Faculty Profiles - TAKAHASHI Toru

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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.

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

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

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

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.

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

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

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

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

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

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)).

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

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

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

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

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

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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Papers - TAKAHASHI Toru