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2010 Fiscal Year Annual Research Report

有限節点法,境界節点法の完全メッシュレス化とその工学的応用

Research Project

Project/Area Number 22360042
Research InstitutionTokyo University of Technology

Principal Investigator

生野 壮一郎  東京工科大学, コンピュータサイエンス学部, 准教授 (70318864)

Co-Investigator(Kenkyū-buntansha) 神谷 淳  山形大学, 大学院・理工学研究科, 教授 (00224668)
齋藤 歩  兵庫県立大学, 大学院・工学研究科, 助教 (20400533)
伊東 拓  成蹊大学, 理工学部, 助教 (80433853)
多田野 寛人  筑波大学, 大学院・システム情報工学研究科, 助教 (50507845)
Keywordsメッシュレス法 / 陰関数曲面 / 数理工学 / シミュレーション工学 / ペナルティ法 / ラグランジェ未定乗数法
Research Abstract

本研究の目的は,境界形状の表現と補間関数の構成を要素から完全に切り離すことによって,要素の概念を全く用いないメッシュレス法を開発することである.本年度は,有限節点法と境界節点法に関して,次の研究成果を得た.
1)EFG法やMLPG法等の有限節点法では,従来,Lagrange未定乗数法やペナルティ法を用いて基本境界条件を弱形式の中に組み込んでいた.本年度の研究では,Lagrange未定乗数法やペナルティ法を全く介さないで,有限節点法を定式化することに成功した.それ故,試験関数と試行関数の選択方法として,Galerkin法だけでなくPetrov-Galerkin法も採用できるようになった.また,基本境界条件を実装する手法として,Lagrange補間関数を用いる従来法だけでなく,選点法も採用した.その結果,4種類の有限節点法を導くことに成功した.さらに,4種類の解法に基づいて2次元Poisson問題を解くための数値コードを開発し,同コードを用いて解法の精度を数値的に検証した.
2)3次元完全境界節点法によってLaplace問題を解くための数値コードを開発した.さらに,同コードの高速化を目指して,影響係数を計算するための効率的アルゴリズムを開発した.その結果,完全境界節点法に要するCPU時間を境界要素法の4倍にまで短縮することに成功した.また,両法が示す解の精度が同程度であることが判明した.
一方,現時点の完全有限節点法で離散化すると,混合型境界値問題は必ず非対称疎行列をもつ連立1次方程式に帰着する.これはNeumann境界条件を含む場合に,完全有限節点法はCPU時間をむやみに浪費することを意味する.そこで,混合型境界値問題からも対称疎係数行列が生み出されるように,完全有限節点法の定式化を修正する必要がある.この問題を次年度の研究課題の1つとする.

  • Research Products

    (61 results)

All 2011 2010

All Journal Article (28 results) (of which Peer Reviewed: 28 results) Presentation (33 results)

  • [Journal Article] Parallel Algorithm for Meshfree Radial Point Interpolation Method on Graphics Hardware2011

    • Author(s)
      S.Nakata, S.Ikuno
    • Journal Title

      IEEE Trans.Magn.

      Volume: Vol.47 Pages: 1206-1209

    • DOI

      10.1109/TMAG.2010.2091110

    • Peer Reviewed
  • [Journal Article] High Performance Iterative Solver for Linear System using Multi GPU2011

    • Author(s)
      S.Ikuno, T.Itoh
    • Journal Title

      Plasma and Fusion Research

      Volume: (in press)

    • Peer Reviewed
  • [Journal Article] Numerical investigations on contactless methods for measuring critical current density in HTS : application of modified constitutive-relation method2011

    • Author(s)
      A.Kamitani, S.Ikuno
    • Journal Title

      PHYSICA C

      Volume: (in press)

    • Peer Reviewed
  • [Journal Article] High-Speed Method for Analyzing Shielding Current Density in High-Temperature Superconductor2011

    • Author(s)
      A.Kamitani, S.Ikuno
    • Journal Title

      IEEE TRANS.MAGN.

      Volume: (in press)

    • Peer Reviewed
  • [Journal Article] Development of Two-Dimensional Meshless Approaches without Using Integration Cells2011

    • Author(s)
      A.Saitoh, T.Itoh, A.Kamitani
    • Journal Title

      IEEE TRANS.MAGN.

      Volume: (in press)

    • Peer Reviewed
  • [Journal Article] High-Performance Simulation of Shielding Current Density in HTS by Constitutive-Relation Relaxation Method2011

    • Author(s)
      A.Kamitani, S.Ikuno
    • Journal Title

      IEEE TRANS.APPL.SUPERCOND.

      Volume: (in press)

    • Peer Reviewed
  • [Journal Article] Numerical Investigations on Applicability of Inductive Method/Permanent Magnet Method to j_c-Measurement in HTS Thin Film2011

    • Author(s)
      T.Takayama, A.Kamitani
    • Journal Title

      IEEE TRANS.APPL.SUPERCOND.

      Volume: (in press)

    • Peer Reviewed
  • [Journal Article] Numerical Investigations on Edge Effects of Shielding Current Density in HTS Thick Film2011

    • Author(s)
      S.Ikuno, A.Kamitani
    • Journal Title

      IEEE TRANS.APPL.SUPERCOND.

      Volume: (in press)

    • Peer Reviewed
  • [Journal Article] Detection of Critical Current Density Distribution of YBCO Coated Conductors by Permanent Magnet Method2011

    • Author(s)
      S.Ohshima, S.Ikuno, A.Kamitani
    • Journal Title

      IEEE TRANS.APPL.SUPERCOND.

      Volume: (in press)

    • Peer Reviewed
  • [Journal Article] Extension of Meshless Galerkin/Petrov-Galerkin Approach without Using Lagrange Multipliers2011

    • Author(s)
      A.Kamitani, T.Itoh
    • Journal Title

      Plasma and Fusion Research

      Volume: (in press)

    • Peer Reviewed
  • [Journal Article] New Implementation Method for Essential Boundary Condition to Extended Element-Free Galerkin Method : Application to Nonlinear Problem2011

    • Author(s)
      A.Saitoh, T.Itoh, A.Kamitani
    • Journal Title

      Plasma and Fusion Research

      Volume: (in press)

    • Peer Reviewed
  • [Journal Article] Efficient Evaluation of Influence Coefficients in Three-Dimensional Extended Boundary-Node Method for Potential Problems2011

    • Author(s)
      T.Itoh, A.Saitoh, A.Kamitani
    • Journal Title

      Plasma and Fusion Research

      Volume: (in press)

    • Peer Reviewed
  • [Journal Article] Numerical Investigation on Accuracy Improvement of Permanent Magnet Method for Measuring j_c in High-Temperature Superconducting Film2011

    • Author(s)
      T.Takayama, A.Kamitani
    • Journal Title

      Plasma and Fusion Research

      Volume: (in press)

    • Peer Reviewed
  • [Journal Article] Smoothing method of shape measurement for low-cost 3D-scanner2011

    • Author(s)
      H.Maruo, A.Saitoh
    • Journal Title

      Plasma and Fusion Research

      Volume: (in press)

    • Peer Reviewed
  • [Journal Article] Numerical simulation of permanent magnet method : Influence of experimental conditions on accuracy of j_c-distribution2010

    • Author(s)
      T.Takayama, A.Kamitani
    • Journal Title

      PHYSICA C

      Volume: 470 Pages: 1354-1357

    • Peer Reviewed
  • [Journal Article] Numerical simulation of inductive method for determining spatial distribution of critical current density2010

    • Author(s)
      A.Kamitani, S.Ikuno
    • Journal Title

      PHYSICA C

      Volume: 470 Pages: 1189-1192

    • Peer Reviewed
  • [Journal Article] Numerical Simulation of Permanent Magnet Method : Applicability to j_c-Measurement in HTS Thick Film2010

    • Author(s)
      T.Takayama, A.Kamitani
    • Journal Title

      IEEE TRANS.APPL.SUPERCOND.

      Volume: 20 Pages: 1021-1024

    • Peer Reviewed
  • [Journal Article] Weight Function Control of Moving Least-Squares Interpolants : Application to Axisymmetric Shielding Current Analysis in HTS2010

    • Author(s)
      S.Ikuno, A.Kamitani
    • Journal Title

      IEEE TRANS.MAGN.

      Volume: 46 Pages: 3097-3100

    • Peer Reviewed
  • [Journal Article] Novel Applications of Inductive Method for Measuring Critical Current Density2010

    • Author(s)
      A.Kamitani, S.Ikuno
    • Journal Title

      IEEE TRANS.MAGN.

      Volume: 46 Pages: 3073-3076

    • Peer Reviewed
  • [Journal Article] Application of Two Dimensional Extended Boundary Node Method to Potential Problem2010

    • Author(s)
      A.Saitoh, T.Itoh, A.Kamitani
    • Journal Title

      Plasma and Fusion Research

      Volume: 5 Pages: S2108

    • Peer Reviewed
  • [Journal Article] Three Dimensional Extended Boundary Node Method to Potential Problem2010

    • Author(s)
      T.Itoh, A.Saitoh, A.Kamitani
    • Journal Title

      Plasma and Fusion Research

      Volume: 5 Pages: S2111

    • Peer Reviewed
  • [Journal Article] High Performance Analysis of Shielding Current Density in High Temperature Superconducting Thin Film2010

    • Author(s)
      A.Kamitani
    • Journal Title

      Plasma and Fusion Research

      Volume: 5 Pages: S2112

    • Peer Reviewed
  • [Journal Article] Numerical Simulation of Contactless Methods for Measuring j_c Distribution of High Temperature Superconducting Thin Film2010

    • Author(s)
      T.Takayama, A.Kamitani
    • Journal Title

      Plasma and Fusion Research

      Volume: 5 Pages: S2113

    • Peer Reviewed
  • [Journal Article] Numerical Investigations of Variable Preconditioned GCR with Mixed Precision on GPU2010

    • Author(s)
      S.Ikuno
    • Journal Title

      Plasma and Fusion Research

      Volume: 5 Pages: S2115

    • Peer Reviewed
  • [Journal Article] A Block Sparse Approximate Inverse with Cutoff Preconditioner for Semi-Sparse Linear Systems Derived from Molecular Orbital Calculations2010

    • Author(s)
      I.Yamazaki, H.Tadano
    • Journal Title

      JSIAM Letters

      Volume: 2 Pages: 41-44

    • Peer Reviewed
  • [Journal Article] A Numerical Method for Polynomial Eigenvalue Problems Using Contour Integral2010

    • Author(s)
      J.Asakura, H.Tadano
    • Journal Title

      Japan J.Indust.Appl.Math.

      Volume: 27 Pages: 73-90

    • Peer Reviewed
  • [Journal Article] A Quadrature-Based Eigensolve with a Krylov Subspace Method for Shifted Linear Systems for Hermitian eigenproblems in Lattice QCD2010

    • Author(s)
      H.Ohno, H.Tadano
    • Journal Title

      JSIAM Letters

      Volume: 2 Pages: 115-118

    • Peer Reviewed
  • [Journal Article] Parallel Stocastic Estimation Method of Eigenvalue Distribution2010

    • Author(s)
      Y.Futamura, H.Tadano
    • Journal Title

      JSIAM Letters

      Volume: 2 Pages: 127-130

    • Peer Reviewed
  • [Presentation] Video Object Segmentation Using Color-Component-Selectable Learning for Self-Organizing Maps2011

    • Author(s)
      S.Umata, A.Saitoh
    • Organizer
      16th International Conference on Artificial Life and Robotics (AROB 16th'11)
    • Place of Presentation
      B-Con Plaza, Beppu, Oita, Japan
    • Year and Date
      20110127-20110129
  • [Presentation] Block BiCGSTAB法の安定化について2011

    • Author(s)
      多田野寛人
    • Organizer
      日本応用数理学会2011年研究部会連合発表会
    • Place of Presentation
      電気通信大学(東京都)
    • Year and Date
      2011-03-07
  • [Presentation] An Analysis on Image Recognition in Complex-Valued Synergetic Computers2010

    • Author(s)
      M.Kimura, A.Saitoh
    • Organizer
      Joint 5th Conference on Soft Computing and Intelligent Systems and 11th International Symposium on Advanced Intelligent Systems (SCIS & ISIS 2010)
    • Place of Presentation
      Okayama Convention Center, Okayama, Japan
    • Year and Date
      20101208-20101212
  • [Presentation] Performance Analysis of Quantum-Inspired Evolutionary Algorithm2010

    • Author(s)
      T.Takata, A.Saitoh
    • Organizer
      Joint 5th Conference on Soft Computing and Intelligent Systems and 11th International Symposium on Advanced Intelligent Systems (SCIS & ISIS 2010)
    • Place of Presentation
      Okayama Convention Center, Okayama, Japan
    • Year and Date
      20101208-20101212
  • [Presentation] On Selection of Intraocular Power Formula Based on Data Classification Using Self-organizing Maps2010

    • Author(s)
      N.Kamiura, H.Tadano
    • Organizer
      2010 IEEE International Conference on Systems, Man and Cybernetics (SMC2010)
    • Place of Presentation
      Istanbul, Turkey
    • Year and Date
      20101010-20101013
  • [Presentation] New Method for Implementing Essential Boundary Condition to Element-Free Galerkin Method2010

    • Author(s)
      A.Saitoh, T.Itoh, A.Kamitani
    • Organizer
      8th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM2010)
    • Place of Presentation
      Rhodes, Greece
    • Year and Date
      20100919-20100925
  • [Presentation] Energy Reduction Using Two Static Voltage Scheduling Approaches for Real-Time Multi-processor Systems2010

    • Author(s)
      N.Kamiura, H.Tadano
    • Organizer
      The First Russia and Pacific Conference on Computer Technology and Applications (RPC2010)
    • Place of Presentation
      Vladivostok, Russia
    • Year and Date
      20100906-20100909
  • [Presentation] Implementing Localization Scheme on ZigBee Wireless Sensor Network2010

    • Author(s)
      J.Ohtsuka, H.Tadano
    • Organizer
      SICE Annual Conference (SICE2010)
    • Place of Presentation
      Taipei, Taiwan
    • Year and Date
      20100818-20100821
  • [Presentation] Spatio-temporal characteristics of honeybee, apis cerana japonica, in shimmering behavior2010

    • Author(s)
      M.Hata, A.Saitoh
    • Organizer
      International Union for the Study of Social Insects (IUSSI2010)
    • Place of Presentation
      Copenhagen, Denmark
    • Year and Date
      20100808-20100814
  • [Presentation] Detection of Tumors on Stomach Wall in X-ray Images2010

    • Author(s)
      T.Minemoto, A.Saitoh
    • Organizer
      IEEE World Congress on Computational Intelligence (WCCI2010)
    • Place of Presentation
      Barcelona, Spain
    • Year and Date
      20100718-20100723
  • [Presentation] 構成方程式修正法による高温超伝導体内遮蔽電流密度解析2010

    • Author(s)
      神谷淳, 生野壮一郎
    • Organizer
      第19回MAGDAコンファレンスin札幌
    • Place of Presentation
      北海道大学学術交流会館(北海道)
    • Year and Date
      2010-11-23
  • [Presentation] EFG法を用いた超伝導内遮蔽電流密度シミュレーション2010

    • Author(s)
      生野壮一郎, 神谷淳
    • Organizer
      第19回MAGDAコンファレンスin札幌
    • Place of Presentation
      北海道大学学術交流会館(北海道)
    • Year and Date
      2010-11-23
  • [Presentation] Novel Numerical Method for Analyzing Shielding Current Density in Various Shaped HTS2010

    • Author(s)
      S.Ikuno, A.Kamitani
    • Organizer
      23^<rd> International Symposium on Superconductivity
    • Place of Presentation
      エポカル筑波(茨城県)
    • Year and Date
      2010-11-03
  • [Presentation] Numerical Simulation of Permanent Magnet Method for Measuring Critical Current Density of HTS Thin Film : Influence of Crack on Accuracy2010

    • Author(s)
      T.Takayama, A.Kamitani
    • Organizer
      23^<rd> International Symposium on Superconductivity
    • Place of Presentation
      エポカル筑波(茨城県)
    • Year and Date
      2010-11-03
  • [Presentation] 可変的前処理付き反復法のGPUによる高速化とそのWebアプリケーション2010

    • Author(s)
      生野壮一郎, 伊東拓
    • Organizer
      静止器/回転機合同研究会
    • Place of Presentation
      かごしま県民交流センター,(鹿児島県)
    • Year and Date
      2010-09-28
  • [Presentation] Web Application for Evaluating Performance of Linear System Solver Using GPU2010

    • Author(s)
      S.Ikuno, T.Itoh
    • Organizer
      8th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM2010)
    • Place of Presentation
      Rhodes, Greece
    • Year and Date
      2010-09-20
  • [Presentation] Generation of a Smooth Implicit Function Distributed Over the Entire Domain from Large Scattered Point Data2010

    • Author(s)
      T.Itoh, A.Saitoh, A.Kamitani
    • Organizer
      8th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM2010)
    • Place of Presentation
      Rhodes, Greece
    • Year and Date
      2010-09-19
  • [Presentation] 多層型高温超伝導体内の遮蔽電流密度解析2010

    • Author(s)
      高山彰優, 神谷淳
    • Organizer
      第4回シミュレーション科学シンポジウム
    • Place of Presentation
      核融合科学研究所(岐阜県)
    • Year and Date
      2010-09-14
  • [Presentation] 3次元拡張境界節点法のための全領域で定義される陰関数生成2010

    • Author(s)
      伊東拓, 齋藤歩, 神谷淳
    • Organizer
      第4回シミュレーション科学シンポジウム
    • Place of Presentation
      核融合科学研究所(岐阜県)
    • Year and Date
      2010-09-14
  • [Presentation] RBF法より得られる連立1次方程式の可変的前処理付き反復法の数値的評価とGPUによる高速化2010

    • Author(s)
      生野壮一郎, 伊東拓
    • Organizer
      第4回シミュレーション科学シンポジウム
    • Place of Presentation
      核融合科学研究所(岐阜県)
    • Year and Date
      2010-09-14
  • [Presentation] 修正構成方程式法による高温超伝導体内遮蔽電流密度解析2010

    • Author(s)
      神谷淳
    • Organizer
      第4回シミュレーション科学シンポジウム
    • Place of Presentation
      核融合科学研究所(岐阜県)
    • Year and Date
      2010-09-14
  • [Presentation] 多層型高温超伝導体内の遮蔽電流密度解析2010

    • Author(s)
      高山彰優, 神谷淳
    • Organizer
      日本応用数理学会
    • Place of Presentation
      明治大学駿河台キャンパス(東京都)
    • Year and Date
      2010-09-09
  • [Presentation] エレメントフリーガラーキン法によるGPUにおける高速化2010

    • Author(s)
      柳沢洋平, 伊東拓
    • Organizer
      日本応用数理学会
    • Place of Presentation
      明治大学駿河台キャンパス(東京都)
    • Year and Date
      2010-09-07
  • [Presentation] RBF法から得られる連立1次方程式の反復解法の数値的評価2010

    • Author(s)
      川口優樹, 生野壮一郎
    • Organizer
      日本応用数理学会
    • Place of Presentation
      明治大学駿河台キャンパス(東京都)
    • Year and Date
      2010-09-07
  • [Presentation] Webアプリケーションを用いた並列処理付き多倍長演算線形方程式解法システム2010

    • Author(s)
      橋野隆弘, 生野壮一郎
    • Organizer
      日本応用数理学会
    • Place of Presentation
      明治大学駿河台キャンパス(東京都)
    • Year and Date
      2010-09-07
  • [Presentation] 近似解の精度劣化を回避するBlock積型Krylov部分空間反復法について2010

    • Author(s)
      多田野寛人
    • Organizer
      日本応用数理学会
    • Place of Presentation
      明治大学駿河台キャンパス(東京都)
    • Year and Date
      2010-09-06
  • [Presentation] 2次元境界型及び領域型拡張メッシュレス法の開発2010

    • Author(s)
      齋藤歩, 伊東拓, 神谷淳
    • Organizer
      日本応用数理学会
    • Place of Presentation
      明治大学駿河台キャンパス(東京都)
    • Year and Date
      2010-09-06
  • [Presentation] 3次元拡張境界節点法における影響係数評価の高速化2010

    • Author(s)
      伊東拓, 齋藤歩, 神谷淳
    • Organizer
      日本応用数理学会
    • Place of Presentation
      明治大学駿河台キャンパス(東京都)
    • Year and Date
      2010-09-06
  • [Presentation] 高温超伝導薄膜内を流れる遮蔽電流密度の高性能解析2010

    • Author(s)
      高山彰優, 神谷淳
    • Organizer
      日本シミュレーション学会
    • Place of Presentation
      山形大学米沢キャンパス(山形県)
    • Year and Date
      2010-06-20
  • [Presentation] 積分セルを用いない領域型および境界型メッシュレス法の開発2010

    • Author(s)
      齋藤歩, 伊東拓, 神谷淳
    • Organizer
      日本シミュレーション学会
    • Place of Presentation
      山形大学米沢キャンパス(山形県)
    • Year and Date
      2010-06-19
  • [Presentation] 3次元拡張境界節点法のためのMRBF法をベースとした陰関数生成2010

    • Author(s)
      伊東拓, 齋藤歩, 神谷淳
    • Organizer
      日本シミュレーション学会
    • Place of Presentation
      山形大学米沢キャンパス(山形県)
    • Year and Date
      2010-06-19
  • [Presentation] Meshless法より得られる連立1次方程式の反復解法-GPUを用いた精度混合型反復法の提案-2010

    • Author(s)
      生野壮一郎
    • Organizer
      日本シミュレーション学会
    • Place of Presentation
      山形大学米沢キャンパス(山形県)
    • Year and Date
      2010-06-19
  • [Presentation] Development of Three-Dimensional Extended Boundary-Node Method for Potential Problem2010

    • Author(s)
      T.Itoh, A.Saitoh, A.Kamitani
    • Organizer
      The 14^<th> Biennial IEEE Conference on Electromagnetic Field Computation
    • Place of Presentation
      Hyatt Regency Hotel O'Hare, Chicago, USA
    • Year and Date
      2010-05-11

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Published: 2012-07-19  

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