Updated on 2024/03/29

写真a

 
TAKAHASHI Toru
 
Organization
Graduate School of Engineering Mechanical Systems Engineering 1 Associate professor
Graduate School
Graduate School of Engineering
Undergraduate School
School of Engineering Mechanical and Aerospace Engineering
Title
Associate professor
Contact information
メールアドレス
External link

Degree 3

  1. 博士(工学) ( 2002.3   京都大学 ) 

  2. 工学修士 ( 1998.3   東京工業大学 ) 

  3. 工学学士 ( 1996.3   東京工業大学 ) 

Research Interests 2

  1. Computational mechanics

  2. Applied mechanics

Research Areas 1

  1. Informatics / Computational science

Current Research Project and SDGs 2

  1. Study on fast multipole boundary integral equation methods

  2. GPU-accelerated computing in science and engineering

Research History 7

  1. Lecturer, Graduate School of Engineering, Nagoya University

    2009.10 - 2015.9

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    Country:Japan

  2. Visiting Researcher, RIKEN

    2007.5 - 2016.3

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    Country:Japan

  3. Assistant Professor, Graduate School of Engineering, Nagoya University

    2007.4 - 2009.9

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    Country:Japan

  4. Research fellow (San-gaku-kan renkei kenkyu-in), Earthquake Research Institute, The University of Tokyo

    2006.4 - 2007.3

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    Country:Japan

  5. Special Postdoctoral Researcher, RIKEN

    2003.4 - 2006.3

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    Country:Japan

  6. Part-time Lecturer, Toyo University

    2003.4 - 2006.3

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    Country:Japan

  7. Postdoc (Kyouryoku kenkyu-in), RIKEN

    2002.4 - 2003.3

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    Country:Japan

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Education 3

  1. Kyoto University   Graduate School, Division of Engineering   Global Earth Engineering

    1998.4 - 2002.3

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    Country: Japan

  2. Tokyo Institute of Technology   Graduate School, Division of Science and Engineering   Mechanical Engineering Science

    1996.4 - 1998.3

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    Country: Japan

  3. Tokyo Institute of Technology   Faculty of Engineering   Mechanical Engineering Science

    1992.4 - 1996.3

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    Country: Japan

Professional Memberships 4

  1. 日本機械学会

  2. 日本物理学会

  3. 日本計算数理工学会   理事

    2010.4

  4. 日本建築学会

 

Papers 84

  1. A time-domain boundary element method for the 3D dissipative wave equation: Case of Neumann problems Reviewed

    Takahashi, T

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING   Vol. 124 ( 23 ) page: 5263 - 5292   2023.12

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1002/nme.7343

    Web of Science

  2. A fast time-domain boundary element method for three-dimensional electromagnetic scattering problems Reviewed

    Takahashi, T

    JOURNAL OF COMPUTATIONAL PHYSICS   Vol. 482   2023.6

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jcp.2023.112053

    Web of Science

  3. An exact volume constraint method for topology optimization via reaction-diffusion equation

    Cui, Y; Takahashi, T; Matsumoto, T

    COMPUTERS & STRUCTURES   Vol. 280   2023.5

  4. A three-dimensional shape optimization for transient acoustic scattering problems using the time-domain boundary element method

    Takahashi, T; Miyazawa, N; Tanigawa, M

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING   Vol. 124 ( 2 ) page: 482 - 512   2023.1

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    Language:Japanese  

    DOI: 10.1002/nme.7130

    Web of Science

  5. A topology optimization of open acoustic waveguides based on a scattering matrix method

    Matsushima, K; Isakari, H; Takahashi, T; Matsumoto, T

    WAVE MOTION   Vol. 113   2022.8

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  6. A robust topology optimisation for wideband structures in acoustic-elastodynamic coupled fields

    Qin, JC; Isakari, H; Takahashi, T; Matsumoto, T

    ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS   Vol. 140   page: 544 - 561   2022.7

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  7. An isogeometric boundary element method for three-dimensional doubly-periodic layered structures in electromagnetics

    Takahashi, T; Hirai, T; Isakari, H; Matsumoto, T

    ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS   Vol. 136   page: 37 - 54   2022.3

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  8. An enhancement of the fast time-domain boundary element method for the three-dimensional wave equation

    Takahashi, T; Tanigawa, M; Miyazawa, N

    COMPUTER PHYSICS COMMUNICATIONS   Vol. 271   2022.2

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    Language:Japanese  

    DOI: 10.1016/j.cpc.2021.108229

    Web of Science

  9. A Shape Optimisation with the Isogeometric Boundary Element Method and Adjoint Variable Method for the Three-Dimensional Helmholtz Equation

    Takahashi, T; Sato, D; Isakari, H; Matsumoto, T

    COMPUTER-AIDED DESIGN   Vol. 142   2022.1

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    Language:Japanese  

    DOI: 10.1016/j.cad.2021.103126

    Web of Science

  10. A time-saving FEM-based approach for structural topology optimization with exact boundary representation

    Cui, Y; Takahashi, T; Matsumoto, T

    MECHANICAL ENGINEERING JOURNAL   Vol. 9 ( 6 )   2022

  11. Topology optimization for incompressible viscous fluid flow using the lattice kinetic scheme

    Xie, SQ; Yaji, K; Takahashi, T; Isakari, H; Yoshino, M; Matsumoto, T

    COMPUTERS & MATHEMATICS WITH APPLICATIONS   Vol. 97   page: 251 - 266   2021.9

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  12. A robust topology optimization for enlarging working bandwidth of acoustic devices

    Qin, JC; Isakari, H; Taji, K; Takahashi, T; Matsumoto, T

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING   Vol. 122 ( 11 ) page: 2694 - 2711   2021.6

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    Language:Japanese  

    DOI: 10.1002/nme.6637

    Web of Science

  13. A topology optimisation of composite elastic metamaterial slabs based on the manipulation of far-field behaviours

    Matsushima Kei, Isakari Hiroshi, Takahashi Toru, Matsumoto Toshiro

    STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION   Vol. 63 ( 1 ) page: 231 - 243   2021.1

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    Language:Japanese   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s00158-020-02689-y

    Web of Science

  14. A numerical method for elastic wave scattering in multi-layered periodic media based on the scattering matrix and BEM

    Matsushima, K; Isakari, H; Takahashi, T; Matsumoto, T

    MECHANICAL ENGINEERING JOURNAL   Vol. 8 ( 1 )   2021

  15. Level-set based topology optimization of transient flow using lattice Boltzmann method considering an oscillating flow condition

    Nguyen Truong, Isakari Hiroshi, Takahashi Toru, Yaji Kentaro, Yoshino Masato, Matsumoto Toshiro

    COMPUTERS & MATHEMATICS WITH APPLICATIONS   Vol. 80 ( 1 ) page: 82 - 108   2020.7

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    Language:Japanese   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.camwa.2020.03.003

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  16. Parallelization of the inverse fast multipole method with an application to boundary element method Reviewed

    Toru Takahashi, Chao Chen, Eric Darve

    Computer Physics Communications   Vol. 247   2020.2

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    Language:Japanese   Publishing type:Research paper (scientific journal)  

    We present an algorithm to parallelize the inverse fast multipole method (IFMM), which is an approximate direct solver for dense linear systems. The parallel scheme is based on a greedy coloring algorithm, where two nodes in the hierarchy with the same color are separated by at least σ nodes. We proved that when σ ≥ 6, the workload associated with one color is embarrassingly parallel. However, the number of nodes in a group (color) may be small when σ = 6. Therefore, we also explored σ = 3, where a small fraction of the algorithm needs to be serialized, and the overall parallel efficiency was improved. We implemented the parallel IFMM using OpenMP for shared-memory machines. Successively, we applied it to a fast-multipole accelerated boundary element method (FMBEM) as a preconditioner, and compared its efficiency with (a) the original IFMM parallelized by linking a multi-threaded linear algebra library and (b) the commonly used parallel block-diagonal preconditioner. Our results showed that our parallel IFMM achieved at most 4 × and 11 × speedups over the reference method (a) and (b), respectively, in realistic examples involving more than one million variables.

    DOI: 10.1016/j.cpc.2019.106975

    Web of Science

    arXiv

  17. A framework of shape optimisation based on the isogeometric boundary element method toward designing thin-silicon photovoltaic devices

    Takahashi Toru, Yamamoto Tatsuro, Shimba Yuta, Isakari Hiroshi, Matsumoto Toshiro

    ENGINEERING WITH COMPUTERS   Vol. 35 ( 2 ) page: 423 - 449   2019.4

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    Language:Japanese   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s00366-018-0606-6

    Web of Science

  18. A Numerical Method for Computing the Scattering Matrix by the Boundary Element Method with Applications to Phononic Band Analysis

    Matsushima K., Isakari H., Takahashi T., Matsumoto T.

    2019 THIRTEENTH INTERNATIONAL CONGRESS ON ARTIFICIAL MATERIALS FOR NOVEL WAVE PHENOMENA (METAMATERIALS))     page: 248 - 250   2019

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1109/metamaterials.2019.8900812

    Web of Science

  19. 3次元音響問題に関するisogeometric BEMに基づく形状感度解析 Reviewed

    高橋徹, 平井哲郎, 佐藤大輔, 飯盛浩司, 松本敏郎

    計算数理工学論文集   Vol. 18   page: 69-74   2018.12

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  20. Application of the inverse fast multipole method as a preconditioner in a 3D Helmholtz boundary element method

    Takahashi Toru, Coulier Pieter, Darve Eric

    JOURNAL OF COMPUTATIONAL PHYSICS   Vol. 341   page: 406 - 428   2017.7

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.jcp.2017.04.016

    Web of Science

  21. A level-set-based topology optimisation for acoustic-elastic coupled problems with a fast BEM-FEM solver

    Isakari Hiroshi, Kondo Toyohiro, Takahashi Toru, Matsumoto Toshiro

    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING   Vol. 315   page: 501 - 521   2017.3

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.cma.2016.11.006

    Web of Science

  22. A level-set-based topology optimisation of carpet cloaking devices with the boundary element method

    Nakamoto Kenta, Isakari Hiroshi, Takahashi Toru, Matsumoto Toshiro

    MECHANICAL ENGINEERING JOURNAL   Vol. 4 ( 1 )   2017

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1299/mej.16-00268

    Web of Science

  23. An efficient blocking M2L translation for low-frequency fast multipole method in three dimensions Reviewed

    Toru Takahashi, Yuta Shimba, Hiroshi Isakari, Toshiro Matsumoto

    Computer Physics Communications   Vol. 202   page: 151-164   2016

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.cpc.2016.01.008

  24. 2次元音響問題における境界要素法を用いたインピーダンス境界を有する散乱体のトポロジー最適化 Reviewed

    花田萌美, 飯盛浩司, 高橋徹, 松本敏郎

    計算数理工学論文集   Vol. 15   page: 37-42   2015

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  25. Helmholtz方程式の境界値問題に関連する固有値のトポロジー導関数と高速直接境界要素法を用いたその数値計算 Reviewed

    飯盛浩司, 北林達也, 高橋徹, 松本敏郎

    計算数理工学論文集   Vol. 15   page: 31-36   2015

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  26. 境界要素法を用いたクローキングデバイスのレベルセット法に基づくトポロジー最適化 Reviewed

    中本謙太, 飯盛浩司, 高橋徹, 松本敏郎

    計算数理工学論文集   Vol. 15   page: 55-60   2015

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  27. Level set-based topology optimization for 2D heat conduction problems using BEM with objective function defined on design-dependent boundary with heat transfer boundary condition Reviewed

    Jing G., Isakari H., Matsumoto T., Yamada T.,Takahashi T.

    Engineering analysis with boundary elements   Vol. 61   page: 61-70   2015

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  28. Task-based FMM for heterogeneous architectures Reviewed

    Emmanuel Agullo, Berenger Bramas, Olivier Coulaud, Eric Darve, Matthias Messner, Toru Takahashi

    Concurrency and Computation: Practice and Experience     2015

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1002/cpe.3723

  29. An interpolation-based fast-multipole accelerated boundary integral equation method for the three-dimensional wave equation Reviewed

    Toru Takahashi

    Journal of Computational Physics   Vol. 258 ( 1 ) page: 809-832   2014.2

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    DOI: 10.1016/j.jcp.2013.11.008

  30. Task-based FMM for multicore architectures Reviewed

    Emmanuel Agullo, Bérenger Bramas, Olivier Coulaud, Eric Darve, Matthias Messner, Toru Takahashi

    SIAM Journal on Scientific Computing   Vol. 36 ( 1 ) page: C66-C93   2014.2

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    Fast multipole methods (FMM) are a fundamental operation for the simulation of many physical problems. The high-performance design of such methods usually requires to carefully tune the algorithm for both the targeted physics and the hardware. In this paper, we propose a new approach that achieves high performance across architectures. Our method consists of expressing the FMM algorithm as a task flow and employing a state-of-the-art runtime system, StarPU, to process the tasks on the different computing units. We carefully design the task flow, the mathematical operators, their implementations, and scheduling schemes. Potentials and forces on 200 million particles are computed in 42.3 seconds on a homogeneous 160-core SGI Altix UV 100 and good scalability is shown.

    DOI: DOI: 10.1137/130915662

  31. Investigation of finite/infinite unidirectional elastic phononic plates by BEM Reviewed

    Haifeng Gao, Toshiro Matsumoto, Toru Takahashi, Hiroshi Isakari

    Engineering Analysis with Boundary Elements   Vol. 40   page: 93-103   2014

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.enganabound.2013.12.003

  32. A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method Reviewed

    Hiroshi Isakari, Kohei Kuriyama, Shinya Harada, Takayuki Yamada, Toru Takahashi, Toshiro Matsumoto

    Mechanical Engineering Journal   Vol. 1 ( 4 )   2014

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    DOI: 10.1299/mej.2014cm0039

  33. A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method Reviewed

    Hiroshi Isakari, Kohei Kuriyama, Shinya Harada, Takayuki Yamada, Toru Takahashi and Toshiro Matsumoto

    Mechanical Engineering Journa   Vol. 1 ( 4 ) page: CM0039   2014

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  34. Topological sensitivity of objective function defined on morphing boundaries of two dimensional heat conduction problems Reviewed

    Jing G., Isakari H., Matsumoto T., Takahashi T., Yamada T.

    WIT Transactions on Modelling and Simulation   Vol. 57   page: 3-11   2014

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  35. Level Set-Based Topology Optimization of Two Dimensional Heat Conduction Problems using the Boundary Element Method Reviewed

    Jing G, Isakari H., Matsumoto T. Takahashi T. Yamada T

    Proceedings of the Twelfth International Conference on Computational Structures Technology     page: -   2014

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  36. 3次元音響問題におけるレベルセット法と高速多重極境界要素法に基づくインピーダンス境界を有する散乱体のトポロジー最適化 Reviewed

    近藤豊大, 飯盛浩司, 高橋徹, 松本敏郎

    計算数理工学論文集   Vol. 14   page: 19-24   2014

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  37. Analysis of band structure for 2D acoustic phononic structure by BEM and the block SS method Reviewed

    H. F. Gao, T. Matsumoto, T. Takahashi, H. Isakari

    Computer Modeling in Engineering and Sciences   Vol. 90 ( 4 ) page: 283-301   2013

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  38. Eigenvalue analysis for acoustic problem in 3D by boundary element method with the block SakuraiSugiura method Reviewed

    Gao H. F., Matsumoto T., Takahashi T., Isakari H.

    Engineering Analysis with Boundary Elements   Vol. 37   page: 914-923   2013

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  39. レベルセット法と境界要素法を用いた二次元電磁波動問題におけるトポロジー最適化について Reviewed

    阿部史昌, 飯盛浩司, 高橋徹, 松本敏郎

    計算数理工学論文集   Vol. 13   page: 37-42   2013

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    Language:Japanese   Publishing type:Research paper (scientific journal)  

  40. Topology optimization for 2D heat conduction problems using boundary element method and level set method Reviewed

    Guoxian JING, Toshiro MATSUMOTO, Toru TAKAHASHI, Hiroshi ISAKARI, Takayuki YAMADA

    Transactions of the Japan Society for Computational Methods in Engineering   Vol. 13   page: 91-96   2013

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  41. 3次元電磁波動問題における境界要素法を用いたトポロジー感度解析とそのレベルセット法に基づく構造最適化への応用について Reviewed

    興梠洋一, 飯盛浩司, 高橋徹, 山田崇恭, 松本敏郎

    計算数理工学論文集   Vol. 13   page: 55-60   2013

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  42. A study on eigensolutions of 2D elastic problem by using BEM and FEM Reviewed

    Haifeng GAO, Toru TAKAHASHI, Hiroshi ISAKARI, Toshiro MATSUMOTO

    Transactions of the Japan Society for Computational Methods in Engineering   Vol. 13   page: 49-54   2013

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  43. An application of fast multipole method to isogeometric boundary element method for Laplace equation in two dimensions Reviewed

    Toru Takahashi, Toshiro Matsumoto

    Engineering Analysis with Boundary Elements   Vol. 36 ( 12 ) page: 1766-1775   2012.12

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    DOI: 10.1016/j.enganabound.2012.06.004

  44. Beaming of inplane elastic waves through a subwavelength channel with periodic corrugations Reviewed

    Toru Takahashi, Kouhei Kuriyama, Toshiro Matsumoto

    Applied Physics Letters   Vol. 101 ( 12 ) page: 124101   2012.9

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    We present an evidence of the beaming phenomenon regarding inplane elastic waves in the context of the enhanced acoustical transmission. Our simulations found emission of a long-range beam through a single subwavelength channel surrounded by periodic structures. The space-time spectral analysis of the inplane displacement field revealed that Rayleigh surface waves principally mediate the energy transmission that leads to the formation of beams. Consequently, we suggest a resonance condition for the beaming in terms of the ratio of the wavelength to the period of the structures. Our findings will be expected to foster the application to ultrasonic devices.

    DOI: http://dx.doi.org/10.1063/1.4753801

  45. A wideband fast multipole accelerated boundary integral equation method for time-harmonic elastodynamics in two dimensions Reviewed

    Toru Takahashi

    International Journal for Numerical Methods in Engineering   Vol. 91 ( 5 ) page: 531-551   2012.8

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    DOI: 10.1002/nme.4288

  46. Optimization of the parallel black-box fast multipole method on CUDA Reviewed

    Toru Takahashi, Cris Cecka, Eric Darve

    Innovative Parallel Computing (InPar), 2012     page: 1-14   2012.5

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    DOI: 10.1109/InPar.2012.6339607

  47. Optimizing the multipole-to-local operator in the fast multipole method for graphical processing units Reviewed

    Toru Takahashi, Cris Cecka, William Fong, Eric Darve

    International Journal for Numerical Methods in Engineering   Vol. 89 ( 1 ) page: 105-133   2012.1

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    DOI: 10.1002/nme.3240

  48. 誘電体ランダム配置系におけるレーザ発振の系内電場強度依存性に関する研究 Reviewed

    藤井雅留太, 松本敏郎, 高橋徹, 山田崇恭, 植田毅

    電気学会論文誌C   Vol. 132 ( 1 ) page: 89-95   2012

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  49. 三次元境界要素法を用いたレベルセット法に基づくトポロジー最適化 Reviewed

    志知晋一郎, 山田崇恭, 鈴木皓久, 松本敏郎, 高橋徹

    日本機械学会論文集(C編)   Vol. 78 ( 785 ) page: 228-239   2012

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  50. レベルセット法に基づく境界要素法を用いた定常動弾性問題のトポロジー最適化 Reviewed

    志知晋一郎, 山田崇恭, 松本敏郎, 高橋徹

    計算数理工学論文集   Vol. 12   page: No.01-121212   2012

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  51. Study on transition from photonic-crystal laser to random laser Reviewed

    G. Fujii, T. Matsumoto, T. Takahashi, T. Ueta

    Optics Express   Vol. 20 ( 7 ) page: 7300-7315   2012

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  52. A study on the effect of filling factor for laser action in dielectric random media Reviewed

    G. Fujii, T. Matsumoto, T. Takahashi, T. Ueta

    Appl. Phys. A   Vol. 107 ( 1 ) page: 35-42   2012

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  53. 3D acoustic shape sensitivity analysis using fast multipole boundary element method Reviewed

    C.J. Zheng, H.B. Chen, T. Matsumoto, T. Takahashi

    International Journal of Computational Methods   Vol. 9 ( 1 ) page: 1240004-1-1240004-11   2012

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  54. A wideband fast multipole boundary element method for three dimensional acoustic shape sensitivity analysis based on direct differentiation method Reviewed

    Changjun Zheng, Toshiro Matsumoto, Toru Takahashi, Haibo Chen

    Engineering Analysis with Boundary Elements   Vol. 36   page: 361-371   2012

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  55. Finite element analysis of laser modes within photonic random media Reviewed

    G. Fujii, T. Matsumoto, T. Takahashi, T. Ueta

    Journal of Physics B: Atomic, Molecular and Optical Physics   Vol. 45 ( 085404 )   2012

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    DOI: 10.1088/0953-4075/45/8/085404

  56. Analysis of acoustic transmission for one directional periodic bounded structure in 2D by BEM Reviewed

    GAO Haifeng, MATSUMOTO Toshiro, TAKAHASHI Toru, ISAKARI Hiroshi

    Transactions of the Japan Society for Computational Methods in Engineering   Vol. 12   page: 67-72   2012

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  57. The fast multipole method on parallel clusters, multicore processors, and graphics processing units Reviewed

    Eric Darve, Cris Cecka, Toru Takahashi

    Comptes Rendus Mecanique   Vol. 339   page: 185-193   2011.1

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    DOI: 10.1016/j.crme.2010.12.005

  58. Eigenvalue analysis for 2D acoustic problem by BEM with SS method Reviewed

    Haifeng Gao, Toshiro Matsumoto, Toru Takahashi, Takayuki Yamada

    Transactions of the Japan Society for Computational Methods in Engineering   Vol. 11   page: 107-110   2011

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  59. レベルセット法に基づく三次元要素生成法と設計変数依存型境界条件を考慮したトポロジー最適化法 Reviewed

    山田崇恭, 鈴木皓久, 松本敏郎, 高橋徹

    日本計算工学会論文集     page: Paper No.19980099   2011

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  60. Acoustic design shape and topology sensitivity formulations based on adjoint method and BEM Reviewed

    Toshiro Matsumoto, Takayuki Yamada, Toru Takahashi, C.J. Zheng, Shinya Harada

    Computer Modeling in Engineering and Sciences   Vol. 78 ( 2 ) page: 78-94   2011

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  61. Three dimensional acoustic shape sensitivity analysis by means of adjoint variable method and fast multipole boundary element approach Reviewed

    C.J. Zheng, H.B. Chen, T. Matsumoto, T. Takahashi

    Computer Modeling in Engineering and Sciences   Vol. 79 ( 1 ) page: 1-29   2011

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  62. Explicit evaluation of hypersingular boundary integral equations for acoustic sensitivity analysis based on direct differentiation method Reviewed

    Changjun Zheng, Toshiro Matsumoto, Toru Takahashi, Haibo Chen

    Engineering Analysis with Boundary Elements   Vol. 35   page: 1225-1235   2011

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  63. 不規則にdangling bondを含む誘電体ハニカム型ボンド構造内でのレーザ発振現象の有限要素解析 Reviewed

    藤井雅留太, 松田仁, 松本敏郎, 高橋徹, 山田崇恭, 植田毅

    計算数理工学論文集   Vol. 11   page: 89-94   2011

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  64. 誘電体ランダム配置系におけるレーザ発振の有限要素解析 Reviewed

    藤井雅留太, 松本敏郎, 高橋徹, 植田毅

    計算数理工学論文集   Vol. 10   page: 117-122   2010

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  65. 三次元音響問題における直接微分法に基づく形状感度解析法の定式化 Reviewed

    Changjun Zheng, 松本 敏郎, 高橋 徹, Haibo Chen

    日本機械学会論文集 (C編)   Vol. 76 ( 771 ) page: 2899-2908   2010

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  66. Explicit evaluation of hypersingular boundary integral equation for 3-D Helmholtz equation discretized with constant triangular element Reviewed

    Toshiro Matsumoto, Changjun Zheng, Shinya Harada, Toru Takahashi

    Journal of Computational Science and Technology   Vol. 4 ( 3 ) page: 194-206   2010

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  67. A study on optical properties of photonic crystals consisting of hollow rods

    G. Fujii, T. Matsumoto, T. Takahashi, T. Ueta

    IOP Conf. Series: Materials Science and Engineering   Vol. 10 ( 1 )   2010

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    Language:English  

    DOI: 10.1088/1757-899X/10/1/012072

  68. GPUによる境界要素法の高速計算 Invited Reviewed

    高橋徹

    シミュレーション   Vol. 28 ( 3 ) page: 23-28   2009.9

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  69. GPU-accelerated boundary element method for Helmholtz' equation in three dimensions Reviewed

    Toru Takahashi, Tsuyoshi Hamada

    International Journal for Numerical Methods in Engineering   Vol. 80 ( 10 ) page: 1295 - 1321   2009

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    Recently, the application of graphics processing units (GPUs) to scientific computations is attracting a great deal of attention, because GPUs are getting faster and more programmable. In particular, NVIDIA's GPUs called compute unified device architecture enable highly mutlithreaded parallel computing for non-graphic applications. This paper proposes a novel way to accelerate the boundary element method (BEM) for three-dimensional Helmholtz' equation using CUDA. Adopting the techniques for the data caching and the double-single precision floating-point arithmetic, we implemented a GPU-accelerated BEM program for GeForce 8-series GPUs. The program performed 6-23 times faster than a normal BEM program, which was optimized for an Intel's quad-core CPU, for a series of boundary value problems with 8000-128000 unknowns, and it sustained a performance of 167 Gflop/s for the largest problem (1 058 000 unknowns). The accuracy of our BEM program was almost the same as that of the regular BEM program using the double precision floating-point arithmetic. In addition, our BEM was applicable to solve realistic problems. In conclusion, the present GPU-accelerated BEM works rapidly and precisely for solving large-scale boundary value problems for Helmholtz' equation.

  70. 境界要素法を用いた弾性体感度解析における随伴変数法の適用 Reviewed

    柴田健士朗, 高橋徹, 松本敏郎

    計算数理工学論文集   Vol. 9   page: 37-42   2009

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  71. 連立Poission方程式の基本解を用いた境界要素法と基本解への代表寸法の導入 Reviewed

    内藤孝広, 高橋徹, 谷口智, 松本敏郎

    計算数理工学論文集   Vol. 7 ( 2 ) page: 313-318   2008

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  72. A fast boundary integral equation method for elastodynamics in time domain and its parallelisation Reviewed

    Yoshinori Otani, Toru Takahashi, Naoshi Nishimura

    Boundary Element Analysis: Mathematical Aspects and Applications, Lecture Notes in Applied and Computational Mechanics (M. Schanz and O. Steinbach eds.), Springer   Vol. 29   page: 161-185   2007

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  73. A hardware acceleration of the time domain boundary integral equation method for the wave equation in two dimensions

    T. Takahashi, T. Ebisuzaki, K. Koketsu

    Engineering Analysis with Boundary Elements   Vol. 31   page: 95-102   2007

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    We aimed at reducing the runtime of the time domain boundary integral equation method (TDBIEM) for the two-dimensional scalar wave equation by the help of a special-purpose computer MDGRAPE-2, which is a high-performance vector-parallel computer dedicated to computing long-range forces in classical molecular dynamics simulations. To this end, we presented a formulation to make MDGRAPE-2 compute the layer potential that is the most time-consuming in a run of the TDBIEM, considering to minimise the amount of data-transfer between MDGRAPE-2 and the host computer. The newly implemented TDBIEM code using three MDGRAPE-2s boards was about 109 times faster than the conventional code in an analysis of 5400 boundary elements and 640 time steps. We also demonstrated that the present hardware acceleration helps to perform large-scale simulations such as light propagation in photonic crystals.

  74. Accelerating boundary integral equation method using a special-purpose computer Reviewed

    T. Takahashi, A. Kawai, T. Ebisuzaki

    International Journal for Numerical Methods in Engineering   Vol. 66   page: 529-548   2006

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    We present a new solution to accelerate the boundary integral equation method (BIEM). The calculation time of the BIEM is dominated by the evaluation of the layer potential in the boundary integral equation. We performed this task using MDGRAPE-2, a special -purpose computer designed for molecular dynamics simulations. MDGRAPE-2 calculates pairwise interactions among particles (e.g. atoms and ions) using hardwired-pipeline processors. We combined this hardware with an iterative solver. During the iteration process, MDGRAPE-2 evaluates the layer potential. The rest of the calculation is performed on a conventional PC connected to MDGRAPE-2. We applied this solution to the Laplace and Helmholtz equations in three dimensions. Numerical tests showed that BIEM is accelerated by a factor of 10-100. Our rather naive Solution has a calculation cost of O(N-2 x N-iter), where N is the number of unknowns and Nitr is the number of iterations.

  75. A fast boundary element method for the analysis of fiber-reinforced composites based on a rigid-inclusion model Reviewed

    Y.J. Liu, N. Nishimura, Y. Otani, T. Takahashi, X.L. Chen, H. Munakata

    Journal of Applied Mechanics - Transactions of the ASME   Vol. 72   page: 115-128   2005

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  76. 専用計算機による3次元静弾性問題に対する境界積分方程式法の高速計算 Reviewed

    高橋徹, 戎崎俊一

    日本機械学会論文集 (A編)   Vol. 71   page: 1620-1625   2005

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    Authorship:Lead author   Language:Japanese   Publishing type:Research paper (scientific journal)  

    DOI: 10.1299/kikaia.71.1620

  77. 3次元電磁波散乱問題に対するモーメント法のハードウェアアクセラレーション Reviewed

    高橋徹, 戎崎俊一

    日本情報処理学会論文誌コンピューティングシステム   Vol. 14   page: 172-182   2005

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  78. 改良円錐孔底法による地山応力測定 Reviewed

    小林昭一, 高橋徹, 吉川太, 吉田次男

    材料   Vol. 52 ( 5 ) page: 500-504   2003

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  79. A fast BIEM for three-dimensional elastodynamics in time domain, Engineering Analysis with Boundary Elements Reviewed

    T. Takahashi, N. Nishimura, S. Kobayashi

    Engineering Analysis with Boundary Elements   Vol. 27   page: 491-506   2003

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    A fast boundary integral equation method for three-dimensional (313) elastodynamics in time domain is proposed. We discuss in detail the plane wave time domain (PWTD) algorithm in 3D elastodynamics, whose complexity is O(N-s log(2)N(s)N(t)) or O((NsNt)-N-3/2), depending on the choice of the algorithms for the Legendre transform, where N-s and N-t are the spatial and temporal degrees of freedom, respectively. An O((NsNt)-N-3/2) implementation is made, whose efficiency is demonstrated in problems of the size of N-s = O(10(4)).

  80. 2次元時間域動弾性問題に対する高速境界積分方程式法 Reviewed

    高橋徹, 西村直志, 小林昭一

    日本機械学会論文集 (A編)   Vol. 67 ( 661 ) page: 1409-1416   2001

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    Authorship:Lead author   Language:Japanese   Publishing type:Research paper (scientific journal)  

    DOI: 10.1299/kikaia.67.1409

  81. 多重極積分方程式法による3次元定常Stokes流の解析 Reviewed

    高橋徹, 浪江雅幸, 西村直志, 小林昭一

    BTEC論文集   Vol. 10   page: 1-4   2000

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    Authorship:Lead author   Language:Japanese   Publishing type:Research paper (scientific journal)  

  82. パネルクラスタリング積分方程式法による二次元拡散方程式の高速解法 Reviewed

    高橋徹, 西村直志, 小林昭一

    日本機械学会論文集 (A編)   Vol. 66 ( 647 ) page: 1268-1273   2000

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    Authorship:Lead author   Language:Japanese   Publishing type:Research paper (scientific journal)  

    DOI: 10.1299/kikaia.66.1268

  83. 改良型円錐孔底応力解放法への多重極積分方程式法の適用 Reviewed

    高橋徹, 小林昭一, 西村直志

    境界要素法論文集   Vol. 15   page: 105-110   1998

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  84. 境界要素法による長大な埋設構造物のガルバニック腐食解析 --- 土壌の電気伝導率がゆるやかに変化する場合 Reviewed

    青木繁, 高橋徹, 浦郷正隆, 天谷賢治, 西川明伸

    材料   Vol. 46 ( 2 ) page: 170-175   1997

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    Language:Japanese   Publishing type:Research paper (scientific journal)  

    DOI: 10.2472/jsms.46.170

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Presentations 37

  1. 境界要素法の高速化

    高橋徹

    日本学術会議 第4回計算力学シンポジウム 

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    Event date: 2014.12

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Venue:日本学術会議事堂   Country:Japan  

  2. 境界要素法とレベルセット法を 用いた2次元電磁波動問題におけ る多目的トポロジー最適化

    北林達也, 飯盛浩司, 高橋徹, 松本敏郎

    日本機械学会 第27回計算力学講演会(CMD2014) 

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    Event date: 2014.11

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:岩手大学   Country:Japan  

  3. 波動問題のBurton-Miller型積分方程式に関するアイソジオメト リック境界要素法の開発

    榛 葉祐太, 高橋徹, 林慎 一, 坂部遥輝, 飯盛浩司, 松本敏郎

    日本機械学会 第27回計算力学講演会(CMD2014) 

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    Event date: 2014.11

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:岩手大学   Country:Japan  

  4. 2次元境界要素法に関する高速多重極型直接解法の実装と性能評価

    高橋徹, 飯盛浩司, 松本敏郎

    日本機械学会 第27回計算力学講演会(CMD2014) 

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    Event date: 2014.11

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:岩手大学   Country:Japan  

  5. 高速直接境界要素法を用いた2次元電磁波動問題のトポロジー感度解析について

    飯盛浩司, 高橋徹, 松本敏郎

    日本機械学会 第27回計算力学講演会(CMD2014) 

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    Event date: 2014.11

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:岩手大学   Country:Japan  

  6. GPU統合型CPUを用いた二次元ヘルムホルツ方程式に対する境界要素法の高速化

    大澤尚希, 高橋徹, 吉田翔太, 飯盛 浩司, 松本敏郎

    日本機械学会 第27回計算力学講演会(CMD2014) 

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    Event date: 2014.11

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:岩手大学   Country:Japan  

  7. 格子ボルツマン法による3次元流れ場のトポロジー最適化

    原 彰宏, 松本敏郎, 山田崇恭, 高橋徹, 飯盛浩司

    日本機械学会 第27回計算力学講演会(CMD2014) 

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    Event date: 2014.11

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:岩手大学   Country:Japan  

  8. An interpolation-based fast multipole boundary integral equation method for wave equation International conference

    Toru Takahashi

    12th U.S. National Congress on Computational Mechanics (USNCCM12) 

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    Event date: 2013.7

    Language:English   Presentation type:Oral presentation (general)  

    Country:United States  

    From the mathematical and numerical viewpoint, the enhancement of the fast multipole method (FMM; Greengard et al, 1987) to time-dependent problems is an interesting and challenging topic in the research field of the boundary integral equation method (BIEM). However, as far as I know, there have been only several works regarding the FMM in time domain, e.g., Strain 1994, Ergin et al 1998, Shanker et al 2003, Takahashi et al 2003, and Tausch 2007. Following these studies, this study purposes to develop a new fast time-domain boundary integral equation method (TDBIEM) for wave equation in three dimensions. The present method is based on the interpolation of the time-dependent Green's function to re-express the function in the form of separation of variables. This enables to construct a time-domain variant of the FMM. The computational complexity of the resulting TDBIEM is estimated to O(N^1.33*M), while that of the conventional TDBIEM is O(N^2*M), where N and M denote the spatial and temporal degrees of freedom, respectively. In this talk, I will mention the theoretical and numerical aspects of the fast method. Acknowledgement: This work was supported by JSPS KAKENHI Grant Number 24656072.

  9. A time-domain BIEM for Wave Equation accelereted by Fast Multipole Method using Interpolation International conference

    Toru Takahashi

    The 11th International Conference on Mathematical and Numerical Aspects of Waves (Waves 2013) 

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    Event date: 2013.6

    Language:English   Presentation type:Oral presentation (general)  

    Country:Tunisia  

  10. Task-based Parallelization of the Fast Multipole Method on NVIDIA GPUs and Multicore Processors International conference

    Emmanuel Agullo, Bérenger Bramas, Olivier Coulaud, Matthias Messner, Eric Darve, Toru Takahashi

    GPU Technology Conference (GTC) 2013 

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    Event date: 2013.3

    Language:English   Presentation type:Oral presentation (general)  

    Country:United States  

    Learn about the fast multipole method (FMM) and its optimization on NVIDIA GPUs. The FMM is a well-known algorithm with a variety of applications in areas like galaxy simulation, electrostatic potential calculations, boundary element methods, integral equations, dislocations dynamics, etc. The FMM offers several difficulties when running on parallel heterogeneous platforms such as multicore processors with GPUs. Some parts of the calculation suffer from limited concurrency, and load-balancing can be very uneven for certain distributions of particles. We will present a new API and runtime system, called StarPU, that allows expressing a calculation as a graph of tasks, with dependencies, and contains a runtime system that can optimally schedule those tasks on a parallel machine. StarPU supports conventional multicore processors as well as NVIDIA GPUs.

  11. An Interpolation-based Fast Multipole Boundary Integral Equation Method for Wave Equation

    Toru Takahashi

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    Event date: 2013.3

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  12. Pipelining the Fast Multipole Method over a Runtime System International conference

    Emmanuel Agullo, Berenger Bramas, Olivier Coulaud, Eric F. Darve, Matthias Messner, Toru Takahashi

    SIAM Conference on Computational Science and Engineering 

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    Event date: 2013.2 - 2013.3

    Language:English   Presentation type:Oral presentation (general)  

    Country:United States  

    Fast multipole methods (FMM) usually require a careful
    tuning of the algorithm for both the targeted physics and
    the hardware. In this talk, we propose a new approach
    that achieves high performance across architectures. We
    express the FMM algorithm as a task flow and employ a
    runtime system to process the tasks on the different processing
    units. We carefully design the task flow, the mathematical
    operators, their CPU and GPU implementations
    and their schedule.

  13. An FMM for Isogeometric BEM for Potential Problems in 2D

    Toru Takahashi, Yuya Nakai, Toshiro Matsumoto

    JSME 25th Computational Mechanics Conference 

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    Event date: 2012.10

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  14. 大規模音響問題における高速 多重極アイソジオメトリック境界要素法の開発

    林慎一,高橋徹,松本敏郎

    日本機械学 会計算力学講演会講演論文集 

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    Event date: 2012

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:神戸   Country:Japan  

  15. An acceleration of multipole-to-local operation for low-frequency fast multipole BIEM with GPU International conference

    Toru Takahashi, Cris Cecka, Eric Darve

    Symposium of the International Association for Boundary Element Methods (IABEM) 2011 

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    Event date: 2011.9

    Language:English   Presentation type:Oral presentation (general)  

    Country:Austria  

  16. An implementation of multipole-to-local (M2L) operation for low-frequency fast multipole BIEM on GPU International conference

    Toru Takahashi, Cris Cecka, Eric Darve

    11th US National Congress on Computational Mechanics 

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    Event date: 2011.7

    Language:English   Presentation type:Oral presentation (general)  

    Country:United States  

  17. An implementation of low-frequency fast multipole BIEM for Helmholtz' equation on GPU

    JSME 23rd Computational Mechanics Division Conference 

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    Event date: 2010.9

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  18. An acceleration of the black-box fast multipole method with GPU

    2nd International Workshops on Advances in Computational Mechanics 

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    Event date: 2010.3

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  19. 境界要素法におけるGPUの活用例

    高橋徹

    第17回 計算数理工学フォーラム 

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    Event date: 2009.9

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  20. The black-box fast multipole method on graphical processing units International conference

    10th US National Congress on Computational Mechanics 

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    Event date: 2009.7

    Language:English   Presentation type:Oral presentation (general)  

  21. Running BEM for wave problems on GPU

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    Event date: 2009.5

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  22. GPUによる境界要素法の高速化

    高橋徹、濱田毅

    日本機械学会第21回計算力学講演会 

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    Event date: 2008.11

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  23. HPC of boundary element method with GPU International conference

    International Supercompter Conference 2008 

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    Event date: 2008.6

    Language:English   Presentation type:Poster presentation  

  24. Hardware Acceleration for Boundary Element Methods International conference

    Toru Takahashi

    Harvard/Riken GPGPU Symposium 2008 

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    Event date: 2008.3

    Language:English   Presentation type:Oral presentation (invited, special)  

  25. An acceleration of time-domain BIEM for elastodynamic crack problems International conference

    Ninth U.S. National Congress on Computational Mechanics 

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    Event date: 2007.7

    Language:English   Presentation type:Oral presentation (general)  

  26. A fast time domain BIEM for elastodynamic crack problems in 3D International conference

    International Conference on Computational Methods (ICCM2007) 

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    Event date: 2007.4

    Language:English   Presentation type:Oral presentation (general)  

  27. A fast boundary integral equation method for elastodynamics in time domain and its parallelisation International conference

    International Association for Boundary Element Methods 2006 Conference 

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    Event date: 2006.7

    Language:English  

  28. GPGPU for BEM International conference

    International Association for Boundary Element Methods 2006 Conference 

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    Event date: 2006.7

    Language:English   Presentation type:Oral presentation (general)  

  29. An acceleration of fast boundary integral equation method using a special-purpose computer International conference

    Eighth U.S. National Congress on Computational Mechanics 

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    Event date: 2005.7

    Language:English   Presentation type:Oral presentation (general)  

  30. A time domain fast boundary integral equation method for 3D elastodynamics International conference

    The Institute of Mathematics and its Applications 3rd International Conference on Boundary Integral Methods: Theory and Applications & Interdisciplinary Workshop on Developments in Boundary Element Methods for Acoustics and Electromagnetics 

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    Event date: 2004.9

    Language:English   Presentation type:Oral presentation (general)  

  31. Fast computing of boundary integral equation method by a special-purpose computer International conference

    Fast Multipole Method, Tree-Code and Related Approximated Algorithms --Trading Exactness and Efficiency-- 

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    Event date: 2004.4

    Language:English   Presentation type:Oral presentation (invited, special)  

  32. Fast computing of boundary element method by using MDGRAPE-2 International conference

    Joint RIKEN-INST Seminar on Application of Fast Computing Methods in Physics, 

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    Event date: 2003.11

    Language:English   Presentation type:Oral presentation (invited, special)  

  33. Application of the special-purpose computer MDGRAPE-2 to the boundary integral equation methods for Helmholtz equation and elastostatics, International conference

    The eighth International Symposium on Simulation Science --New Methodology of Science in the 21st Century-- 

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    Event date: 2003.3

    Language:English   Presentation type:Poster presentation  

    Country:Japan  

  34. A time domain fast multipole boundary integral equation method for elastodynamics International conference

    Sixth U.S. National Congress on Computational Mechanics 

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    Event date: 2001.8

    Language:English   Presentation type:Oral presentation (general)  

  35. Improved conical-end borehole method International conference

    European Rock Mechanics Symposium (EUROCK) 2001 

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    Event date: 2001.1

    Language:English   Presentation type:Oral presentation (general)  

  36. Applications of fast multipole boundary integral equation methods in crack problems International conference

    36th Annual Technical Meeting Society of Engineering Science 

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    Event date: 1999.10

    Language:English   Presentation type:Oral presentation (general)  

  37. B.E. analysis of galvanic corrosion of long structure buried in soil with gradient electrical conductivity International conference

    Boundary Element XIX 

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    Event date: 1997.9

    Language:English   Presentation type:Oral presentation (general)  

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KAKENHI (Grants-in-Aid for Scientific Research) 10

  1. 3次元電磁波動散乱問題に対する時間領域境界要素法の高速アルゴリズムの開発

    Grant number:21H03454  2021.4 - 2024.3

    科学研究費助成事業  基盤研究(B)

    高橋 徹

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    Authorship:Principal investigator 

    Grant amount:\18070000 ( Direct Cost: \13900000 、 Indirect Cost:\4170000 )

    現代社会において、電波を利用した機器の重要性が増しており、その設計・開発等を効率化するために数値シミュレーションの果たす役割も増している。時間領域の電磁場解析に対して今日標準的な解法は時間領域差分法(FDTD法)である。FDTD法は計算コストは低いが、曲面等のモデル化が不得意であり、自由空間の解析には近似が必須である。一方、本研究が注目する時間領域境界要素法(TDBEM)はFDTD法の欠点を有しないが、計算コストが膨大である。そこで本研究は、3次元スカラー波動方程式に対する研究代表者の先行研究を基盤として、補間型高速多重極法に基づく高速かつ低メモリ消費なTDBEMを確立する。
    2022年度は、前年度に課題として残した3次元電磁波動散乱問題用の高速時間領域境界要素法(TDBEM)の改善に取り組んだ。具体的には、電場積分方程式(EFIE)の時間微分を行うことによって、計算コストをO(M)(ここで、Mは時間ステップ数)に保ちつつ、Herzベクトルeの代わりに表面電流Jを直接扱うこととした。しかし、時間微分されたEFIEは時間不安定であるため、何らかの磁場方程式(MFIE)との結合が必要であるが、時間微分されたEFIEに時間微分されたMFIEとMFIEそれ自体の両方を結合して得た結合型CFIEが時間安定であることを数値実験的に見い出した。これをもって本研究課題の核心である高速TDBEMの完成とした。これは3次元電磁波動散乱問題に対する新しい数値解析手法の提案であり、その計算科学/物理分野における基礎研究的な意義は深い。この成果は11月に国内学会発表を行い、計算物理学の専門誌に論文が受理された(3月)。なお、前年度に定式化した高速TDBEMに関する国内学会発表(6月)および国際学会発表(7月)もそれに先立ち行った。次に、本研究経費で調達したPCクラスタ上で当該高速TDBEMのハイブリッド並列化(=OpenMPとMPIの併用による並列化)の実装に成功した。並列化効率は概ね高々50%程度に留まったが、メモリ分散が可能である点は大規模解析の実行に有用である。
    一方、最終年度に研究予定している形状最適化に関する予備的検討として、3次元スカラー波動方程式に関する随伴変数法に基づく形状最適化の研究を行い、6月に関連論文が専門誌に受理され、11月に国内にて研究発表に至った。
    前年度に持ち越しとなった本研究課題の核心部分の研究、すなわち高速かつ時間安定な時間領域境界要素法(TDBEM)の構成が達成された点において本研究の進捗状況は、昨年度の「やや遅れている」から一転して、順調化したと言える。
    また、研究開始当初のR4年度の目的であったメモリ分散計算環境(本研究はPCクラスタ)における当該TDBEMの並列コードの開発は、計算ノードのロードバランスの均等化の観点から苦心したが、並列コードの実装上の観点から最もシンプルである空間分割を採用することとした。結果、並列コード開発は大きな支障なく遂行できた。ただし、並列化効率が高々50%程度に留まった一因はロードバランスの不均一性が原因である可能性もあり、より多くの問題(特に、散乱体の空間配置が一様でない問題)を解析して、その結果から並列化の指針を探索する必要がある。
    さらに、3次元スカラー波動問題に対する形状最適化の開発に成功した点は、最終年度に予定している3次元電磁波動散乱問題に形状最適化の土台となる。この意味においても進捗状況は概ね順調と言える。
    開発したハイブリッド並列化高速TDBEMの応用可能性および付加価値を高める観点から、(時間領域境界要素法を含む)境界要素法が元来得意とする形状最適化に取り組む。その基礎となるのがR4年度に開発した3次元スカラー波動問題に対する形状最適化である。当最適化では、形状感度(形状微分)に基づく非線形最適化手法によるものであり、設計変数は散乱体の表面をNURBS曲面でモデル化した際の制御点である。本電磁波動散乱問題においても同様なフレームワークを構築することを最終目的とする。その形状感度については既往研究において導出されていることが本研究課題の開始後に文献調査を経て判明したが、具体的かつ大規模な問題に対する数値解析については研究例がない。したがって、本高速TDBEMを用いた形状最適化問題の実行は依然として大きなインパクトがあると考えられる。ただし、形状感度(あるいは目的関数)を計算するためには、本境界要素法にいわゆる内点計算を組み込む必要があり、その開発から始める必要がある。その上で、形状感度を用いない場合(例えばCOBYLA法を用いる)の最適化計算が実行できるかについて確認後、形状感度の計算ルーチンの数値実装し、形状感度に基づく形状最適化手法の構築を行う。

  2. 局所共振現象を取り入れた弾性波動・電磁メタマテリアル構造の創成

    Grant number:19H00740  2019.4 - 2024.3

    科学研究費助成事業  基盤研究(A)

    松本 敏郎, 田地 宏一, 植田 毅, 山田 崇恭, 飯盛 浩司, 高木 賢太郎, 高橋 徹

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    Authorship:Coinvestigator(s) 

    本研究ではトポロジー最適化を用いて、局所共振現象を組み込んだ新しい特性を有するメタマテリアルの創成を試みる。多材料からなる単位構造の周期構造に対し、波動問題の解析手法として適した境界要素法を用い、周期構造の解析に必要な高速化を行い、多材料に対するトポロジー最適化アルゴリズムや新しい形状表現法を開発する。これらを基に局所共振弾性波動・電磁メタマテリアルのトポロジー最適化法を開発し、弾性波ダイオード、波動変換、クローキングデバイス等のメタマテリアルを創成する。
    振動遮断特性を有する複数の材料から構成される局所的な微細構造が埋め込まれた周期構造により,振動や騒音を格段に遮断することが可能フォノニックメタマテリアルのトポロジー最適化を行う方法論を実際の応用例で検証を行うとともに、体積制約条件を厳密に満足するレベルセット関数の更新方法、構造材料が非線形変形挙動を有する場合や境界条件が非線形である場合へのトポロジー最適化などへの計算法の拡張を行っている。
    まず、広帯域の周波数に対して、目的汎関数を最小化できるよう、周波数応答のパデ近似を用いる方法を開発した。さらに境界の目的関数が微分方程式の解の接線微分で構成されている場合について、解法の拡張を行い、単位周期構造に対する解析例を通じて有効性を確認した。
    レベルセット法は、材料分布が定義された領域中の1点を考えたとき、その点が材料中にあるときは正、材料の境界にあるときは0,材料の外部にあるときは負の値を取るように定義されたスカラー関数であり、その分布が変化すると材料分布の境界が変化する。構造内の各点のレベルセット関数の変化は、その点における変位や歪に関係づけられるトポロジー導関数の値に比例して変化するものとしているが、異方性の材料定数を有する材料や、場の支配方程式は線形でも境界条件が非線形の場合のトポロジー導関数の導出は困難であった。そこで、まず簡単な支配方程式としてラプラス方程式を考え、境界条件が任意の非線形性を有する問題について、トポロジー導関数を導出した。また、材料挙動が非線形の場合と材料定数が異方性を示す問題についても、レベルセット法の拡張を行った。
    本研究では、振動遮断特性を有する複数の材料から構成される局所的な微細構造が埋め込まれた周期構造により、振動や騒音を格段に遮断することが可能な3次元フォノニックメタマテリアルのトポロジー最適化を行うことを目的としており、最終的には単位周期構造に対する様々な目的関数、境界条件、材料定数、線形・非線形挙動の考察が必要となる。令和4年度は目的関数として広帯域の周波数に対するトポロジー最適化、通常の随伴方程式の導出が困難な未知関数の接線微分を含む目的関数に対する単位周期構造のトポロジー最適化、変形挙動が非線形の場合、境界条件が非線形の場合、材料定数が異方性の場合についてのレベルセット法の開発を行うなど、順調に成果を挙げている。特に、広帯域の周波数に対するトポロジー最適化報の開発においては、パデ近似による方法を提案し、計算量の大きな削減を図った。また、未知関数の接線微分を含む目的関数に対するトポロジー最適化では、これまで存在しなかった新しい境界値問題の数学的考察につながる提案を行った。
    2022年度はまず1つの解決方法を示すことが出来た。2023年度はさらにこの方法を新しい数学的問題として発展させる。また、様々な材料構成からなる局所共振構造を考えうることから、材料の異方性に対してのトポロジー最適化の一般理論を構築する。材料定数が悲報星の場合、座標変換を行うと等方性の問題として解の漸近展開を得ることができるが、異方性の場における微小円孔境界で境界条件を考える必要があり、異方性の解を等方性の漸近展開に変換する必要がある。これは未知の問題であり、2023年度はこの問題の解決を行うとともに、局所共振フォノニック単位構造の様々な非線形境界条件の取扱い方法の構築を完了する。開発したこれらの解法を組み合わせて用いることにより、局所共振フォノニック単位構造のレベルセット法によるトポロジー最適化法の完成を目指す。

  3. アイソジオメトリック境界要素法によるプラズモニクス用3次元形状最適化システム

    2018.4

    科学研究費補助金  基盤研究(C)

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    Authorship:Principal investigator 

  4. A 3D shape optimisation system for plasmonics using isogeometric BEM

    Grant number:18K11335  2018.4 - 2021.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    Takahashi Toru

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    Authorship:Principal investigator 

    Grant amount:\4160000 ( Direct Cost: \3200000 、 Indirect Cost:\960000 )

    As a numerical simulation method to develop and design devices regarding plasmonics, which is based on the surface plasmons, the (frequency-domain) boundary element method, in particular, isogeometric boundary element method (IGBEM) is more appropriate and promising than the time-domain finite-difference method, which is the de facto standard method nowadays. Therefore, we aimed at developping an 3D IGBEM for doubly-periodic layer systems and, then, constructing an shape optimisation system. We successfully developeed the IGBEM by considering the periodicity into the existing researches for non-perodic problems. Also, we could establish the shape optimisation system via the investigation for 3D acoustics.

  5. On the stability of boundary integral methods in wave problems

    Grant number:18H03251  2018.4 - 2021.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    Nishimura Naoshi

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    Authorship:Coinvestigator(s) 

    Stability of time domain boundary integral methods for wave problems using collocation is a long standing tough problem which still remains open in spite of many efforts to solve it. This study proposes a method to investigate the stability of boundary integral methods in time domain using a solver of non-linear eigenvalue problems called the Sakurai Sugiura method. We test the proposed method via numerical experiments. It is found that the proposed method is effective not only in assessing the stability but in studying the accuracy of boundary integral formulations. We also proposed a stable fast method in 3D as well as a space-time method for variable domains, both of which turned out to be effective.

  6. 薄型シリコン太陽電池の高効率化に向けた高速・高精度な形状最適化システムの開発

    2015.4 - 2018.3

    科学研究費補助金  基盤研究(C)

    高橋徹

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    Authorship:Principal investigator 

  7. Development of fast and accurate shape optimisation system to design high efficient thin Silicon solar cells

    Grant number:15K06683  2015.4 - 2018.3

    Takahashi Toru

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    Authorship:Principal investigator 

    Grant amount:\4810000 ( Direct Cost: \3700000 、 Indirect Cost:\1110000 )

    We proposed a new isogeometric boundary element method for 2D singly periodic boundary value problems of 2D Helmholtz equation and developed a shape optimisation system based on the boundary element method, adjoint variable method, and quasi-Newton method. The system is capable to design high-efficient thin Silicon solar cells. In an optimisation problem to maximise the relative energy absorption rate in the silicon layer of a four-layer (air/Si/Ag/air) model, we could obtain the optimal shape that can absorb 67% of the incident energy. The present result together with the computer program posted on the Internet is significant to design plasmonic devices. Meanwhile, we obtained some results for 3D problems, which can be exploited for the succeeding research starting from FY2018.

  8. 非定常問題に対する時間域境界要素法の高速アルゴリズムの開発と応用

    2012.4 - 2014.3

    科学研究費補助金 

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    Authorship:Principal investigator 

  9. 波動問題に対する高速多重極積分方程式法のGPUを利用した並列計算手法の開発

    2010.4 - 2012.3

    科学研究費補助金  若手研究(B)

    高橋 徹

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    Authorship:Principal investigator 

  10. 境界要素法の高速化のための専用計算機の援用と開発に関する研究

    2003.4 - 2005.3

    科学研究費補助金  若手研究(B)

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    Authorship:Principal investigator 

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Teaching Experience (On-campus) 45

  1. 機械・航空工学科実験第二

    2018

  2. 機械・航空工学科実験第一

    2018

  3. 工場見学

    2018

  4. 工場実習

    2018

  5. 基礎セミナーA

    2018

  6. Advanced Lecture for Computaional Physics

    2018

  7. 機械・航空工学設計製図第2

    2018

  8. Linear Algebra II

    2017

  9. 機械・航空工学設計製図第2

    2017

  10. Advanced Lecture for Computaional Physics

    2017

  11. 応用解析学特論

    2016

  12. Electromagnetics II

    2016

  13. Linear Algebra II

    2016

  14. 機械・航空工学設計製図第2

    2016

  15. 機械・航空工学設計製図第2

    2015

  16. 応用解析学特論

    2015

  17. Linear Algebra II

    2015

  18. Electromagnetics II

    2015

  19. 機械・航空工学設計製図第2

    2014

  20. 応用解析学特論

    2014

  21. Linear Algebra II

    2014

  22. Electromagnetics II

    2014

  23. Linear Algebra II

    2013

  24. 機械・航空工学設計製図第2

    2013

  25. 工場見学

    2013

  26. 工場実習

    2013

  27. 機械・航空工学科実験第2

    2013

  28. Electromagnetics II

    2013

  29. 応用解析学特論

    2013

  30. 機械・航空工学科実験第1

    2013

  31. Linear Algebra II

    2012

  32. 機械・航空工学設計製図第2

    2012

  33. 応用解析学特論

    2012

  34. Electromagnetics II

    2012

  35. 応用解析学特論

    2011

  36. Linear Algebra II

    2011

  37. 機械・航空工学設計製図第2

    2011

  38. 線形代数学Ⅱ

    2010

  39. 応用解析学特論

    2010

  40. 機械・航空工学科実験第一

    2009

  41. 機械・航空工学科実験第二

    2009

  42. 機械・航空工学科実験第二

    2008

  43. 機械・航空工学科実験第一

    2008

  44. 機械・航空工学科実験第一

    2007

  45. 機械・航空工学科実験第二

    2007

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Teaching Experience (Off-campus) 5

  1. 計算工学実験III

    2005.4 - 2006.3 東洋大学)

  2. ソフトウェア演習A/プログラミングA

    2005.4 - 2006.3 東洋大学)

  3. 計算工学実験III

    2004.4 - 2005.3 東洋大学)

  4. プログラミング技法

    2004.4 - 2005.3 東洋大学)

  5. 計算工学実験III

    2003.4 - 2004.3 東洋大学)

 

Social Contribution 4

  1. 名大MIRAI GSC(第2ステージ)

    Role(s):Advisor

    名古屋大学高等研究院  2019.7

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    Audience: High school students

  2. 名大MIRAI GSC(第1ステージ)

    Role(s):Lecturer

    名古屋大学高等研究院  2019.6

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    Audience: High school students

  3. 豊西総合大学

    Role(s):Lecturer

    愛知県立豊田西高校  2016.11

  4. 高大連携講座

    2010.10

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    愛知県立横須賀高校において、講座8(工学1)「計算力学最前線:GPU」について講演した。