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On the fast multipole method for periodic and non-periodic boundary value problems in periodic domains

Research Project

Project/Area Number 20360047
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionKyoto University

Principal Investigator

NISHIMURA Naoshi  Kyoto University, 大学院・情報学研究科, 教授 (90127118)

Co-Investigator(Kenkyū-buntansha) YOSHIKAWA Hitoshi  京都大学, 大学院・情報学研究科, 講師 (90359836)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥14,560,000 (Direct Cost: ¥11,200,000、Indirect Cost: ¥3,360,000)
Fiscal Year 2010: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2009: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2008: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Keywords計算力学 / 高速多重極法 / フォトニック結晶 / メタマテリアル / フォノニック結晶 / 波動問題 / 周期問題 / 前処理 / Maxwell方程式 / 弾性波動
Research Abstract

Wave problems in periodic structures constitute an interesting academic area of research which has applications such as photonic crystals and metamaterials in optics and phononic crystals in elastodynamics. We have developed the periodic fast multipole method (FMM) as a fast solver of wave problems in periodic structures. But, this method still has a few restrictions which have to be removed. In this research we have extended the applicability of the periodic FMM in acoustics, elastodynamics and electromagnetics. Specifically, we have developed methods for analysing responses of periodic structures subject to non-periodic incident waves or waves in slightly perturbed periodic structures.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (51 results)

All 2011 2010 2009 2008

All Journal Article (20 results) (of which Peer Reviewed: 20 results) Presentation (31 results)

  • [Journal Article] Helmholtz方程式のGalerkin法を用いた周期多重極法におけるCalderonの式に基づく前処理法について2010

    • Author(s)
      新納和樹、西村直志
    • Journal Title

      10

      Pages: 39-44

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 3次元動弾性学の周期多重極法におけるCalderonの式に基づく前処理について2010

    • Author(s)
      飯盛浩司、新納和樹、吉川仁、西村直志
    • Journal Title

      計算数理工学論文集 10

      Pages: 45-50

    • NAID

      40018997680

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 3次元動弾性学の周期多重極法と、その平面2周期構造による散乱問題への適用2010

    • Author(s)
      飯盛浩司、吉川仁、西村直志
    • Journal Title

      応用力学論文集 13

      Pages: 169-178

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Helmholtz方程式のGalerkin法を用いた周期多重極法におけるCalderonの式に基づく前処理法について2010

    • Author(s)
      新納和樹、西村直志
    • Journal Title

      計算数理工学論文集

      Volume: 10 Pages: 39-44

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 3次元動弾性学の周期多重極法におけるCalderonの式に基づく前処理について2010

    • Author(s)
      飯盛浩司, 他
    • Journal Title

      計算数理工学論文集

      Volume: 10 Pages: 45-50

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 3次元動弾性学の周期多重極法と、その平面2周期構造による散乱問題への適用2010

    • Author(s)
      飯盛浩司, 他
    • Journal Title

      応用力学論文集

      Volume: 13 Pages: 169-178

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Behaviour of periodic fast multipole boundary integral equation method for Maxwell's equations near Wood's anomalies2009

    • Author(s)
      Y.Otani, N.Nishimura
    • Journal Title

      Contemporary Mathematics 494

      Pages: 43-59

    • Related Report
      2010 Final Research Report 2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 3次元動弾性学における周期多重極法とWoodのanomalyに関する基礎的考察2009

    • Author(s)
      飯盛浩司、大谷佳広、吉川仁、西村直志
    • Journal Title

      応用力学論文集 12

      Pages: 171-178

    • NAID

      40016868725

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 2次元Helmholtz方程式の1周期境界値問題に対するCalderonの式に基づく前処理について2009

    • Author(s)
      新納和樹、西村直志
    • Journal Title

      計算数理工学論文集 9

      Pages: 1-6

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Maxwell方程式における周期多重極法のtall cell問題への拡張2009

    • Author(s)
      大谷佳広、西村直志
    • Journal Title

      計算数理工学論文集 9

      Pages: 55-60

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] An FMM for orthotropic periodic boundary value problems for Maxwell's equations2009

    • Author(s)
      Y.Otani, N.Nishimura
    • Journal Title

      Waves in Random and Complex Media 19

      Pages: 80-104

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Maxwell 方程式における周期多重極法の tall cell 問題への拡張2009

    • Author(s)
      大谷佳広, 西村直志
    • Journal Title

      計算数理工学論文集 9

      Pages: 55-60

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 2次元 Helmholtz 方程式の1周期境界値問題に対する Calderon の式に基づく前処理について2009

    • Author(s)
      新納和樹, 西村直志
    • Journal Title

      計算数理工学論文集 9

      Pages: 1-6

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 3次元動弾性学における周期多重極法と Wood の anomaly に関する基礎的考察2009

    • Author(s)
      飯盛浩司, 大谷佳広, 吉川仁, 西村直志
    • Journal Title

      応用力学論文集 12

      Pages: 171-178

    • NAID

      40016868725

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 周期多重極法とそのフォトニック結晶やメタマテリアルへの応用2009

    • Author(s)
      大谷佳広, 倉見洋輔, 西村直志
    • Journal Title

      シミュレーション 28

      Pages: 112-118

    • NAID

      110007387262

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An FMM for orthotropic periodic boundary value problems for Maxwell's equations2009

    • Author(s)
      Y. Otani, N. Nishimura
    • Journal Title

      Waves in Random and Complex Media 19

      Pages: 80-104

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 2次元弾性波動問題における周期多重極境界積分方程式法2008

    • Author(s)
      坂本和穂・大谷佳広・西村直志
    • Journal Title

      計算数理工学論文集 8

      Pages: 77-82

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 3次元Maxwell方程式直交異方周期散乱問題における高速多重極境界要素法2008

    • Author(s)
      大谷佳広・西村直志
    • Journal Title

      計算数理工学論文集 8

      Pages: 71-76

    • NAID

      10025651436

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 3次元Maxwell方程式直交異方周期散乱問題における高速多重極境界要素法2008

    • Author(s)
      大谷佳広, 西村直志
    • Journal Title

      計算数理工学論文集 8

      Pages: 71-76

    • NAID

      10025651436

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 2次元弾性波動問題における周期多重極境界積分方程式法2008

    • Author(s)
      坂本和穂, 大谷佳広, 西村直志
    • Journal Title

      計算数理工学論文集 8

      Pages: 77-82

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Calderon preconditioners for periodic FMMs in wave transmission problems2011

    • Author(s)
      西村直志
    • Organizer
      Trefftz/MFS2011
    • Place of Presentation
      Kaohsiung, Taiwan
    • Year and Date
      2011-03-17
    • Related Report
      2010 Final Research Report
  • [Presentation] Calderon preconditioners for periodic FMMs in wave transmission problems2011

    • Author(s)
      N.Nishimura
    • Organizer
      Trefftz/MFS2011
    • Place of Presentation
      Kaohsiung, Taiwan(招待講演)
    • Year and Date
      2011-03-17
    • Related Report
      2010 Annual Research Report
  • [Presentation] 2次元波動方程式の周期問題の時間域解法について2010

    • Author(s)
      渡辺慧、西村直志
    • Organizer
      機械学会計算力学講演会
    • Place of Presentation
      北見工業大学
    • Year and Date
      2010-09-24
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 3次元動弾性学の2周期境界値問題に対するCalderonの式に基づく前処理について2010

    • Author(s)
      飯盛浩司, 他
    • Organizer
      機械学会計算力学講演会
    • Place of Presentation
      北見工業大学
    • Year and Date
      2010-09-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] Fast BEMs for elastodynamics and periodic problems2010

    • Author(s)
      西村直志
    • Organizer
      NSF workshop on emerging applications and future directions of the boundary element method
    • Place of Presentation
      Akron, Ohio, USA
    • Year and Date
      2010-09-02
    • Related Report
      2010 Final Research Report
  • [Presentation] Fast BEMs for elastodynamics and periodic problems2010

    • Author(s)
      N.Nishimura
    • Organizer
      NSF workshop on emerging applications and future directions of the boundary element method
    • Place of Presentation
      Akron, Ohio, USA(招待講演)
    • Year and Date
      2010-09-02
    • Related Report
      2010 Annual Research Report
  • [Presentation] Preconditioners based on Calderon's formulae for FMMs in periodic wave problems2010

    • Author(s)
      西村直志
    • Organizer
      Workshop on Integral equation methods, fast algorithms and applications
    • Place of Presentation
      Minneapolis, USA
    • Year and Date
      2010-08-04
    • Related Report
      2010 Final Research Report
  • [Presentation] Preconditioners based on Calderon's formulae for FMMs in periodic wave problems2010

    • Author(s)
      N.Nishimura
    • Organizer
      Workshop on Integral equation methods, fast algorithms and application
    • Place of Presentation
      Minneapolis, USA(招待講演)
    • Year and Date
      2010-08-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] 3次元動弾性学における周期多重極法とフォノニック結晶の解析へのその適用に関する研究2010

    • Author(s)
      飯盛浩司、西村直志
    • Organizer
      計算工学講演会
    • Place of Presentation
      九州大学
    • Year and Date
      2010-05-26
    • Related Report
      2010 Annual Research Report
  • [Presentation] 3次元Helmholtz方程式の周期境界値問題に対するCalderonの式に基づく前処理について2010

    • Author(s)
      新納和樹、西村直志
    • Organizer
      計算工学講演会
    • Place of Presentation
      九州大学
    • Year and Date
      2010-05-26
    • Related Report
      2010 Annual Research Report
  • [Presentation] A periodic FMM for three dimensional elastodynamics2010

    • Author(s)
      H.Isakari, et. al.
    • Organizer
      ECCM2010
    • Place of Presentation
      Paris, France
    • Year and Date
      2010-05-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] Preconditioning based on Calderon's formulae for periodic boundary value problems for Helmholtz' equations2010

    • Author(s)
      K.Niino, N.Nishimura
    • Organizer
      ECCM2010
    • Place of Presentation
      Paris, France
    • Year and Date
      2010-05-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] Applications of periodic FMM for Maxwell's equations in optical problems2010

    • Author(s)
      西村直志
    • Organizer
      2nd German-Japanese workshop on computational mechanics
    • Place of Presentation
      地球シミュレータセンター
    • Year and Date
      2010-03-29
    • Related Report
      2010 Final Research Report
  • [Presentation] Applications of periodic FMM for Maxwell's equations in optical problems (keynote lecture)2010

    • Author(s)
      西村直志
    • Organizer
      2nd German-Japanese workshop on computational mechanics
    • Place of Presentation
      地球シミュレータセンター
    • Year and Date
      2010-03-29
    • Related Report
      2009 Annual Research Report
  • [Presentation] Applications of periodic FMM for Maxwell's equations in optics2010

    • Author(s)
      西村直志
    • Organizer
      Piers 2010 in Xi'an
    • Place of Presentation
      Xi'an, China
    • Year and Date
      2010-03-23
    • Related Report
      2009 Annual Research Report
  • [Presentation] Preconditioners based on Calderon's formulae for 1 periodic boundary value problems for Helmholtz' equation (invited talk)2009

    • Author(s)
      K.Niinou
    • Organizer
      2009 Taiwan-Japan Joint Workshop on Numerical Analysis and Scientific Computation
    • Place of Presentation
      Taipei, Taiwan
    • Year and Date
      2009-11-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] Boundary integral equation methods and fast multipole methods in periodic wave problems2009

    • Author(s)
      西村直志
    • Organizer
      2009 Taiwan-Japan Joint Workshop on Numerical Analysis and Scientific Computation
    • Place of Presentation
      Taipei, Taiwan
    • Year and Date
      2009-11-07
    • Related Report
      2010 Final Research Report
  • [Presentation] Boundary integral equation methods and fast multipole methods in periodic wave problems (invited talk)2009

    • Author(s)
      西村直志
    • Organizer
      2009 Taiwan-Japan Joint Workshop on Numerical Analysis and Scientific Computation
    • Place of Presentation
      Taipei, Taiwan
    • Year and Date
      2009-11-07
    • Related Report
      2009 Annual Research Report
  • [Presentation] Applications of periodic FMM for Maxwell's equations in optics2009

    • Author(s)
      西村直志
    • Organizer
      ICOME2009
    • Place of Presentation
      Hohai University, Nanjing, China
    • Year and Date
      2009-10-20
    • Related Report
      2010 Final Research Report
  • [Presentation] Applications of periodic FMM for Maxwell's equations in optics (plenary talk)2009

    • Author(s)
      西村直志
    • Organizer
      ICOME2009
    • Place of Presentation
      Nanjing, China
    • Year and Date
      2009-10-20
    • Related Report
      2009 Annual Research Report
  • [Presentation] An FMM for orthotropic periodic problems in Maxwell's equations with applications in nanophotonics2009

    • Author(s)
      西村直志
    • Organizer
      10th USNCCM
    • Place of Presentation
      Columbus, USA
    • Year and Date
      2009-07-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] An FMM for orthotropic periodic problems in elastodynamics in 3D2009

    • Author(s)
      H.Isakari
    • Organizer
      10th USNCCM
    • Place of Presentation
      Columbus, USA
    • Year and Date
      2009-07-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] A periodic FMM for Maxwell's equations with applications to nanophotonics2009

    • Author(s)
      西村直志
    • Organizer
      Waves 2009
    • Place of Presentation
      Pau, France
    • Year and Date
      2009-06-18
    • Related Report
      2009 Annual Research Report
  • [Presentation] 高速多重極境界要素法-弾性体からメタマテリアルまで2009

    • Author(s)
      西村直志
    • Organizer
      理論応用力学講演会
    • Place of Presentation
      日本学術会議
    • Year and Date
      2009-06-09
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] 3次元Maxwell方程式直交異方性周期境界値問題における高速多重極法2008

    • Author(s)
      大谷佳広
    • Organizer
      機械学会計算力学講演会
    • Place of Presentation
      琉球大学
    • Year and Date
      2008-11-03
    • Related Report
      2008 Annual Research Report
  • [Presentation] Boundary integral equation method and fast multipole methods in periodic wave problems2008

    • Author(s)
      西村直志
    • Organizer
      CoMFoS 2008
    • Place of Presentation
      京大会館
    • Year and Date
      2008-10-28
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] An FMM for Periodic Scattering Problems in Electromagnetics2008

    • Author(s)
      Y. Otani
    • Organizer
      WCCM2008
    • Place of Presentation
      Venice, Italy
    • Year and Date
      2008-07-03
    • Related Report
      2008 Annual Research Report
  • [Presentation] A fast multipole method for 3 dimensional periodic boundary value problems for Maxwell's equations2008

    • Author(s)
      西村直志
    • Organizer
      Imaging microstructures, Mathematical and computational challenges
    • Place of Presentation
      Institut Henri Poincare, Paris, France
    • Year and Date
      2008-06-18
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] On the periodic FMM for Maxwell's equations2008

    • Author(s)
      西村直志
    • Organizer
      BEM/FEM techniques for time dependent and time harmonic problems
    • Place of Presentation
      Saarland Univ., Germany
    • Year and Date
      2008-05-28
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] 周期多重極法を用いたHelmholtz方程式の周期領域非周期境界値問題の解法2008

    • Author(s)
      新納和樹
    • Organizer
      計算工学会
    • Place of Presentation
      仙台市民会館
    • Year and Date
      2008-05-21
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] 周期多重極境界要素法を用いたメタマテリアルの解析2008

    • Author(s)
      倉見洋輔
    • Organizer
      計算工学会
    • Place of Presentation
      仙台市民会館
    • Year and Date
      2008-05-21
    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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