- ポテンシャルの高速計算について (On fast methods for computing potentials)
- 吉田研一, 西村直志, 京都大学学術情報メディアセンター全国共同利用版 広報, Vol.2, pp.123--128, 2003.3 (K. Yoshida and N. Nishimura, Trans ACCMS, Kyoto Univ, Vol.2, pp.123--128, 2003.3)
- This paper compares performance of fast methods of computing Coulomb's potentials including FMM, tree methods, and the use of MDGRAPE.
- Diagonal form 多重極 積分方程式法の並列化 (A Parallel Implementaion of Diagonal Fast Multipole BIEM)
- 吉田研一, 西村直志, 境界要素法論文集, Vol.19, pp.75--78, 2002.12 (Trans. JASCOME, Journal of Boundary Element Methods, Vol.19, pp.75--78, 2002.12)
- This paper discusses a parallel implementation of the diagonal form fast multipole BIEM. Diagonal form FM-BIEMs are suitable for parallelization because the M2L operations are dianonalized. Taking this advantage, we parallelize an implementation of the diagonal form fast multipole BIEM with MPI. In the numerical analysis we deal with crack problems for three-dimensional Helmholtz' equation. We use a PC cluster to test the parallel implementation. The numerical results show the efficiency of the proposed method.
- A time domain fast boundary integral equation method for threee dimensional elastodynamics
- T. Takahashi and N. Nishimura, RIMS Kokyuroku 1265 229-240, 2002.5 (数理解析研究所講究録 1265, 229-240, 2002.5)
- A fast boundary integral equation method for three dimensional elastodynamics in time domain is proposed. It is shown that the complexity of the proposed method is $O(N_s \log ^2 N_s N_t)$ or $O(N_s^{3/2} N_t)$, depending on the choice of the algorithms for the Legendre transform, in problems with spatial and temporal degrees of freedom of $N_s$ and $N_t$, respectively. The efficiency of the proposed approach is demonstrated in problems of the size of $N_s=O(10^4)$.
- Application of a diagonal form fast multipole BIEM to the analysis of three dimensional scattering of elastic waves by cracks
- K. Yoshida, N. Nishimura and S. Kobayashi, Trans JASCOME, 18, 77--80, 2001
- This paper presents a 4 moment formulation of the diagonal form FMM in three dimensional elastodynamics in the frequency domain. This formulation enables a fast construction of the coefficient matrix of BIEM (boundary integral equation method) with O(N log N) operations when the domain size is much larger than the wavelength, where N is the number of unknowns. The proposed formulation is utilised and concluded to be effective in an analysis of the scattering of elastic waves by cracks.
- 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 (Fast Boundary Integral Equation Method for Elastodynamic Problems in 2D in Time Domain)
- 高橋 徹, 西村 直志, 小林 昭一, 日本機械学会論文集 vol.67 vol 661(A), 1409--1416, 2001 (T. Takahashi, N. Nishimura and S. Kobayashi, Trans JSME (A) Vol.67, No.661, 1409--1416, 2001)
- This paper describes a fast boundary integral equation method (BIEM) for elastodynamic problems in 2D in time domain for solving very large scale initial-boundary value problems which can not be analyzed with the conventional BIEM within an affordable amount of time. At first, we derive a plane wave expansion of the fundamental solution of elastodynamic problems. This expansion formula enables us to construct a fast algorithm for evaluating the layer potentials in BIE which uses the multilevel plane wave time domain (PWTD) algorithm, that was originally developed by A. Ergin and M. Lu et al. in scalar wave problems. Finally, a fast solution method is obtained with the help of this algorithm and an iterative solver for linear algebraic equations. Some numerical examples show that the proposed method solves large scale problems faster than the conventional one. Keywords (Boundary Integral Equation Method, Elastodynamics, Fast Solution Method, Plane Wave Time Domain Algorithm, Iterative Solution Method, GMRES, Scattering Problem)
- Applications of Fast Multipole Method to Boundary Integral Equation Method (in English!)
- K. Yoshida (Doctoral thesis, Kyoto University, March, 2001)
- Postscript or PDF
- 多重極境界積分方程式法における並列計算について (A parallel implementation of fast multipole boundary integral equation method)
- 井上延亮，吉田研一，西村直志，小林昭一，計算工学講演会論文集 vol.6 p.211--214, 2001 (N. Inoue, K. Yoshida, N. Nishimura and S. Kobayashi, Proc. Conf. Comp. Eng. Sci., 6-1, 211--214, 2001)
- (postscript)
- Application of Boundary Integral Equation Method (BIEM) has so far been limited to relatively small problems because of the full matrix property of BIEM. However the use of Fast Multipole Method (FMM) with an iterative solver has enabled us to apply BIEM to large scale problems. In this paper we discuss a parallel implementation of Fast Multipole Boundary Integral Equation Method (FM-BIEM) for two-dimensional Laplace's equation with MPI. keywords(BIEM, FMM, FM-BIEM, MPI)
- Application of new fast multipole boundary integral equation method to elastostatic crack problems in 3D (In English!)
- K. Yoshida, N. Nishimura and S. Kobayashi, J. Structural Eng. JSCE, 47A, 169--179, 2001
- (postscript) (pdf)
- Fast Multipole Method (FMM) has been developed as a technique to reduce the computational cost and memory requirements in solving large scale problems. This paper discusses an application of the new FMM to three-dimensional boundary integral equation method(BIEM) for elastostatic crack problems. The boundary integral equation is discretised with collocation method. The resulting algebraic equation is solved with Generalised Minimum RESidual method (GMRES). The numerical results show that the new FMM is more efficient than the original FMM.
- Application of new fast multipole boundary integral equation method to crack problems in 3D
- K. Yoshida, N. Nishimura and S. Kobayashi, Eng. Anal. Boundary Elements, 25, 239--247, 2001
- (keywords: FMM, New version of FMM, BIEM, Laplace's equation, GMRES, Crack)
- Please follow links from the above referenced URL. You may not be able to retrieve the full text, though, depending on your subsription status with Elsevier.
- Application of fast multipole Galerkin boundary integral equation method to elastostatic crack problems
- K. Yoshida, N. Nishimura and S. Kobayashi, Int. J. Num. Meth. Eng. Vol.50, pp.523-547, 2001
- (keywords: BIEM, BEM, FMM, Galerkin's method, GMRES, crack)
- Please follow links from the above referenced URL. You may not be able to retrieve the full text, though, depending on your subsription status with Wiley.
- 多重極積分方程式法を用いたクラックによる3次元弾性波動散乱問題の解析(Analysis of three dimensional scattering of elastic waves by a crack with fast multipole boundary integral equation method)
- 吉田研一, 西村直志, 小林昭一, 土木学会応用力学論文集 Vol.3, pp.143--150, 2000 (K. Yoshida, N. Nishimura and S. Kobayashi, J. Appl. Mech. JSCE, Vol.3, pp.143--150, 2000)
- ps 版
- This paper discusses an application of FMM (Fast Multipole Method) using Wigner-3j symbols to the BIE (Boundary Integral Equation) analysis of the three dimensional scattering of elastic waves by a crack. The boundary integral equation is discretised with piecewise constant shape functions. The resulting algebraic equation is solved with preconditioned GMRES (Generalised Minimun RESidual method). It is shown that FMM is more efficient than the conventional BIEM (Boundary Integral Equation Method) when the number of unknowns is larger than several thousands. (keywords: FMM, Wigner-3j symbol, BIE, GMRES, BIEM )
- 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(Fast Solution Method of Diffusion Equation in 2D using Panel Clustering Boundary Integral Equation Method)
- 高橋 徹, 西村 直志, 小林 昭一，機械学会論文集(A)，66巻647号, 2000 (Toru TAKAHASHI, Naoshi NISHIMURA and Shoichi KOBAYASHI, Trans JSME (A) Vol.66, No.647, pp.1268--1273, 2000)
- In this paper, a panel clustering boundary integral equation method for the diffusion equation in 2D in time domain is developed. The present method can reduce the computational costs and memory requirement drastically. In numerical examples, it is shown that the proposed method solves the large scale problems faster than the conventional one. keywords Boundary Integral Equation Method, Panel Clustering Method, 2D Diffusion Equation, Time Domain, Iterative Solution, GMRES
- 多重極積分方程式法による3次元定常Stokes流の解析 (A MULTIPOLE BOUNDARY INTEGRAL EQUATION METHOD FOR STATIONARY STOKES FLOW PROBLEMS IN 3D)
- 高橋 徹, 浪江 雅幸, 西村 直志, 小林 昭一, BTEC論文集 Vol.10, (2000年7月) JASCOME (Toru TAKAHASHI, Masayuki NAMIE, Naoshi NISHIMURA, and Shoichi KOBAYASHI, Proc. BTEC, 10, pp.1--4, 2000)
- ps 版
- This paper presents a fast multipole boundary integral equation formulation for three dimensional stationary Stokes flow problems. The efficiency of the proposed method is demonstrated in applications to viscous flow through porous materials. Keywords: Fast Multipole Boundary Integral Equation Method, FMM, Stokes Flow
- 動弾性問題における多重極境界積分方程式法の新しい定式化 (A NEW FORMULATION OF FMBIEM IN ELASTODYNAMICS)
- 入谷 琢哉, 吉田 研一, 西村 直志, 小林 昭一, 計算工学会講演会論文集 Vol.5, pp.301--304, 2000) (Takuya IRITANI, Ken-Ichi YOSHIDA, Naoshi NISHIMURA and Shoichi KOBAYASHI, Proc. Conf. Comp. Eng. Sci., 5, pp.301--304, 2000)
- ps 版
- A new FMM (fast multipole method) formulation for elastodynamic BIEM (boundary integral equation method) in frequency domain is presented. Key Words: Boundary Integral Equation Method, FMM, Elastodynamics, Frequency Domain, GMRES
- 新しい多重極積分方程式法によるクラック問題の解析について (APPLICATION OF NEW MULTIPOLE BOUNDARY INTEGRAL EQUATION METHOD)
- 西村直志, 宮越 優, 小林 昭一, BTEC論文集 Vol.9, pp.75-78 (1999年7月) JASCOME (N. Nishimura, M. Miyakoshi, S. Kobayashi, Proc. BTEC, 9, pp.75-78, 1999)
- ps 版
- This paper discusses applications of a new multipole boundary integral equation method for crack problems in Laplace's equation. The proposed implementation uses a new multipole expansion proposed by Hrycak and Rokhlin in conjunction with collocation in the solution of a discretised hypersingular boundary integral equation for crack problems. The resulting numerical equation is solved with GMRES (generalised minimum residual method). It is found that the obtained code is faster than another based on the original FMM.
- FAST MULTIPOLE BEM SIMULATION OF OVERCORING IN AN IMPROVED CONICAL-END BOREHOLE STRAIN MEASUREMENT METHOD (Yes, in English!)
- T. Takahashi, S. Kobayashi and N. Nishimura (Mechanics and Engineering --- In Honor of Prof. Qinghua Du's 80th Anniversary, Z. Yao et al. (eds.), (1999), Tsinghua Univ. Press. pp.120--127.)
- (Keywords) Fast Multipole BEM, GMRES, Strain Measurement, Conical-end Borehole, Funnel-end Borehole, Initial Stresses
- 高速多重極境界要素法について (On Fast Multipole Boundary Element Methods)
- 西村 直志, 吉田 研一, 小林 昭一 、第11回計算力学講演会講演論文集、機械学会, 299--300, 1998 (N. Nishimura, K. Yoshida and S. Kobayashi, The 11th computational mechanics conference, JSME, 299--300, 1998 (in Japanese)).
- (Keywords) Fast Multipole Boundary Element Method, BIEM, FMM, Panel Clustering, Fast Me thod, GMRES, Wavelet
- 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 (An application of multipole integral equation method to an improved over-coring method of conical-end bore-hole)
- 高橋徹、小林昭一、西村直志、境界要素法論文集 15, 105--110, 1998 (T. Takahashi, S. Kobayashi and N. Nishimura, Proc. 15th Japan Nat. Symp. BEM, 15, 105--110, 1998 (in Japanese)).
- (ABSTRACT) The present paper describes an application of a three dimensional multipole boundary integral equation method to an improved over-coring stress relief method of a conical-end bore-hole, which is used to estimate stress states in rock mass from the measured strains on the face of a funnel-end bore-hole (a conical-end bore-hole attached at its appex with a small-diameter inspection bore-hole) induced by over-coring with the same diameter as that of the bore-hole. Since the geometry of the over-coring is complicated and moreover precise conversion matrix is required in obtaining stresses from the measured strains, the fast multipole method is most advantageously applied. In implementation, piecewise constant shape functions with collocation technique are used to discretise the boundary integral equation and the resulting equation is solved using preconditioned GMRES. The strains induced by over-coring are simulated and shown for simple states of initial stresses.
- 多重極積分方程式法を用いた3次元静弾性クラック問題の解析 (Analysis of three dimensional elastostatic crack problems with fast multipole boundary integral equation method)
- 吉田研一、西村直志、小林昭一、 土木学会応用力学論文集 1, 365--372, 1998 (K. Yoshida N. Nishimura, and S. Kobayashi, J. Appl. Mech. JSCE, 1, 365--372, 1998 (in Japanese)).
- (ABSTRACT) FMM(Fast Multipole Method) has been developed as a technique to reduce the computational time and memory requirements in solving big sized multibody problems. This paper applies FMM to elastostatic crack problems in 3D, discretizing BIE (boundary integral equation) with piecewise constant shape functions. The resulting algebraic equation is solved with GMRES (generalized minimun residual method). It is shown that FMM is more efficient than the conventional method.
- 多重極積分方程式法による3次元クラック問題の解析について (A multipole boundary integral equation method for crack problems in 3D)
- 西村直志、吉田研一、小林昭一、 境界要素法論文集 14, 37--42, 1997 (N. Nishimura, K. Yoshida and S. Kobayashi, Proc. 14th Japan Nat. Symp. BEM, 14, 37--42, 1997 (in Japanese)).
- (ABSTRACT) This paper discusses a three dimensional multipole boundary integral equation method for crack problems in Laplace's equation. The proposed implementation uses collocation and piecewise constant shape functions to discretise the hypersingular boundary integral equation for crack problems. The resulting numerical equation is solved with GMRES (generalised minimum residual method) in connection with FMM (fast multipole method). It is found that the obtained code is faster than a conventional one when the number of unknowns is greater than about 1300.
- Crack determination Problems (without figures....)
- N. Nishimura, Theoretical and Applied Mechanics 46 (Eds. G. Yagawa and C. Miki), Hokusen-Sha Publ. (supervised by Univ. Tokyo Press), Tokyo, 39--57, 1997
- (ABSTRACT) This paper describes recent developments in the inverse problem of crack determination. We review mathematical, numerical and experimental researches in this field. Also, some details of the numerical methods by the present author in Laplace and elastodynamic cases, including some new results, are presented.
- 構造力学online text (未完) (Structural Mechanics online text (unfinished. in Japanese))

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