito Takahashi, Koji Fujiwara, Takeshi Iwashita, and Hiroshi Nakashima
    • Journal Title

      IEEE Transactions on Magnetics

      Volume: 57 Issue: 6 Pages: 1-4

    • DOI

      10.1109/tmag.2021.3064320

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Hierarchical block multi-color ordering: a new parallel ordering method for vectorization and parallelization of the sparse triangular solver in the ICCG method2020

    • Author(s)
      Iwashita Takeshi, Li Senxi, Fukaya Takeshi
    • Journal Title

      CCF Transactions on High Performance Computing

      Volume: 2 Issue: 2 Pages: 84-97

    • DOI

      10.1007/s42514-020-00030-z

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Lattice H-matrices for Massively Parallel Micromagnetic Simulations of Current-induced Domain Wall Motion2020

    • Author(s)
      Akihiro Ida, Tadashi Ataka, Atsushi Furuya
    • Journal Title

      IEEE Transactions on Magnetics

      Volume: 56(4) Issue: 4 Pages: 1-4

    • DOI

      10.1109/tmag.2019.2959349

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Parallel TP-EEC Method based on Polyphase Time-periodic Condition for Magnetic Field Analysis of Induction Motors2019

    • Author(s)
      Yasuhito Takahashi , Koji Fujiwara , Tadashi Tokumasu, Takeshi Iwashita , and Hiroshi Nakashima
    • Journal Title

      IEEE Transactions on Magnetics

      Volume: 56 Issue: 3 Pages: 7511305-7511305

    • DOI

      10.1109/tmag.2019.2950100

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] QR Factorization of Block Low-rank Matrices with Weak Admissibility Condition2019

    • Author(s)
      Akihiro Ida, Hiroshi Nakashima, Tasuku Hiraishi, Ichitaro Yamazaki, Rio Yokota, Takeshi Iwashita
    • Journal Title

      Journal of Information Processing

      Volume: 27 Issue: 0 Pages: 831-839

    • DOI

      10.2197/ipsjjip.27.831

    • NAID

      130007762323

    • ISSN
      1882-6652
    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] Performance Evaluation of Parallel-in-Space-and-Time Finite-Element Analysis of Electric Machines based on Domain Decomposition and Parallel TP-EEC Method in Massively Parallel Computing Environment2022

    • Author(s)
      Y. Takahashi, K. Fujiwara, and T. Iwashita
    • Organizer
      the 23rd International Conference on the Computation of Electromagnetic Fields (COMPUMAG 2021)
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Parallelization of Matrix Partitioning in Hierarchical Matrix Construction Using Node-aware Work Stealing2022

    • Author(s)
      Zhengyang Bai、Tasuku Hiraishi、Akihiro Ida、Masahiro Yasugi
    • Organizer
      情報処理学会 第138回プログラミング研究発表会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Numerical Evaluation of Dynamic Core Binding Library with H-matrix Application2022

    • Author(s)
      Masatoshi Kawai, Akihiro Ida
    • Organizer
      2022 Conference on Advanced Topics and Auto Tuning in High-Performance Scientific Computing
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Optimizations of Lattice H-Matrix-Vector Multiplication for Modern Supercomputers2022

    • Author(s)
      Tetsuya Hoshino, Akihiro Ida, Toshihiro Hanawa
    • Organizer
      SIAM Conference on Parallel Processing for Scientific Computing (PP22)
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Offloading Integer GMRES Method to Accelerators2022

    • Author(s)
      Yijie Yu, Toshihiro Hanawa
    • Organizer
      HPC Asia 2022
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Algebraic Auxiliary Matrix Construction for Subspace Correction and Deflation based on Error Vector Sampling for a Sequence of Linear Systems2022

    • Author(s)
      Takeshi Iwashita, Kota Ikehara and Takeshi Fukaya
    • Organizer
      SIAM Conference on Parallel Processing and Scientific Computing
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Algebraic Auxiliary Matrix Construction for Subspace Correction and Deflation in Solving a Series of Linear Systems2022

    • Author(s)
      Takeshi Iwashita
    • Organizer
      1st Advanced Supercomputing Environment (ASE) Seminar: Ode to Numerical Linear Algebra
    • Related Report
      2021 Annual Research Report
  • [Presentation] ブロック低ランク行列の近似固有値計算2021

    • Author(s)
      伊田明弘
    • Organizer
      日本応用数理学会(2021年度年会)
    • Related Report
      2021 Annual Research Report
  • [Presentation] 低精度演算を活用したGMRES(m)法の研究2021

    • Author(s)
      深谷猛, Yingqi Zhao, 岩下武史
    • Organizer
      第13回 自動チューニング技術の現状と応用に関するシンポジウム
    • Related Report
      2021 Annual Research Report
  • [Presentation] 誤差ベクトルのサンプリングに基づくSubspace CorrectionおよびDeflationによる前処理付きCGソルバの収束性改善2021

    • Author(s)
      池原紘太, 深谷猛, 岩下武史
    • Organizer
      日本応用数理学会 「行列・固有値問題の解法とその応用」研究部会 第32回研究会
    • Related Report
      2021 Annual Research Report
  • [Presentation] 気象雷モデルでの数値予報に向けたモデル改良の取り組み2021

    • Author(s)
      佐藤陽祐, 林修吾, 橋本明弘, 岩下武史
    • Organizer
      日本気象学会2021年度秋季大会
    • Related Report
      2021 Annual Research Report
  • [Presentation] GPU に適した近似逆行列前処理の簡略化手法2021

    • Author(s)
      鈴木謙吾, 深谷猛, 岩下武史
    • Organizer
      日本応用数理学会2021年度年会
    • Related Report
      2021 Annual Research Report
  • [Presentation] GMRES(m) 法に対する低精度演算・データの積極的導入の可能性に関する検証2021

    • Author(s)
      深谷猛, 岩下武史
    • Organizer
      日本応用数理学会2021年度年会
    • Related Report
      2021 Annual Research Report
  • [Presentation] 最近のマルチコアCPU環境における疎行列ベクトル積の性能に関する一考察2021

    • Author(s)
      深谷猛, 岩下武史, 中島浩
    • Organizer
      2021年並列/分散/協調処理に関するサマー・ワークショップ (SWoPP2021) / 日本応用数理学会 「行列・固有値問題の解法とその応用」研究部会 (MEPA)
    • Related Report
      2021 Annual Research Report
  • [Presentation] HBMC Ordering for SIMD Vectorization of IC Preconditioning2021

    • Author(s)
      Takeshi Iwashita and Takeshi Fukaya
    • Organizer
      International Workshop on the Integration of (Simulation+Data+Learning); Towards Society 5.0 by h3-Open-BDEC
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Exploiting Lower Precision Computing in the GMRES(m) Method2021

    • Author(s)
      Takeshi Fukaya, Yingqi Zhao and Takeshi Iwashita
    • Organizer
      SIAM Conference on Applied Linear Algebra (LA21)
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 近似逆行列前処理における前処理行列生成部の簡略化とスレッド並列化2021

    • Author(s)
      鈴木謙吾, 深谷猛, 岩下武史
    • Organizer
      第182回HPC研究会
    • Related Report
      2021 Annual Research Report
  • [Presentation] SIMD演算に適したブロック構造を有する新しいILU分解前処理手法2021

    • Author(s)
      鈴木謙吾, 深谷猛, 岩下武史
    • Organizer
      The 5th cross-disciplinary Workshop on Computing Systems, Infrastructures, and Programming (xSIG2021)
    • Related Report
      2021 Annual Research Report
  • [Presentation] 領域分割と並列TP-EEC法に基づく 空間分割・時間分割併用型並列有限要素法を用いた大規模磁界解析の 高並列計算環境下での性能評価2021

    • Author(s)
      髙橋康人,藤原耕二,岩下武史
    • Organizer
      電気学会静止器・回転機合同研究会
    • Related Report
      2020 Annual Research Report
  • [Presentation] GMRES(m)法における行列データの低精度化に関する検討2021

    • Author(s)
      深谷猛,岩下武史
    • Organizer
      日本応用数理学会 2021年研究部会連合発表会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Parallel-in-space-and-time Finite-element Analysis of Electric Machines using Domain Decomposition and Time-periodic Finite-element Method2020

    • Author(s)
      Yasuhito Takahashi, Koji Fujiwara and Takeshi Iwashita
    • Organizer
      19th IEEE Conference on Electromagnetic Field Computation (CEFC 2020)
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] ブロックに基づくfill-in選択手法を利用したILU-GMRESソルバ2020

    • Author(s)
      鈴木 謙吾,深谷猛,岩下武史
    • Organizer
      第177回HPC研究発表会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Automated Subspace Correction法を前処理とするCGソルバの開発と評価2020

    • Author(s)
      池原紘太,深谷猛,岩下武史
    • Organizer
      The 4th cross-disciplinary Workshop on Computing Systems, Infrastructures, and Programming (xSIG2020)
    • Related Report
      2020 Annual Research Report
  • [Presentation] 格子H行列法を用いた実アプリの分散メモリ並列化2020

    • Author(s)
      伊田明弘,安宅正,古屋篤史
    • Organizer
      2020年並列/分散/協調処理に関する『福井』サマー・ワークショップ
    • Related Report
      2020 Annual Research Report
  • [Presentation] Effect of Mixed Precision Computing on H-matrix Vector Multiplication in BEM Analysis2020

    • Author(s)
      Rise Ooi, Takeshi Iwashita, Takeshi Fukaya, Akihiro Ida and Rio Yokota
    • Organizer
      International Conference on High Performance Computing in Asia-Pacific Region (HPC Asia 2020)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Numerical Linear Algebra Based on Lattice H-Matrices2020

    • Author(s)
      Akihiro Ida, Ichitaro Yamazaki, Rio Yokota, Satoshi Ohshima, Tasuku Hiraishi, Takeshi Iwashita, Tetsuya Hoshino and Toshihiro Hanawa
    • Organizer
      International Conference on High Performance Computing in Asia-Pacific Region (HPC Asia 2020)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 倍精度と単精度を用いた混合精度GMRES(m)法の収束性に関する実験的評価2019

    • Author(s)
      深谷猛, グドール聖哉, 張臨傑, 岩下武史
    • Organizer
      日本応用数理学会2019年度年会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Parallel TP-EEC Method based on Polyphase Time-periodic Condition for Magnetic Field Analysis of Induction Motors2019

    • Author(s)
      Yasuhito Takahashi, Koji Fujiwara, Tadashi Tokumasu, Takeshi Iwashita, Hiroshi Nakashima
    • Organizer
      The 22nd International Conference on the Computation of Electromagnetic Fields (COMPUMAG2019)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Lattice H-matrices for Massively Parallel Micromagnetic Simulations of Current-induced Domain Wall Motion2019

    • Author(s)
      Akihiro Ida, Tadashi Ataka and Atsushi Furuya
    • Organizer
      The 22nd International Conference on the Computation of Electromagnetic Fields (COMPUMAG2019)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research

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Published: 2019-04-18   Modified: 2023-01-30  

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