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2002 Fiscal Year Final Research Report Summary

Fast Implementation of the Boundary Element Method and its Application to Inverse Problems

Research Project

Project/Area Number 12650060
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionNational Institute of Informatics (2001-2002)
The University of Tokyo (2000)

Principal Investigator

HAYAMI Ken  National Institute of Informatics, Foundations of Informatics Research Division, Professor, 情報学基礎研究系, 教授 (20251358)

Co-Investigator(Kenkyū-buntansha) NARA Takaaki  National Institute of Informatics, Foundations of Informatics Research Division, Research Associate, 情報学基礎研究系, 助手 (80353423)
NISHIDA Tetsushi  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 (80302751)
Project Period (FY) 2000 – 2002
KeywordsBoundary Element Method / inverse problem / system of linear equations / least-squares problem / singular system / Krylov subspace iterative method / MEG / source term identification
Research Abstract

1) Direct simulation of large amplitude standing waves using the boundary element method
We developed a method using the two-dimensional boundary element method for the time dependent direct simulation of the free surface of liquids, and succeeded in the direct simulation of large amplitude standing waves, which was considered to be difficult.
2) Inverse Problem
We developed efficient direct methods for the inverse problem of source term identification of the three-dimensional Poisson equation, which is applied to MEG etc. Depending on whether the source is 1) relatively uniformly distributed in the domain, 2) concentrated near the boundary of the domain, infinite series of the 1) low-order moments, 2) high-order moments of the multipole expansion of the field are used in order to obtain reconstruction formulae concerning the position of the projection of the source on to the 1) xy-plane, 2) Riemann sphere.
3) Iterative methods on singular systems
We analyzed the behavior of Krylov subspace … More iterative methods on least-squares problems whose coefficient matrices are singular. Namely, we derived necessary and sufficient conditions for the CR (Conjugate Residual), GCR(k) (Generalized Conjugate Residual) and GMRES (Generalized Minimal Residual) methods to give a least-square solution without break-down. The methodology is to decompose the algorithms in to the range of the coefficient matrix and its orthogonal complement.
We also developed a method of applying the GMRES method after preconditioning by incomplete QR decomposition, for (over-determined) least-squares problems.
4) Iterative methods for eigenvalue problems
We derived necessary and sufficient conditions for a solution to exist to the correction equation of the Jacobi-Davidson method, clarified the relation between the subspace expanded by such a solution and the invariant space of the coefficient matrix, and proposed a method for generating efficient starting vectors for the method. We also proposed methods for the validated numerics of the method. Less

  • Research Products

    (64 results)

All Other

All Publications (64 results)

  • [Publications] 速水 謙: "GMRES and GCR(k) on singular systems"第32回数値解析シンポジウム 講演予稿集. 71-74 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 速水 謙: "特異な系に対する共役残差法の収束性について"日本応用数理学会論文誌. 13巻1号. 1-33 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kenji Hamano: "Boundary element simulation of large amplitude standing waves in vessels"Engineering Analysis with Boundary Elements. Vol.27, Issue 6. 565-574 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ken Hayami: "On the behaviour of the conjugate residual method for singular systems"Z.-C. Shi and H. Kawarada eds., Proceedings of Fifth China-Japan Seminar on Numerical Mathematics, Shanghai, 2000, Science Press, Beijing/New York. 117-126 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 速水 謙: "特異な系に対するGCR(k)法の収束性について"京都大学数理解析研究所講究録. 1265. 129-139 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 速水 謙: "反復法の数理"数理科学,特集/数理工学の地平. 12月号. 36-42 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ken Hayami: "A panel clustering method for 3-D elastostatics using spherical harmonics"Integral Methods in Science and Engineering (Chapman & Hall/CRC). 179-184 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Masayuki Nakajima: "Identification of tractions based on displacement observations at interior points"Inverse Problems in Engineering Mechanics II (Elsevier). 119-128 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 伊藤 徳史: "不完全QR-GMRES(k)法による線形最小二乗問題の解法"情報処理学会第65回全国大会講演論文集. 1-117-1-118 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 西田 徹志: "スポーツビデオデータからの選手の位置検出システム"電子情報通信学会 信学技報. PRMU 2002-32. 9-14 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takaaki Nara: "A projective method for an inverse source problem of the Poisson equation"Inverse Problems. Vol.19, No.2. 355-369 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 奈良 高明: "リーマン球面への射影によるポアソン方程式のソース項同定"京都大学数理解析研究所講究録. 1320. 101-111 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 奈良 高明: "ポアソン方程式ソース項同定逆問題の射影解法"計算数理工学会論文集. Vol.2. 21-26 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takaaki Nara: "Projection method for an inverse source problem of the Poisson equation"Proceedings of the Society for Instrument and Control Engineers Annual Conference (SICE2002). 1590-1597 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 奈良 高明: "リーマン球面への射影によるポアソン方程式のソース項同定"日本応用数理学会2002年度年会予稿集. http://pjsiam.jstage.jst.go.jp/ja/ (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 奈良 高明: "局所的計測によるソース項推定逆問題の代数解法"第19回センシングフォーラム予稿集. 341-346 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 奈良 高明: "リーマン球面への射影によるポアソン方程式のソース項同定"京都大学数理解析研究所研究集会 微分方程式の数値解法と線形計算. 43-45 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takaaki Nara: "An inverse source problem of the Poisson equation via projection onto the Riemann sphere"5^<th> International Congress on Industrial and Applied Mathematics (ICIAM2003), July, 2003, Sydney, Book of Abstracts. 258 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ken Hayami: "GCR(k) and GMRES on singular systems"5^<th> International Congress on Industrial and Applied Mathematics (ICIAM2003), July, 2003, Sydney, Book of Abstracts. 81 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 伊藤 徳史: "GMRES法による線形最小二乗問題の解法"LA研究会 第26回研究会. http://phase.hpcc.jp/la/SLIDES/0303-ito/index.html (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 速水 謙: "特異な系に対するクリロフ部分空間法の収束性について"日本応用数理学会2002年度年会予稿集. http://pjsia m.jstage.jst.go.jp/ja/ (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 伊藤 徳史: "GMRES(k)法の線型最小二乗問題への適用"日本応用数理学会2002年度年会予稿集. http://pjsiam.jstage.jst.go.jp/ja/ (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ken Hayami: "On the convergence of Krylov subspace methods for singular systems"MILOVY 2002, Computational Linear Algebraw with Applications, August, 2002, Milovy, Czech Republic, Book of Abstracts. 36-37 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ken Hayami: "On the convergence of the GCR(k) method for singular systems"Latsis Symposium 2002. Iterative Solvers for Large Linear Systems, February, 2002, ETH Zuerich, Abstracts. 22-23 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ken Hayami: "On the convergence of the GCR(k) method for singular systems"微分方程式の離散化手法と数値計算アルゴリズム,2001年11月,京都大学数理解析研究所. 31-33 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Ken Hayami: "On the convergence of conjugate residual and related methods for singular systems"Abstracts of Talks, ICRACM2001, International Conference on Recent Advances in Computational Mathematics, October, 2001, Matsuyama. 24-25 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Masato Kamiyama: "Validated numerical solution of large scale eigenvalue problems"日本応用数理学会2001年度年会 講演予稿集. 22-23 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 今井 聡: "Jacobi-Davidson法における初期ベクトルの改良"日本応用数理学会2001年度年会予稿集. 276-277 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 濱野 健二: "大振幅定在波の境界要素法による直接シミュレーション"京都大学数理解析研究所講究録 (非線形波動現象のメカニズムと数理). 1209. 105-114 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 速水 謙: "特異な系に対する共役残差法の収束性について"日本応用数理学会2000年度年会講演予稿集. 58-59 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 濱野 健二: "自由表面定在波の境界要素解析"BTEC論文集. 10. 43-48 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 濱野 健二: "大振幅定在波の境界要素法による直接シミュレーション"境界要素論文集. 17. 91-96 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hayami, K.: "GMRES and GCRC(k) on singular systems"Proceedings of the 32nd Numerical Analysis Symposium, Hakone. 71-74 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hayami, K.: "On the convergence of the conjugate residual method for singular systems (in Japanese)"Transactions of the Japan Society for Industrial and Applied Mathematics. Vol. 13, No. 1. 1-33 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hamano, K, Murashige, S. and Hayami, K: "Boundary element simulation of large amplitude standing waves in vessels"Engineering Analysis with Boundaty Elements. Vol. 27, Issue 6. 565-574 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hayami, K.: "On the convergence of the GCR(k) method for singular systems, (in Japanese)"Kokyuroku 1265, Discretization Methods and Numerical Algorithms for Differential Equations, Research Institute for Mathematical Sciences, Kyoto University. 129-139 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hayami, K.: "The mathematics of iterative methods (in Japanese)"Suuri-Kagaku (Mathematical Sciences), Special Issue on the Horizon of Mathematical Engineering. Vol. 12. 3 6-42 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ito, T. and Hayami, K.: "Solution of linear least-squares problems by the incomplete QR-GMRES(k) method (in Japanese)"Proceedings of the 65th Meeting of the Information Processing Society of Japan. 1_117-1_118 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Nishida, T. and Sugihara, K.: "System for detecting players' positions out of video data (in Japanese)"Tech. Rep. of IEICE. PRMU 2002-32. 9-14 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Nara, T. and Ando, S.: "A projective method for an inverse source problem of the Poisson equation"Inverse Problems. Vol.19, No. 2. 355-369 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Nara, T. and Ando, S.: "Source term identification of the Poisson equation by projection on to the Riemann sphere (in Japanese)"Kokyuroku 1320, The Numerical Solution of Differential Equations and Linear Computation, Research Institute for Mathematical Sciences, Kyoto University. 101-111 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Nara, T. and Ando, S.: "Projection method for an inverse source problem of Poisson equation (in Japanese)"Transactions of the Japan Society for Computational Methods in Engineering. Vol. 2. 21-26 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Nara, T. and Ando, S.: "Projection method for an inverse source problem of the Poisson equation"Proceedings of the Society for Instrument and Control Engineering Annual Conference (SICE2002). 1590-1597 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Nara, T. and Ando, S.: "Source term identification of the Poisson equation by projection on to the Riemann sphere (in Japanese)"Proceedings of the 2002 Annual Meeting of the Japan Society for Industrial and Applied Mathematics, http://pjsiam. jstage.jst.go.jp/ja/. (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Nara, T. and Ando, S.: "An algebraic solution of the inverse problem of source term estimation based on local measurements (in Japanese)"Proceedings of the 19th Sensing Forum. 341-346 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Nara, T. and Ando, S.: "Source term identification of the Poisson equation by projection on to the Riemann sphere (in Japanese)"Abstracts of the Workshop : The Numerical Solution of Differential Equations and Linear Computation, Research Institute for Mathematical Sciences, Kyoto University. 43-45 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Nara, T, and Ando, S.: "An inverse source problem of the Poisson equation via projection onto the Riemann sphere"5^<th> International Congress on Industrial and Applied Mathematics (ICIAM2003), Sydney, Book of Abstracts. 258 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hayami, K.: "GCR(k) and GMRES on singular systems"5^<th> In ternational Congress on In dustrial andApplied Mathema tics (ICIAM2003), July, 2003, Sydney, Book of Abstracts. 81 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ito, T. and Hayarai, K.: "Solution of linear least-squares problems by the GMRES method (in Japanese)"The 26^<th> LA Seminar, http://phase.hpcc.ip/la/SLIDES/0303-ito/index.html. (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hayami, K.: "On the convergence of Krylov subspace Methods on Singular systems (in Japanese)"Proceedings of the 2002 Annual Meeting of the Japan Society for Industrial and Applied Mathematics, http://pjsiam. jstage,jst.go.jp/ja/. (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Ito, T. and Hayami, K.: "Application of the GMRES(k) method to linear least-squares problem (in Japanese)"Proceedings of the 2002 Annual Meeting of the Japan Society for Industrial and Applied Mathematics, http://pjsiam. Jstage,jst.go.jp/Ja/. (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hayami, K.: "On the convergence of Krylov subspace methods for singular systems"MILOVY 2002, Computational Linear Algebra with Applications, August, 2002, Milovy, Czech Republic, Book of Abstracts. 36-37 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hayami, K.: "On the convergence of the GCR(k) method for singular systems"Latsis Symposium 2002 : Iterative Solvers for Large Linear Systems, February, 2002, ETH Zuerich, Abstracts. 22-23 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hayami, K.: "On the convergence of the GCR(k) method for singular systems"Abstracts of the Workshop ' Discretization Methods and Numerical Algorithms for Differential Equations, Research Institute for Mathematical Sciences, Kyoto University. 31-33 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hayami, K.: "On the convergence of conjugate residual and related methods for singular systems"Abstracts of Talks, ICRACM2001, International Conference on Recent Advances in Computational Mathematics, October, 2001, Matsuyama. 24-25 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kamiyama, M., Hayami, K., Murashige, S. and Oishi, S.: "Validated numerical solution of large scale eigenvalue problems"Proceedings of the 2001 Annual Meeting of the Japan Society for Industrial and Applied Mathematics, October, 2001. 22-23 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Imai, S. and Hayami, K.: "On the improvement of the initial vector in the Jacobi-Davidson method"Proceedings of the 2001 Annual Meeting of the Japan Society for Industrial and Applied Mathetmatics, October, 2001. 276-277 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hamano, K., Murashige, S. and Hayami, K.: "Boundary element simulation of large amplitude standing waves in vessels(in Japanese)"Kokyuroku 1209, Mechanism and Mathematical Aspects of Nonlinear Wave Propagation, Research Institute for Mathematical Sciences, Kyoto University, May. 105-114 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hayami, K.: "On the convergence of the conjugate residual method on singular systems"Proceedings of the 2000 Annual Meeting of the Japan Society for Industrial and Applied Mathematics. 58-59 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hamano, K, Murashige, S. and Hayami, K.: "The analysis of standing waves of free surfaces using the boundary element method"Proceedings of the 10th BEM Technology Conference (BTBC 2000). Vol. 10. 43-48 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hamano, K., Murashige, S. and Hayami, K.: "The direct Numerical simulation of large amplitude standing waves Using the boundary element method"Proceedings of the 17th Japan National Symposium on Boundary Element Methods. Vol. 17. 91-96 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hayami, K., Z.-C. Shi and H. Kawarada eds.: "On the behaviour of the conjugate residual method for singular systems, in Proceedings of Fifth China-Japan Seminar on Numerical Mathematics, Shanghai, 2000"Science Press. 117-126 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hayami, K.: "A panel clustering method for 3-D elastostatics using spherical harmonics, in Integral Methods in Science and Engineering"Chapman & Hall / CRC. 179-184 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Nakajima, M., Hayami, K., Terao, J., Watanabe, S., and Ando, S., M. Tanaka and G.S. Dulikravich eds.: "Identification of tractions based on displacement observations at interior points, in Inverse Problems in Engineering Mechanics 2000 (ISIP 2000), Nagano"Elsevier. 119-128 (2000)

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

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Published: 2004-04-14  

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