博士(工学), 東京大学

function approximation

numerical integration

etc.

関数近似

数値積分

偏微分方程式の数値解法（代用電荷法など）

numerical solvers for partial differential equations such as the charge simulation method

numerical analysis based on the hyperfunction theory

Informatics, Computational science

Natural sciences, Applied mathematics and statistics

Natural sciences, Basic mathematics

Apr. 2013 - Present
The University of Electro-Communications, Graduate School of Informatics and Engineering, professor, Ph.D, Japan

01 Apr. 2007
Department of Computer Science, Faculty of Electro-Communications, The University of Electro-Communications, associate professor

01 Oct. 2005 - 31 Mar. 2007
Department of Computer Science, Faculty of Electro-Communications, The University of Electro-Communications, assistant professor

01 Apr. 1999 - 30 Sep. 2005
Department of Computer Science, Faculty of Engineering, Ehime University, lecturer

01 Apr. 1997 - 31 Mar. 1999
Department of Applied Physics, School of Engineering, The University of Tokyo, research assistant

01 May 1992 - 31 Mar. 1999
Department of Applied Physics, Faculty of Engineering, The University of Tokyo, research assistant

Apr. 1990 - Mar. 1992
The University of Tokyo, The Graduate School of Engineering, Department of Applied Physics, Japan

Apr. 1988 - Mar. 1990
The University of Tokyo, The Faculty of Engineering, Department of Applied Physics, Japan

Apr. 1986 - Mar. 1988
The University of Tokyo, College of Arts and Sciences, 理科一類

31 Mar. 1986
福井県立武生高等学校, 普通科

Mar. 2017
JSIAM Letters 編集委員

Sep. 2024
日本応用数理学会
日本応用数理学会論文誌2024年度論文賞（理論部門）, 緒方秀教

Sep. 2022
The Japan Society for Industrial and Applied Mathematics
二重周期的ポテンシャル問題に対する代用電荷法
日本応用数理学会論文誌論文賞2022年度（理論部門）, 緒方秀教
Official journal

Sep. 2002
日本応用数理学会論文誌論文賞（理論部門）

2000
情報処理学会創立40周年記念論文賞

Sep. 1998
日本応用数理学会論文誌論文賞(理論部門)

On the invariance of the invariant scheme of the charge simulation method
Hidenori Ogata
Lead, 日本応用数理学会論文誌, 34, 4, 127-130, Dec. 2024, Peer-reviwed
Scientific journal, Japanese

Method of Fundamental Solutions for Doubly Periodic Potential Problems
Hidenori Ogata
Lead, Proceedings of the Tenth International Conference on Mathematics and Computing. ICMC 2024. Lecture Notes in Networks and Systems, Springer Nature Singapore, 964, 137-149, 30 Jun. 2024, Peer-reviwed
International conference proceedings, English

Numerical Solver for Initial Value Problems of Ordinary Differential Equations by the IMT-DE Type Numerical Indefinite Integration Formula
Hidenori Ogata
日本応用数理学会論文誌, 33, 2, 36-65, Jun. 2023, Peer-reviwed
Scientific journal, Japanese

佐藤超函数論に基づく関数近似，数値微分および数値不定積分
緒方秀教
日本応用数理学会論文誌, 32, 3, 101-122, 28 Sep. 2022, Peer-reviwed, 本論文では，佐藤超函数論に基づく関数近似，数値微分および数値不定積分の方法を提案する．本方法では，計算したい関数を超函数とみなして，それを与える解析関数である標準定義関数を数値的に求めることにより関数近似を行う．そして，簡単な手続きにより数値微分，数値不定積分を求める．数値例により本論文の方法の有効性が示される．
Scientific journal, Japanese

Numerical Indefinite Integration Using the IMT-Type DE Transform and the Sinc Approximation for Periodic Functions
Hidenori Ogata
日本応用数理学会論文誌, 32, 1, 1-19, 25 Mar. 2022, Peer-reviwed
Scientific journal, Japanese

Method of fundamental solutions for doubly-periodic potential problems
Hidenori Ogata
Transactions of the Japan Society for Industrial and Applied Mathematics, 31, 1, 1-19, Mar. 2021, Peer-reviwed
Scientific journal, Japanese

A numerical method for Fredholm integral equations of the second kind by the IMT-type DE rules
Hidenori Ogata
Japan Journal of Industrial and Applied Mathematics, 28 Jan. 2021, Peer-reviwed
Scientific journal, English

Numerical calculation of Fourier transforms based on hyperfunction theory
Hidenori Ogata
Journal of Computational and Applied Mathematics, 378, 000, 112921-000, Nov. 2020, Peer-reviwed
Scientific journal, English

Numerical method of computing Hadamard finite-part integrals with a non-integral power singularity at the endpoint over a half infinite interval
Hidenori Ogata
arXiv, arXiv:1910.04058, 08 Oct. 2019
Research society, English

A numerical method of computing Hadamard finite-part integrals with an integral power singularity at the endpoint on a half infinite interval
Hidenori Ogata
arXiv, arXiv:1910.00807, 02 Oct. 2019
Research society, English

Numerical method for computing Hadamard finite-part integrals with a non-integral power singularity at an endpoint
Hidenori Ogata
arXiv, arXiv:1909.11398, 25 Sep. 2019
Research society, English

A numerical method for Hadamard finite-part integrals with an integral power singularity at an endpoint
Hidenori Ogata
arXiv, arXiv:1909.08872, 19 Sep. 2019
Research society, English

A numerical method of computing oscillatory integral related to hyperfunction theory
Hidenori Ogata
arXiv, arXiv:1909.04911, 11 Sep. 2019
Research society, English

A numerical method of Fourier transform based on hyperfunction theory
Hidenori Ogata
arXiv, arXiv:1808.03460, 10 Aug. 2018
Research society, English

Numerical integration based on hyperfunction theory
Hidenori Ogata; Hiroshi Hirayama
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, ELSEVIER SCIENCE BV, 327, 243-259, Jan. 2018, Peer-reviwed, In this paper, we propose an application of hyperfunction theory to numerical integration. Hyperfunction theory is a generalized version of function theory where functions with singularities such as poles, discontinuities and delta impulses are expressed in terms of complex analytic functions. This feature of hyperfunction theory allows us to construct a numerical integration method for analytic functions. Theoretical error estimates show that our method converges geometrically, and numerical examples show that our method is very efficient especially for integrals with strong end-point singularities. In addition, we present an automatic integration method based on our hyperfunction method. (C) 2017 Elsevier B.V. All rights reserved.
Scientific journal, English

佐藤超函数論に基づく数値解析
緒方秀教
応用数理, 27, 4, 152-159, Dec. 2017, Peer-reviwed
Scientific journal, Japanese

佐藤超函数論に基づく数値積分
緒方秀教
京都大学数理解析研究所講究録, 京都大学数理解析研究所, 2037, 57-60, Jul. 2017
Research institution, Japanese

Hyperfunction method for numerical integrations
Hidenori Ogata; Hiroshi Hirayama
Transactions of the Japan Society for Industrial and Applied Mathematics, The Japan Society for Industrial and Applied Mathematics, 26, 1, 33-43, 28 Mar. 2016, Peer-reviwed, We examine Hirayama's numerical integration method for integrals over finite intervals, which is called the "hyperfunction method" in this paper. In the hyperfunction method, an integral is transformed into a complex integrals on a closed contour and is approximated by the trapezoidal rule, which gives good results for integrals in the case that the integrands are periodic functions. Numerical examples show that the hyperfunction method is effective for integrals with strong end-point singularities. We also remark the relation between the hyperfunction method and the hyperfunction theory.
Scientific journal, Japanese

Numerical conformal mappings onto the canonical slit domains of Koebe(1916) by the charge simulation method
Kaname Amano; Dai Okano; Keiichi Endo; Hidenori Ogata
Transaction of the Japan Society for Industrial and Applied Mathematics, The Japan Society for Industrial and Applied Mathematics, 24, 3, 157-183, 25 Sep. 2014, Peer-reviwed
Scientific journal, Japanese

Convergence of the invariant scheme of the method of fundamental solutions for two-dimensional potential problems in a Jordan region
Hidenori Ogata; Masashi Katsurada
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, KINOKUNIYA CO LTD, 31, 1, 231-262, Feb. 2014, Peer-reviwed, We examine the invariant scheme of the method of fundamental solutions for two-dimensional potential problems, that is, Dirichlet boundary value problems of the Laplace equation in a Jordan region, with the charge points and the collocation points obtained by a conformal mapping of the exterior of a disk to the exterior of the problem region. By a theoretical error analysis, we show that the approximate solution of the invariant scheme converges to the exact solution exponentially and some unnatural assumptions needed in the conventional scheme are removed in the convergence theorem of the invariant scheme.
Scientific journal, English

Dipole simulation method for two-dimensional potential problems
Hidenori Ogata
Nonlinear Theory and Its Applications, IEICE, The Institute of Electronics, Information and Communication Engineers, 5, 1, 1-13, Jan. 2014, Peer-reviwed, In this paper, we propose to apply the dipole simulation method proposed by Katsurada to two-dimensional potential problems in general regions. The dipole simulation method is an extension of the charge simulation method (the method of fundamental solutions) and gives an approximate solution by a linear combination of the dipole potentials. We also present an application of the proposed method to numerical conformal mapping. Some numerical examples show the effectiveness of the proposed method.
Scientific journal, English

Numerical Conformal Mappings onto the Spiral Slit Domain by the Charge Simulation Method
Kaname Amano; Dai Okano; Keiichi Endo; Hidenori Ogata
Information-An International Interdisciplinary Journal, 16, 12(B), 8575-8578, Dec. 2013, Peer-reviwed, We present a numerical method for the conformal mapping of unbounded multiply connected domains exterior to closed Jordan curves onto the general spiral slit domain, which is a natural extension of the circular and radial slit domains. ©2013 International Information Institute.
Scientific journal, English

Charge simulation method using electric dipoles and its application to numerical conformal mappings
Hidenori Ogata
Kokyuroku, RIMS, Kyoto University, 1791, 0, 97-106, Apr. 2012
Research institution, Japanese

Numerical conformal mappings onto the linear slit domain
Kaname Amano; Dai Okano; Hidenori Ogata; Masaaki Sugihara
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, KINOKUNIYA CO LTD, 29, 2, 165-186, Apr. 2012, Peer-reviwed, We propose a numerical method for the conformal mapping of unbounded multiply connected domains exterior to closed Jordan curves C-1, ... , C-n onto a canonical linear slit domain, which is the entire plane with linear slits S-1, ... , S-n of angles theta(1), ... , theta(n) arbitrarily assigned to the real axis, respectively. If theta(1) = ... = theta(n) = theta then it is the well-known parallel slit domain, which is important in the problem of potential flows past obstacles. In the method, we reduce the mapping problem to a boundary value problem for an analytic function, and approximate it by a linear combination of complex logarithmic functions based on the charge simulation method. Numerical examples show the effectiveness of our method.
Scientific journal, English

A new theoretical error estimate of the method of fundamental solutions applied to reduced wave problems in the exterior region of a disk
Hidenori Ogata; Fumihiro Chiba; Teruo Ushijima
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, ELSEVIER SCIENCE BV, 235, 12, 3395-3412, Apr. 2011, Peer-reviwed, In this paper, we present a mathematical study of the method of fundamental solutions (MFS) applied to reduced wave problems with Dirichlet boundary conditions in the exterior domain of a disk. A theorem in this paper shows that the MFS with N source points in equi-distantly equally phased arrangement with assignment parameter q (0 < q < 1), which characterizes the position of the source points and the collocation points, gives an approximate solution with error of O(q(N)) if the Fourier coefficients of the boundary data decay exponentially. This error estimate is an extension of the results of the previous studies. Numerical examples make good agreements with the results of the theoretical study. (C) 2011 Elsevier B.V. All rights reserved.
Scientific journal, English

Fundamental solution method for two-dimensional Stokes flow problems with one-dimensional periodicity
Hidenori Ogata; Kaname Amano
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, KINOKUNIYA CO LTD, 27, 2, 191-215, Sep. 2010, Peer-reviwed, In this paper, we propose a fundamental solution method for two-dimensional Stokes flow problems with a one-dimensional infinite periodic array of obstacles. In the proposed method, we approximate the solution by a linear combination of periodic fundamental solutions of the Stokes flow equation. In terms of physics, this approximation illustrates Stokes flows due to forces acting on one-dimensional infinite periodic points. Numerical examples are included to demonstrate the effectiveness of the proposed method.
Scientific journal, English

Fundamental Solution Method for Periodic Plane Elasticity
Hidenori Ogata
Journal of Numerical Analysis Industrial and Applied Mathematics, 3, 3-4, 249-267, Oct. 2008, Peer-reviwed
Scientific journal, English

Complex Variable Boundary Element Method for Two-Dimensional Potential Problems with One-Dimensional Periodicity
Hidenori Ogata
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, AMER INST PHYSICS, 1048, 411-414, Sep. 2008, Peer-reviwed, In this paper, we propose a complex variable boundary element method for two-dimensional potential problems with one-dimensional periodicity. In the presented method, we reduce the potential problem of interest to the boundary integral equation problem for a complex analytic function where an extension of Cauchy's integral formula for periodic analytic functions is regarded as a Fredholm integral equation and, by solving a discretized equation of the boundary integral equation, we obtain an approximate solution. Numerical examples are also included.
International conference proceedings, English

Fundamental Solution Method for Two-Dimensional Stokes Flow Problems with One-Dimensional Periodicity
Hidenori Ogata
京都大学数理解析研究所講究録, 京都大学数理解析研究所, 1566, 1566, 119-131, Jul. 2007
Research institution, English

Fundamental solution method for three-dimensional elasticity problems with two-dimensional periodicity
Hidenori Ogata
International Conference on Numerical Analysis and Applied Mathematics 2006, 267-270, Sep. 2006, Peer-reviwed
International conference proceedings, English

A fundamental solution method for three-dimensional viscous flow problems with obstacles in a periodic array
H Ogata; K Amano
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, ELSEVIER SCIENCE BV, 193, 1, 302-318, Aug. 2006, Peer-reviwed, In this paper, we propose a fundamental solution method for three-dimensional viscous flow problems with obstacles in a periodic array. Our problem is mathematically a boundary value problem of the Stokes equation with periodic boundary conditions, to which it is difficult to give a good approximation by the ordinary fundamental solution method. Our method gives an approximate solution by a linear combination of the periodic fundamental solutions. In addition, we can compute the drag forces on the obstacles by using the data obtained in our method. Numerical examples for the problems of flows past spheres show the effectiveness of our method. (c) 2005 Elsevier B.V. All rights reserved.
Scientific journal, English

Bi-directional method for numerical conformal mappings of multiply connected domains by the charge simulation method
Dai Okano; Masatoshi Terazono; Kaname Amano; Hidenori Ogata
Theoretical and Applied Mechanics Japan, 54, 357-363, May 2006, Usually, on computation of conformal mappings, different methods are used to obtain the mapping functions of two directions between a problem domain and a canonical domain. Amano proposed a method based on the numerical conformal mappings by the charge simulation method, and it offers the both mapping functions of simply connected problem domains and the canonical domains like the unit disk. However, his method cannot be used to obtain the mapping function on the canonical slit domains, which are important for the potential flow analysis of multiply connected domains. Here, we provide a solution to this difficulty, and propose a new method which improves the method of numerical conformal mappings by the charge simulation method, and expands the bi-directional applicability to the problem of multiply connected domains.
Scientific journal

A fundamental solution method for three-dimensional Stokes flow problems with obstacles in a planar periodic array
H Ogata
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, ELSEVIER SCIENCE BV, 189, 1-2, 622-634, May 2006, Peer-reviwed, In this paper, we propose a fundamental solution method for the problems of steady three-dimensional Stokes flow past obstacles in a planar periodic array. The solutions of these problems are periodic functions which are difficult to be approximated by the conventional fundamental solution method. In the presented method, we approximate the solutions by linear combinations of the periodic fundamental solutions presented by Ishii. Some numerical examples are also included in this paper and their results make a good agreement with the ones of the previous works. (c) 2005 Elsevier B.V. All rights reserved.
Scientific journal, English

A numerical integration formula based on the Bessel functions
H Ogata
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, KYOTO UNIV, 41, 4, 949-970, Dec. 2005, Peer-reviwed, In this paper, we discuss the properties of a quadrature formula with the zeros of the Bessel functions as nodes for integrals integral(-infinity)(infinity)vertical bar x vertical bar(2v+1)f(x)dx, where v is a real constant greater than -1 and f(x) is a function analytic on the real axis (-infinity, +infinity). We show from theoretical error analysis that (i) the quadrature formula converges exponentially, (ii) it is as accurate as the trapezoidal formula over (-infinity, +infinity) and (iii) the accuracy of the quadrature formula doubles that of an interpolation formula with the same nodes. Numerical examples support the above theoretical results. We also apply the quadrature formula to the numerical integration of integral involving the Bessel function.
Scientific journal, English

Fundamental Solution Method for Periodic Plane Elasticity
Hidenori Ogata
ICNAAM2005 International Conference on Numerical Analysis and Applied Mathematics 2005 (eds. T.E. Simos, G. Psihoyios and Gh. Tsitouras), 428-431, Sep. 2005, Peer-reviwed
International conference proceedings, English

A Bidirectional Method of Numerical Conformal Mappings for Multiply-Connected Domains by the Charge Simulation Method
Okano Dai; Terazono Masatoshi; Amano Kaname; Ogata Hidenori
NCTAM papers, National Congress of Theoretical and Applied Mechanics, Japan, National Committee for IUTAM, 54, 0, 99-99, Apr. 2005, On computation of conformal mappings, the mapping functions between a given problem domain and its corresponding canonical domains are concerned.Usually, two different methods are used to obtain the mapping functions, which map the problem domain onto and from the canonical domains.Our method of the numerical conformal mappings by the charge simulation method is applicable to such problems in two directions and offers the both mapping functions in similar way.However, the method was not applicable to the problem with the canonical slit domains, which are important for the potential flow analysis of multiply connected domains.Here, we provide a solution to this difficulty, which improve the method and expand its bi-directional applicability to the problem with multiply connected domains.

Charge simulation method for two-dimensional compressible fluid flow
H Ogata
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, KINOKUNIYA CO LTD, 22, 1, 1-20, Feb. 2005, Peer-reviwed, In this paper, we propose a numerical method for problems of two-dimensional steady irrotational flows of compressible fluid. The basic equations are nonlinear partial differential equations, which are difficult to solve. But, in the cases of subsonic flow, the so-called M-2-expansion method, where the solutions are expressed as power series of the Mach numbers, reduces our problem to the Dirichlet problems of analytic functions, whose real and imaginary parts obey the Laplace equation. We apply the charge simulation method, a fast solver for potential problems, to these Dirichlet problems and obtain an approximate solution including linear combinations of the complex logarithmic potentials. Numerical examples for some typical cases show the effectiveness of our method.
Scientific journal, English

代用電荷法による数値等角写像とポテンシャル流問題への応用
天野要; 玉井政行; 岡野大; 緒方秀教; 杉原正顯
情報処理学会論文誌, Information Processing Society of Japan (IPSJ), 45, 5, 1322-1325, May 2004, Peer-reviwed, In this paper, we propose a method of conformal mapping w = f (z) of an unbounded multiply-connected domain D subject to the condition f (∞) = ∞, where v is a given finite point in the problem domain. In the method, we reduce the mapping problem to a Dirichlet problem of a pair of conjugate harmonic functions and approximate them, using the charge simulation method, by a linear combination of complex logarithmic functions. The method can be applied to the analysis of a potential flow with a vortex pair past obstacles. A typical example shows the effectiveness of the method. Besides, the idea described here is applicable to some other comformal mappings which are important in potential flow problems.
Scientific journal, Japanese

3境界点の像により定まる数値等角写像の代用電荷法による方法
緒方秀教
京都大学数理解析研究所講究録, Kyoto University, 1362, 1362, 169-177, Apr. 2004
Research society, Japanese

Charge Simulation Methods for Partial Differential Equation Problems with Spatial Periodicities
Hidenori Ogata
Annual Journal of Engineering, Ehime University, Ehime University, 3, 107-117, Mar. 2004, In this paper, we present an extension of the charge simulation method, a solver for the problems of partial differential equations, to the problems of partial differential equations with spatial periodicities, especially to the problems of numerical conformal mappings of periodic structure domains and the problems of viscous flows (Stokes flows) past obstacles in a periodic array. In our method, we present approximate solutions expressed by linear combinations of the periodic fundamental solutions so that the solutions including periodic functions are approximated accurately. Some numerical examples show the effectiveness of our method.
Research institution, Japanese

代用電荷法による数値等角写像とポテンシャル流問題への応用
天野要; 玉井政行; 岡野大; 緒方秀教; 杉原正顯
京都大学数理解析研究所講究録, Kyoto University, 1352, 1352, 127-139, Jan. 2004
Research society, Japanese

周期的Stokes流問題に対する基本解法
緒方秀教; 天野要; 岡野大; 安田雄二; 杉原正顯
京都大学数理解析研究所講究録, Kyoto University, 1352, 1352, 140-152, Jan. 2004
Research society, Japanese

Numerical conformal mappings of bounded multiply connected domains by the charge simulation method
D Okano; H Ogata; K Amano; M Sugihara
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, ELSEVIER SCIENCE BV, 159, 1, 109-117, Oct. 2003, Peer-reviwed, We present here a simple method of numerical conformal mappings from bounded multiply connected domains onto the bounded canonical slit domains of Nehari, i.e., a disk with concentric circular slits, and an annulus with concentric circular slits. In this method, we express the mapping functions in terms of a pair of conjugate harmonic functions and approximate them, using the charge simulation method, by a linear combination of complex logarithmic functions. Some numerical examples show the effectiveness of the method. (C) 2003 Elsevier B.V. All rights reserved.
Scientific journal, English

A charge simulation method for spatially periodic problems
H Ogata; D Okano; K Amano; M Sugihara
PROGRESS IN ANALYSIS, VOLS I AND II, WORLD SCIENTIFIC PUBL CO PTE LTD, 1459-1468, Aug. 2003, Peer-reviwed, We present here a charge simulation method for problems of two-dimensional flows past obstacles in a two-dimensional periodic array. Our problem is mathematically a boundary value problem of the Stokes equation with periodic boundary conditions, to which it is difficult to give a good approximation by the ordinary charge simulation method. We propose a charge simulation method for our problem based on the periodic fundamental solution obtained by Hasimoto. In our method, the solution is approximated by using a linear combination of the periodic fundamental solutions.
International conference proceedings, English

パターンの良さ判断に関する変換群構造説
小西敏雄; 岡野大; 緒方秀教; 芝田安裕; 天野要; 福士コウ士; 濱田治良; 今井四郎
情報処理学会論文誌, 44, 8, 2274-2283, Aug. 2003, Peer-reviwed
Scientific journal, Japanese

A fundamental solution method for viscous flow problems with obstacles in a periodic array
H Ogata; K Amano; M Sugihara; D Okano
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, ELSEVIER SCIENCE BV, 152, 1-2, 411-425, Mar. 2003, Peer-reviwed, We present here a fundamental solution method for two-dimensional viscous flow problems with obstacles in a two-dimensional periodic array. Our problem is mathematically a boundary value problem of the Stokes equations with periodic boundary conditions, to which it is difficult to give a good approximation by the ordinary fundamental solution method. We propose a fundamental solution method for our problem based on the periodic fundamental solution obtained by Hasimoto (J. Fluid Mech. 5 (1959) 317). In our method, the solution is approximated by using a linear combination of the periodic fundamental solutions. (C) 2002 Elsevier Science B.V. All rights reserved.
Scientific journal, English

A method of numerical conformal mapping of curved slit domains by the charge simulation method
D Okano; H Ogata; K Amano
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, ELSEVIER SCIENCE BV, 152, 1-2, 441-450, Mar. 2003, Peer-reviwed, In this paper, we propose a method of numerical conformal mappings from a domain with a curved slit onto the canonical slit domains. Our method is based on Amano's method, which uses the charge simulation method as a rapid solver for potential problems. Due to the potential solver, his method gives high accuracy in many cases. The basic idea of the preceding method is to provide an approximation of harmonic functions by a linear combination of the complex logarithmic functions, g(z) = Sigma(j) Q(j) log(z - zeta(j)), where the singularity points zeta(j) are placed outside the problem domain. However, there are some difficulties on applying it to the problem domain with corners on the boundary, and the problem domain without enough space to place the singularity points properly. The problem domain with a curved slit is a typical example of such a difficulty. A technique we provide here is based on use of the Joukowski transformation. It inherits all the good properties of the original method. We show the effectiveness of our proposal by some numerical examples. (C) 2002 Elsevier Science B.V. All rights reserved.
Scientific journal, English

Unique solvability of the linear system appearing in the invariant scheme of the charge simulation method
H Ogata; D Okano; M Sugihara; K Amano
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, KINOKUNIYA CO LTD, 20, 1, 17-35, Feb. 2003, Peer-reviwed, We show that the linear system appearing in the invariant scheme of the charge simulation method is uniquely solvable when the scheme is applied to a two-dimensional Dirichlet problem for a disk, for an ellipse, and for an annulus with properly chosen charge points and collocation ones, which are extensions of the previous results due to Katsurada-Okamoto, Nishida, and Murota. We also prove the unique solvability in a ball of dimension greater than or equal to 3, which we believe is entirely new.
Scientific journal, English

Unique solvability of the linear system appearing in the invariant scheme of the charge simulation method
H Ogata; D Okano; M Sugihara; K Amano
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, KINOKUNIYA CO LTD, 20, 1, 17-35, Feb. 2003, We show that the linear system appearing in the invariant scheme of the charge simulation method is uniquely solvable when the scheme is applied to a two-dimensional Dirichlet problem for a disk, for an ellipse, and for an annulus with properly chosen charge points and collocation ones, which are extensions of the previous results due to Katsurada-Okamoto, Nishida, and Murota. We also prove the unique solvability in a ball of dimension greater than or equal to 3, which we believe is entirely new.
Scientific journal, English

Numerical Conformal Mappings from Domains with Multiple Slits onto the Canonical Slit Domains by the Charge Simulation Method
Dai Okano; Masayuki Terazono; Hidenori Ogata; Kaname Amano
Information, 6, 1, 107-118, Jan. 2003, Peer-reviwed
Scientific journal, English

類似性判断に関する変換群構造説の2次元ドットパターンへの拡張
芝田安裕; 高崎昌浩; 小西敏雄; 岡野大; 緒方秀教; 天野要
情報処理学会論文誌, Information Processing Society of Japan (IPSJ), 43, 12, 4067-4070, Dec. 2002, Peer-reviwed, We extend the transformational group structure theory on similarity judgments of one dimensional elliptic patterns (linear binary patterns) to that of two-dimensional dot patterns (square binary matrix patterns). Specifically speaking, we define the transformational group structures of pattern pairs by the four cognitive transformation groups, i.e., the identity, the dihedral, the translation and the value-reversal transformation groups, and then predict their orders of similarity by the structures. Simple experiments and tests show the validity of the model.
Scientific journal, Japanese

Computations of the Forces on Obstacles in Two-Dimensional Potential Flows by the Charge Simulation Method
Hidenori Ogata; Dai Okano; Kaname Amano
Information, 5, 3, 307-318, Jul. 2002, Peer-reviwed
Scientific journal, English

Numerical conformal mapping of periodic structure domains
H Ogata; D Okano; K Amano
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, KINOKUNIYA CO LTD, 19, 2, 257-275, Jun. 2002, Peer-reviwed, We propose a method of numerical conformal mapping of periodic structure domains onto periodic parallel slit domains. In the method presented here, the mapping problem is reduced to a Dirichlet one for a pair of conjugate harmonic functions with a periodic boundary condition. We modify the charge simulation method for solving periodic boundary value problem and apply it to our mapping problem. Some numerical examples show that our method is efficient. We also show an application of our method to the analysis of potential flow past obstacles in a periodic array.
Scientific journal, English

代用電荷法による円弧スリット円環領域への数値等角写像の方法
岡野大; 牧直正; 緒方秀教; 天野要
情報処理学会論文誌, Information Processing Society of Japan (IPSJ), 43, 5, 1382-1389, May 2002, Peer-reviwed, We present a method of numerical conformal mapping of a bounded multiply-connected domain onto a circular annulus with concentric circular slits. In the method, we reduce the mapping problem to a Dirichlet one for a pair of conjugate harmonic functions and solve it using the charge simulation method, which yields an approximate mapping function expressed with a linear combination of complex logarithmic potentials. We also present continuous schemes for practical computations in order to avoid the discontinuities due to using the principal value of the complex logarithmic function. Numerical results for a typical problem show the effectiveness of our method. This paper completes a series of our studies on the numerical conformal mappings onto the standard slit domains of Nehari (1952).
Scientific journal, Japanese

Stagnation Point Analysis by the Numerical Conformal Mapping Using the Charge Simulation Method
Dai Okano; Hidenori Ogata; Kaname Amano
Theoretical and Applied Mechanics, 50, 303-309, Apr. 2002, Peer-reviwed, Recently, we proposed an integrated method for the problem of numerical conformal mappings of the unbounded multiply-connected domains onto the canonical slit domains of Nehari(l952). The problem is important in potential flow analysis. Our method which uses the charge simulation method offers not only highly accurate mapping functions, but also their analytical derivatives. This enables us to use various formulas for applications, which would be useful but lack easy numerical implementation. In this paper, as a simple example, we offer a Newton's iteration method for computing the stagnation points around obstacles placed in the uniform potential flow. The algorithm is simple, and as shown, the numerical experiments give high accuracy.
Scientific journal, English

パターンの類似性判断に関する変換群構造説
天野要; 岡野大; 緒方秀教; 芝田安裕; 小西敏雄; 福士コウ士; 濱田治良; 今井四郎
情報処理学会論文誌, 42, 11, 2733-2742, Nov. 2001, Peer-reviwed
Scientific journal, Japanese

代用電荷法による非有界な多重連結領域の統一的な数値等角写像の方法
天野要; 岡野大; 緒方秀教; 下平博巳; 杉原正顯
情報処理学会論文誌, Information Processing Society of Japan (IPSJ), 42, 3, 385-395, Mar. 2001, Peer-reviwed, The parallel, circular and radial slit domains are the entire planes with parallel rectilinear slits, circular slits concentric to the origin and radial slits pointing at the orgin, respectively. We here present a simple method of numerical conformal mappings of an unbounded multiply-connected domain exterior to closed Jordan curves onto the parallel, circular and radial slit domains. These conformal mappings are familiar in science and engineering, and especially important in problems of two-dimensional potential flows around obstacles with vortices and point-sources or sinks together with a uniform flow. But, no systematic method of computation has been established. We reduce the problems of conformal mapping to the Dirichlet problem with a pair of conjugate harmonic functions and employ the charge simulation method, where the conjugate harmonic functions are approximated by a linear combination of complex logarithmic potentials. The problems are finally reduced to a set of linear equations with a same coefficient matrix. The approximate mapping functions are continuous and analytic using the principal value of logarithmic function, and invariant to the scaling of the coordinate system. The numerical method for simple, accurate approximate mapping functions was a missing link between theory and applications of the conformal mappings.
Scientific journal, Japanese

Continuous Schemes of Numerical Conformal Mapping by the Charge Simulation Method
Kaname Amano; Dai Okano; Hidenori Ogata; Shigeru Katayama; Naomasa Maki
Information, 4, 1, 37-48, Jan. 2001, Peer-reviwed
Scientific journal, English

代用電荷法による円弧スリット単位円板領域への数値等角写像の方法
天野要; 岡野大; 緒方秀教
情報処理学会論文誌, Information Processing Society of Japan (IPSJ), 41, 4, 998-1008, Apr. 2000, Peer-reviwed, We present a method of numerical conformal mapping of multiply-connected domains with closed boundary Jordan curves onto the unit disk with concentric circular slits. It is a basic problem of conformal mapping of multiply-connected domains. If the domain is bounded by a single closed Jordan curve, the problem is identified as Riemann's mapping theorem. We reduce the mapping problem to a Dirichlet problem with a pair of conjugate harmonic functions and apply the charge simulation method, where the conjugate harmonic functions are approximated by a linear combination of complex logarithmic potentials. We here give an explicit form of approximate mapping function which is continuous using the pricipal value of logarithmic function.
Scientific journal, Japanese

Convergence Theory of the CR Method for Linear Singular Systems
Kuniyoshi Abe; Hidenori Ogata; Masaaki Sugihara; Shao-Liang Zhang; Taketomo Mitsui
日本応用数理学会論文誌, The Japan Society for Industrial and Applied Mathematics, 9, 1, 1-13, Mar. 1999, Peer-reviwed, The convergence rate of the residual vector of the conjugate residual (CR) method is well known for a linear system Ax=b, where A is nonsingular. In this paper, we consider the convergence theory of the CR method for a linear system, where the coefficient matrix is singular. First, when we give a certain condition, we show that the algorithm of the CR method can be decomposed into components in the range space of A, which we denote by R(A), and the orthogonal complement space of R(A). Secondly, we present a bound of the residual norms of the CR method in R(A). These two results imply that we can derive an estimate of the error bound for a linear singular system. Moreover, we show necessary and sufficient conditions for the convergence of the CR method starting with an arbitrary right-hand side vector. As a byproduct, the residual norm of the CR method for symmetric positive semi-definite coefficient matrices is also analyzed.
Scientific journal, Japanese

超大型固有値問題の解法
Henk van der Vorst; ranslated into Japanese; y; Hidenori Ogata
応用数理, 8, 4, 6-20, Dec. 1998, Peer-reviwed
Research society, Japanese

代用電荷法による実関数の近似
岡野大; 緒方秀教; 天野要; 井上哲男
情報処理学会論文誌, Information Processing Society of Japan (IPSJ), 39, 12, 3337-3340, Dec. 1998, Peer-reviwed, In this note, we present a method of approximating the real function f(x)analytic on a bounded closed interval by applying the charge simulation method and the Joukowski transformation.
Scientific journal, Japanese

Bessel関数の零点を標本点に持つ数値積分公式が厳密な関数値を与える関数族--Grozev-Rahmanの定理の別証--
緒方秀教; 杉原正顯
日本応用数理学会論文誌, The Japan Society for Industrial and Applied Mathematics, 8, 2, 307-315, Jun. 1998, Peer-reviwed, In this note, we give another proof of a theorem, due to Grozev and Rahman [3], on a class of functions for which the quadrature formulae whose abscissae are the zeros of the Bessel functions give the exact value of integral. Our proof is based on the complex integral representation of the integration error and is much simpler than Grozev and Rahman's
Scientific journal, Japanese

Bessel関数を含む振動無限積分に対する数値積分公式
緒方秀教; 杉原正顯
日本応用数理学会論文誌, The Japan Society for Industrial and Applied Mathematics, 8, 2, 223-256, Jun. 1998, Peer-reviwed, Quadrature formulae for oscillatory infinite integrals involving the Bessel functions are proposed. Those formulae are obtained by the so-called double exponential type of variable transformations followed by an application of quadrature formulae whose abscissae are the zeros of the Bessel functions, which are developed in [3]. Numerical examples are included.
Scientific journal, Japanese

Bessel関数の零点を標本点に持つ補間および数値積分公式
緒方秀教; 杉原正顯
日本応用数理学会論文誌, 6, 1, 39-66, Mar. 1996, Peer-reviwed
Scientific journal, Japanese

Cauchyの主値及びHadamardの有限部分積分に対するDE公式
緒方秀教; 杉原正顯; 森正武
日本応用数理学会論文誌, The Japan Society for Industrial and Applied Mathematics, 3, 4, 309-322, Dec. 1993, Peer-reviwed, A Double exponential-type(DE-type)quadrature formula is proposed for evaluating the Cauchy principal-value integral:p.v.∫^1_<-1>F(x)(x-λ)^(-1)dx, and the Hadamard finite-part integral:f.p.∫^1_<-1>F(x)(x-λ)^<-n>dx, whereF(x) is a given analytic function, λ is a constant such that -1 < λ < 1, and n is an integer n = 2, 3, ・・・. This formula is theoretically based on the "Sinc method"[4], [6]. This quadrature error is of the order O(exp(-c_λN/logN)), where N is the number of nodes used, and c_λ is a positive constant which depends on λ. Numerical examples are presented.
Scientific journal, Japanese

I-070 Experimental Study on Transformational Structures and Similarity Judgment of Patterns
荒木, 正人; 小西, 敏雄; 岡野, 大; 緒方, 秀教; 天野, 要
Forum on Information Technology, 20 Aug. 2004, 情報科学技術フォーラム一般講演論文集, 3, 3, 165-166, Japanese, 110007683968, AA11740605

A Potential Flow Analysis by the Numerical Conformal Mapping
Amano Kaname; Tamai Masayuki; Okano Dai; Ogata Hidenori; Sugihara Masaaki
We propose a method of numerical conformal mappings of unbounded multiply-connected domains, and apply the method to ploblems of potential flow past obstacles caused by a pair of vortexes or a pair of point source and sink. A typical example shows the effectiveness of our method., National Committee for IUTAM, 2004, NCTAM papers, National Congress of Theoretical and Applied Mechanics, Japan, 53, 0, 163-163, 130005020121

Recent Topics on the Numerical Conformal Mapping Using the Charge Simulation Method (The Numerical Solution of Differential Equations and Linear Computation)
Amano Kaname; Okano Dai; Ogata Hidenori; Sugihara Masaaki
Kyoto University, May 2003, RIMS Kokyuroku, 1320, 47-59, Japanese, 1880-2818, 110000167315, AN00061013

代用電荷法による多重連結領域の数値等角写像について
天野 要; 岡野 大; 緒方 秀教
愛媛大学工学部, Mar. 2002, 工学ジャーナル, 1, 197-206, Japanese, 40005606033, AA1164817X

Numerical Conformal Mapping of Periodic Structure Domains (Numerical Solution of Partial Differential Equations and Related Topics II)
Ogata Hidenori; Okano Dai; Amano Kaname
Kyoto University, Apr. 2001, RIMS Kokyuroku, 1198, 108-116, English, 1880-2818, 110000165238, AN00061013

数値等角写像による淀み点の数値計算
片山 茂; 岡野 大; 緒方 秀教
愛媛大学工学部, Feb. 2001, 愛媛大学工学部紀要, 20, 253-263, Japanese, 0285-6107, 40004431636, AN00024855

A Mathematical Model of Pattern Cognition Based on the Transformational Structure Theory
AMANO Kaname; SHIBATA Yasuhiro; OKANO Dai; OGATA Hidenori; KONISHI Toshio
The transformational structure theory systematically explains how different types of cognitive judgments of patterns such as similarity and goodness are performed, and predicts their ordinal relations by the concepts of cognitive tranformations and transformational structures. We here present a mathematical model, the transformational group structure theory, of similarity judgments of linear binary patterns based on the transformational structure theory., Information Processing Society of Japan (IPSJ), 19 Jan. 2001, IPSJ SIG Notes, 2001, 6, 33-40, Japanese, 0919-6072, 110002930116, AN1010060X

数値等角写像の連続スキームによる導関数の近似
片山 茂; 岡野 大; 緒方 秀教; 天野 要
03 Oct. 2000, 第61回全国大会講演論文集, 2000, 1, 159-160, Japanese, 170000162236, AN00349328

代用電荷法による円弧スリット円還領域への数値等角写像の方法
牧 直正; 岡野 大; 緒方 秀教; 天野 要
03 Oct. 2000, 第61回全国大会講演論文集, 2000, 1, 161-162, Japanese, 170000162237, AN00349328

パターン認知の変換構造説
天野 要; 芝 田安裕; 岡野 大; 緒方 秀教; 小西 敏雄
03 Oct. 2000, 第61回全国大会講演論文集, 2000, 1, 211-212, Japanese, 170000162425, AN00349328

変換構造説の２値行列パターンへの拡張
芝 田安裕; 岡野 大; 緒方 秀教; 天野 要; 小西 敏雄
03 Oct. 2000, 第61回全国大会講演論文集, 2000, 1, 213-214, Japanese, 170000162426, AN00349328

Numerical Conformal Mapping onto the Unit Disk with Concentric Circular Slits by the Charge Simulation Method (Numerical Solution of Partial Differential Equations and Related Topics)
Amano Kaname; Okano Dai; Ogata Hidenori; Okamoto Takesi
Kyoto University, Apr. 2000, RIMS Kokyuroku, 1145, 41-49, English, 1880-2818, 110000164327, AN00061013

非有界な多重連結領域の数値等角写像と2次元ポテンシャル流解析
天野 要; 岡野 大; 緒方 秀教
愛媛大学工学部, Feb. 2000, 愛媛大学工学部紀要, 19, 387-399, Japanese, 0285-6107, 40004431601, AN00024855

積分方程式法によるスリット領域への数値等角写像
伊賀上 義夫; 岡野 大; 緒方 秀教
愛媛大学工学部, Feb. 2000, 愛媛大学工学部紀要, 19, 401-410, Japanese, 0285-6107, 40004431602, AN00024855

ガイダンス微分方程式 自然法則を語る数学
緒方秀教
Scholarly book, Japanese, Single work, サイエンス社, 10 Jun. 2022

Calculus of Variations
Hidenori Ogata
Japanese, Editor, Corona Publishing Co., Ltd., Jul. 2011

数値積分に対するDE公式とIMT型公式との関係について
緒方秀教
Oral presentation, Japanese, 日本応用数理学会2024年度年会
14 Sep. 2024
14 Sep. 2024- 16 Sep. 2024

IMT-DE変換による常微分方程式初期値問題の直接数値解法
森口麟太郎; 緒方秀教
Oral presentation, Japanese, 日本応用数理学会研究部会連合発表会
04 Mar. 2024
04 Mar. 2024- 06 Mar. 2024

佐藤超函数論による数値不定積分と常微分方程式への応用
緒方秀教
Oral presentation, Japanese, 日本応用数理学会研究部会連合発表会
04 Mar. 2024
04 Mar. 2024- 06 Mar. 2024

Method of fundamental solutions for doubly periodic problems
Hidenori Ogata
Oral presentation, English, 10th International Conference for Mathematics and Computing ICMC 2024, Peer-reviewed
04 Jan. 2024
02 Jan. 2024- 07 Feb. 2024

Numerical solver for ordinary differential equations based on IMT-DE variable transformation
Hidenori Ogata
English, ICIAM2023
22 Aug. 2023
20 Aug. 2023- 25 Aug. 2023

代用電荷法不変スキームの等角写像不変性について
緒方秀教
Oral presentation, Japanese, 日本応用数理学会第19回研究部会連合発表会
09 Mar. 2023
08 Mar. 2023- 10 Mar. 2023

IMT型変換と周期的Sinc近似による数値不定積分
緒方秀教
Oral presentation, Japanese, 日本応用数理学会2021年度年会, 日本応用数理学会, Domestic conference
09 Sep. 2021

佐藤超函数論に基づく無限区間上での関数近似、数値微分および数値不定積分
緒方秀教
Oral presentation, Japanese, 日本応用数理学会2021年度年会, 日本応用数理学会, Domestic conference
07 Sep. 2021

二重周期的ポテンシャル流に対する代用電荷法とそのユニモジュラー変換不変性
緒方秀教
Oral presentation, Japanese, 日本数学会2021年度年会, 日本数学会
17 Mar. 2021

佐藤超函数論に基づく補間、数値微分、および数値不定積分
緒方秀教
Oral presentation, Japanese, 日本応用数理学会研究部会連合発表会, 日本応用数理学会, Domestic conference
05 Mar. 2021

Method of fundamental solutions for doubly-periodic potential flow
Hidenori Ogata
Oral presentation, Japanese, 日本数学会2020年度秋季総合分科会, Domestic conference
24 Sep. 2020

Method of fundamental solutions for doubly-periodic potential flow using the Weierstrass elliptic functions
Hidenori Ogata
Oral presentation, Japanese, 日本応用数理学会2020年度年会
10 Sep. 2020

Numerical solution of Fredholm integral equations of the second kind using the IMT-type DE rules
Hidenori Ogata
Oral presentation, Japanese, 日本応用数理学会2020年度年会, Domestic conference
08 Sep. 2020

IMT型DE公式を用いた第2種Fredholm積分方程式の数値解法
緒方秀教
Oral presentation, Japanese, 日本応用数理学会2020年研究部会連合発表会, 中央大学, Domestic conference
04 Mar. 2020

振動積分に対する佐藤超函数論に基づく数値計算法
緒方秀教
Oral presentation, Japanese, 日本応用数理学会2019年度年会
03 Sep. 2019

Numerical methods for the Fourier transforms of hyperfunctions
Hidenori Ogata
Oral presentation, English, ICIAM2019, Valencia, Spain
16 Jul. 2019

佐藤超函数のフーリエ変換の数値計算法
緒方秀教
Oral presentation, Japanese, 日本応用数理学会2019年研究部会連合発表会, Domestic conference
05 Mar. 2019

A numerical analytic continuation and its application to Fourier transform
Hidenori Ogata
Oral presentation, English, ApplMath18 (Ninth Conference on Applied Mathematics and Scientific Computing), Sibenik, Croatia, International conference
18 Sep. 2018

連分数を用いた数値解析接続とFourier変換への応用
緒方秀教
Oral presentation, Japanese, 日本応用数理学会2018年度年会, 名古屋大学東山キャンパス, Domestic conference
05 Sep. 2018

佐藤超函数と数値解析への応用
緒方秀教
Oral presentation, Japanese, 常微分方程式の数値解法とその周辺, 大阪大学豊中キャンパス・サイバーメディアセンター, Domestic conference
09 Jul. 2018

Numerical Fourier transform based on hyperfunction theory
Hidenori Ogata
Oral presentation, English, ECMI2018 (The 20th European Conference on Mathematics for Industry), International conference
21 Jun. 2018

佐藤超函数論に基づくフーリエ変換の数値計算法
緒方秀教
Oral presentation, Japanese, 日本応用数理学会2018年研究部会連合発表会, Domestic conference
15 Mar. 2018

非整数次べき的特異性をもつHadamard有限部分積分に対する超函数法
Oral presentation, Japanese, 応用数学合同研究集会, Domestic conference
16 Dec. 2017

第2種Fredholm積分方程式に対する超函数法
緒方秀教
Oral presentation, Japanese, 日本応用数理学会年会, 武蔵野大学有明キャンパス, Domestic conference
08 Sep. 2017

Hyperfunction method for numerical integration and Fredholm integral equations of the second kind
Hidenori Ogata
Oral presentation, English, Computational Methods and Function Theory, Maria Curie Skłodowska University, Lublin, Poland
13 Jul. 2017

Numerical integration based on the hyperfunction theory
Hidenori Ogata
Invited oral presentation, Japanese, Numerical Analysis: New Developments for Elucidating Interdisciplinary Problems II, Invited, Research Institute of Mathematical Sciences, Kyoto University, Domestic conference
21 Oct. 2016

Hyperfunction method for Hadamard's finite part integrals
Hidenori Ogata
Oral presentation, Japanese, 日本応用数理学会2016年度年会, Domestic conference
12 Sep. 2016

Numerical integration based on the hyperfunction theory
Hidenori Ogata
Invited oral presentation, English, The 6th China-Japan-Korea Joint Conference on Numerical Analysis, Invited, NIMS, Daejeon, Korea, International conference
23 Aug. 2016

An application of the hyperfunction thoery to numerical integration
Hidenori Ogata; Hiroshi Hirayama
Oral presentation, English, ECMI2016 (The 19th European Conference on Mathematics for Industry), Santiago de Compostela, Spain, International conference
17 Jun. 2016

Numerical integration method based on the hyperfunction theory
Hidenori Ogata; Hiroshi Hirayama
Oral presentation, Japanese, 日本数学会2016年度年会, The Mathematical Society of Japan, Tsukuba University, In this study, we examine the numerical integration method proposed by Hirayama. In the method, we transform a desired one-dimensional integral into a complex loop integral and, by evaluating it by the trapezoidal rule, we obtain an approximate integral. In this method, the approximate integral converges geometrically to the exact value if the integrand is an analytic function, and the method is efficient especially for integrals with strong end-point singularities. Besides, the method is closely related to the hyperfunction theory., Domestic conference
19 Mar. 2016

Numerical Integration Based on the Hyperfunction Theory
Hidenori Ogata; Hiroshi Hirayama
Invited oral presentation, English, Second International ACCA-JP/UK Workshop, Invited, ACCA-JP/UK, Kyoto University, International conference
19 Jan. 2016

Numerical Integration Method Based on the Hyperfunction Theory
Hidenori Ogata; Hiroshi Hirayama
Oral presentation, English, ICMSA2015 (The 11th IMT-GT International Conference on Mathematics, Statistics and its Applications 2015), Department of Mathematics, King Mongkut's Institute of Technology Ladkrabang (KMITL) in association with the Indonesia-Malaysia-Thailand Growth Triangle (IMT-GT), Pattaya, Thailand, http://www.icmsa2015.kmitl.ac.th/website/index.html, International conference
23 Nov. 2015

佐藤超函数論に基づく数値積分
緒方秀教
Invited oral presentation, Japanese, 武蔵野大学数理工学シンポジウム2015, Invited, 武蔵野大学, Domestic conference
19 Nov. 2015

Theoretical error estimate of the numerical integration method by complex loop integral
Hidenori Ogata; Hiroshi Hirayama
Oral presentation, Japanese, 日本応用数理学会2015年度年会, 日本応用数理学会, 金沢大学, Domestic conference
11 Sep. 2015

Hyperfunction method for numerical integrations
Hidenori Ogata; Hiroshi Hirayama
Oral presentation, English, ICPAM 2015 (International Conference on Pure and Applied Mathematics), Department of Mathematics, Yuzuncu Yil University Van, Turkey, Van, Turkey, http://icpam.yyu.edu.tr/index.html, International conference
25 Aug. 2015

代用電荷法および双極子法による複素解析関数の近似
緒方秀教; 榊原航也; 桂田祐史
Oral presentation, Japanese, 日本数学会年会, 明治大学駿河台キャンパス, Domestic conference
24 Mar. 2015

Charge or dipole simulation method for approximation of complex analytic functions
Hidenori Ogata; K. Sakakibara; M. Katsurada
Oral presentation, English, ICRAPAM 2014 (International Conference on Recent Advances in Pure and Applied Mathematics), Antalya, Turkey, International conference
07 Nov. 2014

Dipole simulation method and its application to numerical conformal mappings
Hidenori Ogata
Oral presentation, English, 5th Asia Pacific Congress on Computational Mechanics (APCOM2013)
Dec. 2013

Dipole simulation method for two-dimensional potential problems in exterior regions and periodic regions
Hidenori Ogata
Oral presentation, English, Conference on Mathematical Modeling in Physical Sciences, Prague, Czech Republic
Sep. 2013

代用電荷法とその発展
緒方秀教
Invited oral presentation, Japanese, 研究集会「ポテンシャル論に現れる逆問題と求積公式」, Invited, 東北大学, Domestic conference
03 Mar. 2013

一般Jordan領域のポテンシャル問題に対する代用電荷法不変スキームの収束定理
緒方秀教; 桂田祐史
Oral presentation, Japanese, 応用数学合同研究集会, 龍谷大学瀬田キャンパス, Domestic conference
20 Dec. 2012

Convergence of the invariant scheme of the method of fundamental solutions for two-dimensional potential problems
Hidenori Ogata; Masashi Katsurada
Oral presentation, English, New Zealand Mathematical Society Colloquium 2012, Massey University, Palmerston North, New Zealand, International conference
05 Dec. 2012

ポテンシャル問題に対する双極子法の検証
緒方秀教
Oral presentation, Japanese, JSIAM2011研究部会連合発表会, 日本応用数理学会, 九州大学伊都キャンパス, Domestic conference
09 Mar. 2012

Theoretical error estimate and near optimality of the method of fundamental solutions for two-dimensional Helmholtz equations in the exterior region of a disk
Hidenori Ogata; Masaaki Sugihara
Oral presentation, English, WISE 2011 (Waves in Science and Engineering 2011), Techno Poli, Mexico City, Mexico, International conference
10 Nov. 2011

電気双極子代用電荷法と数値等角写像への応用
緒方秀教
Invited oral presentation, Japanese, RIMS研究集会「科学技術計算における理論と応用の新展開」, Invited, 京都大学数理解析研究所, Domestic conference
26 Oct. 2011

2次元Helmholtz方程式に対する基本解近似解法の理論誤差評価と最適性
緒方秀教
Oral presentation, Japanese, 日本応用数理学会2011年度年会, 日本応用数理学会, 同志社大学今出川キャンパス, Domestic conference
16 Sep. 2011

周期的領域問題に対する基本解近似解法
緒方秀教
Oral presentation, Japanese, 第60回理論応用力学講演会(NCTAM 2011), 日本学術会議、機械工学委員会、土木工学・建築学委員会、合同IUTAM分科会, 東京工業大学, Domestic conference
10 Mar. 2011

2次元円板外部領域におけるHelmholtz方程式Neumann境界値問題に対する基本解数値解法の理論誤差評価
緒方秀教
Oral presentation, Japanese, 日本応用数理学会2010年度年会, 日本応用数理学会, 明治大学駿河台キャンパス, Domestic conference
06 Sep. 2010

A Theoretical Study of Fundamental Solution Method for Wave Problem
Hidenori Ogata; Fumihiro Chiba; Teruo Ushijima
Oral presentation, English, The 2010 NIMS Conference & The Third China-Japan-Korea Joint Conference on Numerical Mathematics, National Institute for Mathematical Science, Gangneung, Korea, International conference
22 Aug. 2010

Mathematical Properties of the Fundamental Solution Method Applied to PDE Problems Such As Wave Problems
Hidenori Ogata
Invited oral presentation, English, Conference at Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan, Invited, Domestic conference
16 Dec. 2009

円外帰着Dirichlet波動問題に対する基本解近似解法の理論誤差評価
Hidenori Ogata; Fumihiro Chiba; Teruo Ushijima
Oral presentation, Japanese, 日本応用数理学会２００９年度年会講演予稿集
Sep. 2009

円外領域における様々な問題に対する代用電荷法の誤差について
緒方秀教
Oral presentation, Japanese, 日本応用数理学会研究部会連合発表会, 日本応用数理学会, 京都大学, Domestic conference
08 Mar. 2009

周期的2次元ポテンシャル問題のための半解析的数値解法
緒方秀教
Invited oral presentation, Japanese, 応用数学に関する愛媛ワークショップ「科学技術計算の数学的基礎」, Invited, 愛媛大学理学部, Domestic conference
30 Nov. 2008

周期的2次元ポテンシャル問題のための半解析的数値解法
緒方秀教
Oral presentation, Japanese, 環瀬戸内応用数理研究部会シンポジウム, 山形大学理学部（小白川キャンパス）, Domestic conference
11 Oct. 2008

Complex variable boundary element method for two-dimensional problems with one-dimensional periodicity
Hidenori Ogata
Oral presentation, English, Numerical Analysis and Applied Mathematics (International Conference on Numerical Analysis and Applied Analysis 2008), Psalidi, Kos, Greece, International conference
19 Sep. 2008

周期的形状壁を過ぎるStokes流に対する基本解法
緒方秀教
Oral presentation, Japanese, 第3回「計算科学研究ステーション」研究集会, 電気通信大学, Domestic conference
27 Mar. 2008

Boundary-element method for spatially-periodic potential problems
Hidenori Ogata
Oral presentation, English, ICIAM 2007 (6th International Congress on Industrial and Applied Mathematics), ETH Zurich, Switzerland, International conference
16 Jul. 2007

1次元周期的2次元Stokes流に対する基本解法
緒方秀教
Oral presentation, Japanese, 研究集会「解析学における問題の計算機による解法」, 京都大学数理解析研究所, Domestic conference
27 Mar. 2007

非斉次変形Helmholtz方程式に対する代用電荷法
緒方秀教
Oral presentation, Japanese, 日本応用数理学会平成19年研究部会連合発表会, 名古屋大学東山キャンパス, Domestic conference
03 Mar. 2007

周期場ポテンシャル問題に対する境界要素法
緒方秀教
Oral presentation, Japanese, 応用数学合同研究集会, 龍谷大学瀬田キャンパス, Domestic conference
20 Dec. 2006

周期場問題に対する代用電荷法
緒方秀教
Invited oral presentation, Japanese, 福島応用数学小研究集会, Invited, 福島大学サテライト教室, Domestic conference
04 Nov. 2006

Fundamental solution method for three-dimensioanl elastic problems with two-dimensional periodicity
Hidenori Ogata
Oral presentation, English, ICNAAM (International Conference on Numerical Analysis and Applied Mathematics 2006), Crete, Greece, International conference
18 Sep. 2006

2次元周期的3次元弾性問題に対する基本解法
緒方秀教
Oral presentation, Japanese, 計算科学研究ステーション研究集会, 電気通信大学, Domestic conference
06 Mar. 2006

周期的弾性問題に対する基本解法
緒方秀教
Oral presentation, Japanese, 応用数学合同研究集会, 龍谷大学瀬田キャンパス, Domestic conference
21 Dec. 2005

周期的弾性問題に対する代用電荷法
緒方秀教
Oral presentation, Japanese, 日本応用数理学会環瀬戸内応用数理研究部会第9回シンポジウム, 金沢大学, Domestic conference
12 Nov. 2005

Fundamental solution method for periodic-plane elasticity
Hidenori Ogata
Oral presentation, English, ICNAAM (International Conference on Numerical Analysis and Applied Mathematics 2005), Rhodes, Greece, International conference
19 Sep. 2005

境界に円を含む多重連結領域における代用電荷法
緒方秀教
Oral presentation, Japanese, 環瀬戸内応用数学合同研究集会, 愛媛大学, Domestic conference
21 Jan. 2005

境界に円を含む多重連結領域から標準スリット領域への代用電荷法による数値等角写像
緒方秀教
Oral presentation, Japanese, 高精度数値計算と逆問題, 岡山理科大学, Domestic conference
05 Nov. 2004

境界に円を含む多重連結領域の代用電荷法による数値等角写像
緒方秀教
Oral presentation, Japanese, 日本応用数理学会2004年度年会, Domestic conference
16 Sep. 2004

代用電荷法による非有界な多重連結領域の数値等角写像
天野要; 玉井政行; 島田英則; 岡野大; 緒方秀教
Oral presentation, Japanese, 日本応用数理学会2004年度年会, 中央大学後楽園キャンパス, Domestic conference
16 Sep. 2004

A numerical integration formula based on the Bessel functions and its relation with the DE rule
Hidenori Ogata
Invited oral presentation, English, Thirty Years of the Double Exponential Transforms, Invited, The Research Institute of Mathematical Sciences, Kyoto University, Domestic conference
02 Sep. 2004

A fundamental solution method for three-dimensional Stokes flow problems with obstacles in a planar periodic array
Hidenori Ogata
Oral presentation, English, ICCAM 2004 (Eleventh Internatioal Congress on Computational and Applied Mathematics), Katholieke Universiteit Leuven, Belgium, International conference
29 Jul. 2004

3境界点の像により定まる数値等角写像の代用電荷法による方法
緒方秀教
Oral presentation, Japanese, 研究集会「数値解析と新しい情報技術」, 京都大学数理解析研究所, Domestic conference
09 Dec. 2003

周期的粘性流問題に対する基本解法
緒方秀教; 天野要; 杉原正顯; 岡野大; 安田雄二
Oral presentation, Japanese, 研究集会「再生核の理論と応用」, 京都大学数理解析研究所, Domestic conference
10 Oct. 2003

代用電荷法による数値等角写像とポテンシャル流問題への応用
天野要; 玉井政行; 岡野大; 緒方秀教; 杉原正顯
Oral presentation, Japanese, 研究集会「再生核の理論と応用」, Domestic conference
10 Oct. 2003

リーマン面上の電荷を用いた代用電荷法による数値等角写像
岡野大; 寺薗正俊; 緒方秀教; 天野要
Oral presentation, Japanese, 研究集会「再生核の理論と応用」, 京都大学数理解析研究所, Domestic conference
10 Oct. 2003

圧縮性流体問題に対する代用電荷法による数値解法
緒方秀教
Oral presentation, Japanese, 日本応用数理学会2003年度年会, 京都大学, Domestic conference
17 Sep. 2003

3次元周期的問題におけるStokes流問題に対する基本解法
緒方秀教; 安田雄二
Oral presentation, Japanese, 第7回環瀬戸内応用数理応用数理研究部会シンポジウム2003, 鹿児島大学, Domestic conference
08 May 2003

代用電荷法による標準スリット領域から多重連結領域への数値等角写像の方法
岡野大; 寺薗正俊; 緒方秀教; 天野要
Oral presentation, Japanese, 第7回環瀬戸内応用数理研究部会シンポジウム2003, Domestic conference
07 May 2003

代用電荷法を用いた数値等角写像に関する最近の話題
天野要; 岡野大; 緒方秀教; 杉原正顯
Invited oral presentation, Japanese, 研究集会「微分方程式の数値解法と線形計算」, Invited, 京都大学数理解析研究所, Domestic conference
20 Nov. 2002

A fundamental solution method for two-dimensional viscous flows past obstacles in a periodic array
Hidenori Ogata
Oral presentation, English, The 11th International Colloquium on Numerical Analysis and Computer Science with Applications, Plovdiv, Bulgaria, International conference
Aug. 2002

A study on the aerofoils by the charge simulation method
Hidenori Ogata; Kaname Amano
Oral presentation, Japanese, 第6回環瀬戸内応用数理研究部会シンポジウム, 岡山理科大学, Domestic conference
28 Jun. 2002

多重スリット領域から標準スリット領域への数値等角写像の方法
寺園正俊; 岡野大; 緒方秀教; 天野要
Oral presentation, Japanese, 第6回環瀬戸内応用数理研究部会シンポジウム, 岡山理科大学, Domestic conference
28 Jun. 2002

角点を持つ単連結外部領域の数値等角写像の方法
清澤佑太; 緒方秀教; 岡野大; 天野要
Oral presentation, Japanese, 第6回環瀬戸内応用数理研究部会シンポジウム, 岡山理科大学, Domestic conference
28 Jun. 2002

A fundamental solution method for the problems of viscous flows past obstacles in a periodic array
Hidenori Ogata
Oral presentation, English, ICRACM 2001 (International Conference on Recent Advances in Computational Mathematics), Hotel JAL City Matsuyama, Japan, International conference
13 Oct. 2001

A method of numerical conformal mapping of curved slit domains by the charge simulation method
Dai Okano; Hidenori Ogata; Kaname Amano
Oral presentation, English, ICRACM 2001 (International Conference on Recent Advances in Computational Mathematics), Hotel JAL City Matsuyama, Japan, International conference
13 Oct. 2001

A charge simulation method for spatially periodic problems
Hidenori Ogata; Dai Okano; Kaname Amano; Masaaki Sugihara
Oral presentation, English, Progress in Analysis (Proceedings of the 3rd International ISAAC Congress), Freie Universitaet Berlin, Germany, International conference
20 Aug. 2001

代用電荷法による2次元ポテンシャル流の力の計算
緒方秀教; 岡野大; 天野要
Oral presentation, Japanese, 第5回環瀬戸内応用数理研究部会シンポジウム, 愛媛大学, Domestic conference
09 Jun. 2001

代用電荷法による曲線スリットを含む領域の数値等角写像の方法
岡野大; 片山茂; 緒方秀教; 天野要
Oral presentation, Japanese, 第5回環瀬戸内応用数理研究部会シンポジウム, 愛媛大学, Domestic conference
09 Jun. 2001

代用電荷法による円弧スリット円環領域への数値等角写像の方法
牧直正; 岡野大; 緒方秀教; 天野要
Oral presentation, Japanese, 第5回環瀬戸内応用数理研究部会シンポジウム, 愛媛大学, Domestic conference
09 Jun. 2001

Numerical conformal mapping of periodic structure domain
Hidenori Ogata; Dai Okano; Kaname Amano
Oral presentation, English, ICFIDCA 2000 (Eighth International Conference on Finite or Infinite Dimensional Complex Analysis, Shandong University, P. R. China, International conference
22 Aug. 2000

代用電荷法の不変スキームに現れる連立一次方程式の可解性
杉原正顯; 岡野大; 緒方秀教; 天野要
Oral presentation, Japanese, 日本応用数理学会1999年度年会, 愛媛大学工学部, Domestic conference
04 Oct. 1999

DE-type quadrature formulae for Cauchy-principal value integrals and for Hadamard finite-part integrals
Hidenori Ogata; Masaaki Sugihara; Masatake Mori
Oral presentation, English, Proceedings of the Second ISAAC Congress, Fukuoka Institute of Technology, International conference
Aug. 1999

球Bessel関数を含む振動積分に対するDE型数値積分公式
緒方秀教
Oral presentation, Japanese, 日本応用数理学会1997年度年会, 名古屋大学東山キャンパス, Domestic conference
02 Oct. 1997

振動積分に対するDE型数値積分公式の理論誤差解析
緒方秀教; 大浦拓哉
Oral presentation, Japanese, 日本応用数理学会平成8年度年会, 東京大学駒場キャンパス, Domestic conference
24 Sep. 1996

Bessel関数の零点を標本点に持つ数値積分公式：正確な値を与える場合と最適性
緒方秀教; 杉原正顯
Oral presentation, Japanese, 研究集会「科学技術における数値計算の理論と応用」, 京都大学数理解析研究所, Domestic conference
Oct. 1995

実数次Bessel関数の零点を標本点にもつ数値積分公式
緒方秀教; 杉原正顯
Oral presentation, Japanese, 日本応用数理学会平成7年度年会, 岡山理科大学理学部, Domestic conference
19 Sep. 1995

Bessel関数を含む振動積分に対する数値積分公式
緒方秀教; 杉原正顯
Oral presentation, Japanese, 研究集会「数値計算アルゴリズムの現状と展望II」, Domestic conference
Oct. 1994

Lagrange-Bessel補間とそれに基づく数値積分則
緒方秀教; 杉原正顯
Oral presentation, Japanese, 日本応用数理学会平成6年度年会, 川崎製鉄株式会社千葉研修所, Domestic conference
21 Sep. 1994

無限区間における補間についての考察
緒方秀教; 杉原正顯
Oral presentation, Japanese, 研究集会「数値計算アルゴリズムの現状と展望」, 京都大学数理解析研究所, Domestic conference
25 Oct. 1993

無限区間におけるLagrange補間の拡張とその応用について
緒方秀教; 杉原正顯
Oral presentation, Japanese, 日本応用数理学会平成5年度年会, 龍谷大学瀬田キャンパス, Domestic conference
16 Sep. 1993

DE変換による境界値問題の解法
緒方秀教; 杉原正顯; 森正武
Oral presentation, Japanese, 日本応用数理学会平成4年度年会, 電気通信大学, Domestic conference
04 Oct. 1992

Hadamard有限部分積分に対するDE公式
緒方秀教; 杉原正顯; 森正武
Oral presentation, Japanese, 研究集会「数値解析とそのアルゴリズム」, 京都大学数理解析研究所, Domestic conference
22 Nov. 1991

変数変換によるHadamard積分の有限部分の数値計算
緒方秀教; 杉原正顯; 森正武
Oral presentation, Japanese, 日本応用数理学会平成3年度年会, 東京大学工学部, Domestic conference
07 Oct. 1991

Mathematical Information Science Laboratory IIB
The University of Electro-Communications

Mathematical Information Science Laboratory ⅡB
The University of Electro-Communications

Mathematical Information Science Laboratory ⅡA
The University of Electro-Communications

情報数理工学実験第二B
The University of Electro-Communications

Mathematical Information Science Laboratory IIA
The University of Electro-Communications

応用解析学特論
The University of Electro-Communications

情報数理工学実験第二B
The University of Electro-Communications

情報数理工学実験第二A
The University of Electro-Communications

応用解析学特論
The University of Electro-Communications

数値計算
The University of Electro-Communications

Numerical calculus
The University of Electro-Communications

数値計算
電気通信大学

Mathematical information science laboratory II B
The University of Electro-Communications

情報数理工学実験第二B
電気通信大学

Mathematical information science laboratory II A
The University of Electro-Communications

情報数理工学実験第二A
電気通信大学

Fundamentals of information and communication engineering
The University of Electro-Communications

情報・通信工学基礎
電気通信大学

Advanced applied analysis
The University of Electro-Communications

応用解析学特論
電気通信大学

Analysis
The University of Electro-Communications

解析学
電気通信大学

Applied mathematics
The University of Electro-Communications

応用数学
電気通信大学

The Japan Society for Industrial and Applied Mathematics

Information Processing Society of Japan

The Japan Society for Computational Engineering and Science

The Mathematical Society of Japan

数値計算における変数変換技法の新展開
緒方 秀教
日本学術振興会, 科学研究費助成事業, 電気通信大学, 基盤研究(C), 24K06840
Apr. 2024 - Mar. 2027

Numerical analysis of analytic functions based on hyperfunction theory
Hidenori Ogata
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, The University of Electro-Communications, Grant-in-Aid for Scientific Research (C), 以下の2点がこれまでの研究実績である． （１．佐藤超函数論に基づく関数近似、数値微分および数値不定積分）佐藤超函数論は複素関数論に基づく一般化関数の理論であり，超函数とよばれる一般化関数を定義関数とよばれる複素解析関数の実軸上の境界値の差で表す．そして，通常の関数も，標準定義関数という定義関数を構成することにより超函数として表すことができる．本研究ではこのことに着目して関数近似・数値微分・数値不定積分を行う方法を考案した．具体的には，近似の対象とする関数に対し，標準定義関数を数値積分および連分数を用いることにより数値的に求め，それを用いて関数近似を超関数として与え，さらに，標準定義関数の導関数・原始関数をもちいて数値微分・数値不定積分を与える．そして，数値実験により本方法の有効性を確かめた．本研究の成果は国内学会で口頭発表し，和文誌に論文投稿した． （２．IMT型変数変換を用いた数値不定積分および第2種Volterra型積分方程式の数値解法）数値計算において変数変換を用いた技法は数値積分でよく用いられてきた．ところで近年DE変換とよばれる変数変換は，Sinc近似という関数近似の技法と組み合わせて，数値積分以外の数値計算（積分方程式、微分方程式など）に用いられるようになった．それに対し本研究では，数値積分で用いられているもうひとつの変数変換「IMT型変換」について，周期関数に対するSinc近似と組み合わて数値不定積分および1次元第2種Volterra積分方程式に応用する数値計算法を考案した．そして，数値実験および理論誤差解析によりその計算法の有効性を示した．本研究の成果について，数値不定積分法は国内学会で口頭発表し和文誌に論文投稿して採録された．積分方程式の数値解法は国内学会で口頭発表した．, 21K03366
01 Apr. 2021 - 31 Mar. 2024

Numerical analysis based on the hyperfunction theory
Hidenori Ogata
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, The University of Electro-Communications, Grant-in-Aid for Scientific Research (C), Principal investigator, The aim of this study is the development and theoretical analysis of numerical computation method based on the hyperfunction theory. The hyperfunction theory is a theory of generalized functions based on the complex analysis, and describes singularities of functions such as poles, discontinuities and the delta functions. In this study, we aim the applications of the hyperfunction theory to numerical computations, namely, we approach to problems involving singularities which make computation difficult by using analytic functions, which are ultimately smooth functions, from the viewpoint of the hyperfunction theory. To be specific, we develop numerical computation methods for integrations with singularities, etc. and consider problems related to numerical computations based on the hyperfunction theory such as the numerical expressions of hyperfunctions., 16K05267
01 Apr. 2016 - 31 Mar. 2019

Validate Computation Library on Time Evolution Equations
YAMAMOTO Nobito; NAKAMURA Ken-ichi; OGATA Hidenori
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, The University of Electro-Communications, Grant-in-Aid for Scientific Research (C), We have investigated in computer program library including validated computation techniques which give the basis of validated computation of time evolution equations, and derived a number of new approaches to numerical verification of ODEs which appear as semi-discretized equations of PDEs. The results were published in academic journals., 21540115
2009 - 2011

Research on the Charge Simulation Method and the Numerical Conformal Mapping
AMANO Kaname; OKANO Dai; TUCHIYA Takuya; OGATA Hidenori; SUGIHARA Masaaki; ENDO Keiichi
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Ehime University, Grant-in-Aid for Scientific Research (B), Using the charge simulation method, we proposed the method of numerical conformal mappings of unbounded multiply connected domains onto the following canonical slit domains: (a) the parallel and the colinear slit domains, (b) the linear slit domain and (c) the circular and radial slit domain; and showed the effectiveness of our method. We studied the property of the charge simulation method, and proposed a fundamental solution method for periodic Stokes flow problems. These are important in scientific and engineering applications. Basic studies on numerical methods for singular integral equations and ill-conditioned linear equations are progressed, which are closely related to the subject of this study., 19340024
2007 - 2009

Numerical methods for wave propagation phenomena in unbounded region and its applications to shape design problems
KAKO Takashi; OGATA Hidenori; IMAMURA Toshiyuki; KOYAMA Daisuke; SUITOU Hiroshi; SUITOU Hiroshi
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, The University of Electro-Communications, Grant-in-Aid for Scientific Research (C), 無限領域における波動現象で現れる周波数応答問題や共鳴現象に対して、有限要素法やFDTD法による数値計算手法の開発と関連する研究を行った。その中で、外部ディリクレ・ノイマン写像の離散化手法の開発とその応用について数値実験を含む検証を行って成果を得た。応用として、音声生成では声道設計問題に対してアルゴリズムを考案して数値実験により有効性を確認した。また騒音低減問題などに関係した構造音場連成問題の数値解法の応用研究を展開した。DtN(Dirichlet-to-Neumann)境界条件を課した問題にたいする有限要素法については、3次元水面波動問題へも適用し数値解法の事前誤差評価を導出すると共にヘルムホルツ問題については修正DtN境界条件や多重DtN境界条件を課した場合についても事前誤差評価を導出した。さらに、アンテナからの電磁波の放射問題とその応用に関してPML技法を用いた無限領域における電磁場の非定常現象の数値解法の開発に取り組み3次元計算コードの基本的な部分を完成させ、幾つかの応用についても成果を得た。また、偏微分方程式の数値解法である基本解解法(代用電荷法)についても、従来同法の適用が難しいとされた周期的構造を持つストークス流問題や弾性問題への拡張をおこない、さらに境界要素法、およびその複素関数論的拡張である複素変数境界要素法について従来適用困難とされた空間周期的2次元ポテンシャル問題への拡張を行った。関連する問題としては、量子多体系で現れる行列の対角化問題においてLOBPCGの効率的な並列実装を行い世界記録となる1600億次元の計算に成功した。さらに、来るべきペタスケール計算機時代に備えた大規模固有値計算ついて、段階的な収束をブロックレベルでコントロールする手法を提案するとともに、密行列の対称行列についてマルチコア向けのブロック化手法により帯行列化の系統のアルゴリズムの研究で成果を得た。, 18540114
2006 - 2008

Numerical Conformal Mappings by the Charge Simulation Method and Their Applications to Fluid Mechanics
AMANO Kaname; OKANO Dai; TSUCHIYA Takuya; OGATA Hidenori; SUGIHARA Masaaki; YOTSUTANI Shoji
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Ehime University, Grant-in-Aid for Scientific Research (B), The numerical conformal mapping has been an important subject in computational and applied mathematics. Our major concern is to develop new methods of numerical conformal mappings by the charge simulation method (or the fundamental solution method) and apply them to potential flow problems. 1.We constructed approximate mapping functions of the conformal mapping w= f(z) of an unbounded multiply connected domains D onto the unbounded canonical slit domains of Nehari (Mc-Graw Hill, 1952) under the condition f(v) = ∞, where v is a finite point given in the problem domain. They were applied to the problem of potential flows past obstacles caused by a dipole source, a pair of positive and negative vortexes or a pair of point source and sink. 2.We constructed by the charge simulation method approximate mapping functions of the conformal mapping of bounded multiply connected domains onto all the unbounded and bounded canonical slit domains of Nehari. 3.We proposed a new technique to apply the charge simulation method to a nonlinear compressible fluid flow problem. We also proposed a fundamental solution method for viscous flow problems with obstacles in a periodic array, which gives an approximate solution by a linear combination of periodic fundamental solutions. 4.We proved the convergence of the approximate mapping function obtained by the charge simulation method. Many other interesting results were obtained in relation to methods of numerical computation and thier application to fluid mechanics., 15340033
2003 - 2005

General Research on the Charge Simulation Method and the Numerical Conformal Mapping
AMANO Kaname; OKANO Dai; OGATA Hidenori; ITO Hiroshi; SUGIHARA Masaaki; YOTSUTANI Shoji
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Ehime University, Grant-in-Aid for Scientific Research (B), The numerical conformal mapping has been an important subject in computational mathematics. On the other hand, the charge simulation method is a simple accurate solver for the Dirichlet problem of the Laplace equation. 1.We have proposed a simple method of numerical conformal mappings of multiply-connected domains onto the canonical domains of Nehari (Mc-Graw Hill, 1952), i.e., (a) the parallel slit domain, (b) the circular slit domain, (c) the radial slit domain, (d) the circle with concentric circular slits and (e) the circular ring with concentric circular slits. The method uses the charge simulation method on the complex plane, i.e., a linear combination of complex logarithmic functions, and gives approximate mapping functions with high accuracy if boundary curves and boundary data are analytic. 2.We have successfully applied the numerical conformal mapping to potential flow analysis, and presented simple methods to find the stagnation points around obstacles and to compute the forces on obstacles. 3.We have presented some techniques to apply the charge simulation method to domains with corners or slits. We also presented new types of the charge simulation method applicable to periodic domains, which use periodic fundamental solutions of the problem instead of logarithmic functions. 4.We proved the unique solvability of the linear systems appearing in the invariant scheme of the charge simulation method. These results revive the classical method using fundamental solutions as a modern method in the computer age., 12440029
2000 - 2002

Numerical Methods Based on Sinc Functions
SUGIURA Masaaki; MATSUO Takayasu; SUGIURA Hiroshi; MITSUI Taketomo; OGATA Hidenori; MORI Masatake
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Nagoya University, Grant-in-Aid for Scientific Research (B), This project aims at developing numerical methods based on Sine functions incorporated with the double exponential transformation technique. The following results have been obtained. 1. A Sinc method using the double exponential transformation technique is developed for computing indefinite integrals. Two Sinc methods using the conventional single exponential transformation technique are well-known : one is due to Kearfott, and the other due to Haber. While these well-known methods converge at the rate exp(-c-√) (n : the number of function evaluations), our method converges at the rate exp(-c'n/ log n). 2. A Sinc-Galerkin method incorporated with the double exponential transformation technique for two-point boundary value problems is developed. While the rate of the convergence of the original Sinc-Galerkin method due to Stenger is exp(-c-√)(n: the number of basis functions), that of our method is exp(-c'n/ logn), which is a remarkable improvement. 3. A Sinc-collocation method combined with the double exponential transformation technique for Sturm-Liouville eigenvalue problems is developed. Our method enjoyes the convergence rate O(exp(-c'n/ logn)) (n : the number of basis functions), whereas the original Sine-collocation method proposed by Lund et al. does the convergence rate O(exp(-c-√)). 4. Three spectral methods using the double exponential transformation technique are developed for solving the Poisson equation on a fan-shaped domain. One employes the Sinc functions as basis functions, another does the Legendre polynomials, and the other does the Chebyshev polynomials. All the methods converge at the rate exp(-c√/logn), where n is the number of basis functions., 11450038
1999 - 2001

Numerical Conformal Mapping and Its Application to the Two-Dimensional Potential Flow Analysis
AMANO Kaname; OGATA Hidenori; TSUDA Koichi; IGARI Katsuju; SUGIHARA Masaaki; OKANO Dai
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Ehima University, Grant-in-Aid for Scientific Research (B), Conformal mappings are familiar in science and engineering. But, exact mapping functions are not known except for special domains. Particularly, conformal mappings of unbounded multiply-connected domains are well known as a method of two-dimensional potential flow analysis. The mappings of a domain exterior to closed Jordan curves onto parallel, circular and radial slit domains are directly related to the problems of uniform, vortex and point-souce flows around obstacles, respectively. We presented a simple method of numerical conformal mappings of the multiply-connected domains onto the parallel, circular and radial slit domains. We reduced the mapping problems to the Dirichlet problem with a pair of conjugate harmonic functions and employed the charge simulation method, where the pair of conjugate harmonic functions are appoximated by a linear combination of complex logarithmic potentials. The method has the following features : 1. Conformal mappings onto the parallel slit domains with slits parallel to the imaginary axis and parallel to the real axis constitute a dual problem and can be computed in a dual way. 2. Conformal mappings onto the circular and radial slit domains constitute a dual problem and can be computed in a dual way. 3. They are reformulated into a more integrated form in which the linear equations to be solved have the same coefficient matrix., 09440081
1997 - 1999

Mathematical Research on Anomalous Diffusion Problem
MORI Masatake; OGATA Hidenori; FURIHATA Daisuke; SUGIHARA Masaaki
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, School of Engineering, University of Tokyo, Grant-in-Aid for Scientific Research (C), Suppose that a uniform mixture of two metals is in an unstable nonequilibrium state and that the mixture evolves from the unstable state to a more stable nonuniform configuration consisting of two phases. Such a phenomenon is call an anomalous diffusion problem and time evolution of such a phenomenon is described by a nonlinear partial differential equation called the Cahn-Hilliard equation. The purpose of the present research project is to establish an efficient difference scheme for stable numerical solution of such kind of nonlinear partial differential equations. The idea of the present method is to start from discretization of the energy of the physical system under consideration and to apply a suitable discrete variation. The key point of the present research exists in this discrete variation. When we discretize the energy we defined the difference operators and the summation operators consistently with the differetial operators and the integration operator. Our method can be applied not only to the Cahn-Hilliard equation but also to a wide class of nonlinear partial differential equations, i. e. partial differential equations for energy dissipative system and for energy conservative system. Examples of equations for the dissipative system and the heat equation and the Cahn-Hilliard equation, and the wave equation and the KdV equation are examples of the equations for the conservative system. Our method were applied successfully to numerical solution of these equations. In the case of the Cahn-Hilliard equation we proved mathematically the stability of the scheme and the convergence of the numerical solution to the exact solution of the original equation., 06650072
1994 - 1996

代用電荷法に関する研究
杉原 正顯; 緒方 秀教; 室田 一雄; 森 正武
日本学術振興会, 科学研究費助成事業, 東京大学, 一般研究(C), 本研究では代用電荷法に関する最も基本的課題「代用電荷法の電荷点・拘束点の同時最適配置を求める算法の開発」の研究を行った. よく知られているように,代用電荷法の精度は電荷点・拘束点の選び方に大きく依存する.従来,数値実験に基づいて,いろいろな方法が提案されてきたが,近年,明確な数学的根拠のある方法が岡本・桂田,研究代表者(杉原)によって提案された.前者は電荷点が与えられたときに最適な拘束点を与える算法を与え,後者は拘束点が与えられたときに最適な電荷点を与える算法である.本研究ではこれらの算法を交互に用いるというアイデアに基づいて電荷点・拘束点の同時最適配置を与える算法を開発した.ただし,岡本・桂田による算法の部分は比較的簡単な算法であるのに対して,杉原による算法の部分は最適化法を必要とするため多大な計算時間を要する.したがって,そのまま2つの算法を交互に用いると,電荷点・拘束点の数が多くなると,算法の効率が非常に悪くなり実用的ではなくなる.そこで,岡本・桂田による算法においては本質的に電荷点の最適配置を与える(近似)等角写像を求めていることに注目し,電荷点・拘束点の数が少ない(例えば8点ぐらい)ときに,2つの算法を交互に用いて電荷点・拘束点の同時最適配置を与える(近似)等角写像を求め,それを基に,電荷点・拘束点の数が多い場合の配置を計算する形の算法を開発した.数多くの数値実験の結果,境界が簡単な形状で滑らかならば,開発した算法が十分実用になることを確認した. なお,今後の課題として,本研究で得られた算法が生成する(近似)等角写像は理論的視点からどのような意味を持つのかを解明することが残されている., 07650074
1995 - 1995

無限区間における補間とその数値計算への応用
緒方 秀教
日本学術振興会, 科学研究費助成事業, 東京大学, 奨励研究(A), 本研究では、無限区間における補間、とくに後で述べる「Lagrange-Bessel補間」の数値積分への応用を、主に行い、最終的には、Bessel関数を含む振動積分の計算に成功した。 無限区間における補間(標本点a_1,a_2,…,a_k,…) (f(x)はa_1,a_2,…,a_k…を零点に持つ整関数)において、標本点をBessel関数J_n(x)(n=0,1,…)の零点に選んだものがLagrange-Bessel補間である。この補間公式をもとに、いわゆる補間形数値積分公式を得る要領で、「対称積分」∫^∞_<-∞>f(x)dx,「反対称積分」∫^∞_<-∞>sgnxf(x)dxに対する数値積分公式、すなわち、「Lagrange-Bessel積分則」を得た。そして、とくに反対称積分に対するLagrange-Bessel積分則は、DE公式などで用いられる、対称積分に対する台形則と、同程度の精度を達成することが、複素積分の理論を用いた誤差解析により分かった。 Lagrange-Bessel積分則の応用として、主にBessel積分則の応用として、主にBessel関数を含む振動積分∫^∞_0f(x)J_n(x)dxの数値計算の研究を行った。上の積分やFourier変換型積分∫^∞_0f(x)sin xdxのような振動積分は、従来の数値積分公式では計算が難しかったが、Fourier変換型積分にたいしては、大浦・森によるDE公式が得られている。この公式はBessel関数を含む振動積分の計算には使えないが、Lagrange-Bessel積分則と大浦・森のアイディアを組み合わせて、Bessel関数を含む振動積分に対するDE公式を考案、数値実験でも有効性が実証された。, 06750067
1994 - 1994

連立一次方程式に対する数値解法の誤差解析
杉原 正顯; 緒方 秀教; 室田 一雄; 森 正武
日本学術振興会, 科学研究費助成事業, 東京大学, 一般研究(C), 連立一次方程式に対する数値解法の誤差解析に関連するつぎのような研究を行った. 1.1-ノルムに関する条件数の推定法の比較研究 1-ノルムに関する条件数の推定法として有名な3つの方法(LINPACKなどにおいて用いられてきた方法,わが国で開発された塚本-名取の方法,LAPACKで用いられているHagerの方法)を計算時間,精度の面から比較した.計算時間の面からは,塚本-名取の方法がもっともよく,精度の面からはHagerの方法がもっともよかった.また,どの方法の計算時間も方程式を解く時間に比べると無視できる時間内に推定値が得らた.したがって,Hagerの方法を1-ノルムに関する条件数の推定法として用いるべきであるという結論が得られた.ただし,塚本-名取の方法はプログラミングが簡単であり簡便な方法としての存在意義はある. 2.共役勾配法の誤差の複雑な振る舞いの解明 近年Greenbaumによって確立された共役勾配法の後退誤差解析の手法を用いて,共役勾配法の誤差の複雑な振舞いと係数行列の固有値の分布との関係について調べることを目標として,研究を行った.その結果,後退退誤差解析の手法によって共役勾配法の誤差の複雑な振る舞いをある程度再現できることが分かった.しかし,この手法においては元の行列の次数をNとするとき10N程度の次数の行列の計算を正確に行う必要があり,計算時間や記憶容量の点で多くの実験が行えなかった。そののため,係数行列の固有値の分布との関係については従来から知られている結果「固有値が密集していれば収束が速い」以上のものは残念ながら得られなかった., 06650074
1994 - 1994

変数変換に基づく数値計算アルゴリズムの研究
緒方 秀教
日本学術振興会, 科学研究費助成事業, 東京大学, 奨励研究(A), 数値積分において強力な手法の一つである「変数変換型公式」は、Stengerにより研究されている「Sinc近似理論」と組み合わせることにより、積分計算以外に、さまざまな数値計算に適用することが出来る。本年度はこのSinc近似理論の基礎を数学的観点から見直し、さらに、Lagrange補間のある種の拡張として理論の一般化を図ることに、研究の主眼を置いた。 数値解析において伝統的な手法の一つである、Lagrange補間とは、未知関数を有限個の標本点で関数値が一致するように多項式で近似する、関数近似の手法である。これは「有限個」の標本点を用いた補間であるが、標本点の数を「無限個」にした極限公式を考える。これが上で述べた、Lagrange補間の拡張である。 今回の研究では、従来の「Sinc補間」も拡張されたLagrange補間のひとつと見なせることが分かった。これは上で述べた「Sinc近似理論」の基礎公式であり、Lagrange補間の拡張という観点から眺めると、sin chiの零点、すなわち、実軸全体に等間隔に分布する標本点を用いた補間と見なせる。 今回の研究においては、「Lagrange-Bessel補間」を新たに考案し、誤差解析及び数値実験を行なった。これはsin chiの代わりにBessel関数の零点を標本点に用いた補間公式である。数値実験を行なったところ、Sinc補間とほぼ同程度の精度を得ることが確認された。 誤差解析では次のことが確認された。解析関数に対して補間を行なったとき、補間誤差は複素積分を用いて表すことが出来るが、被積分関数に補間標本点を零点に持つ整関数(全複素平面で正則な関数)を含む。整関数の値分布は零点の分布に大いに依存することが分かっており、よって標本点の分布が補間誤差を最も大きく決定付けることが言える。とくに標本点が漸近的に等間隔に分布する場合(Sinc補間、Lagrange-Bessel補間はこれに含まれる)、誤差は標本点数密度に対し指数関数的に減少することが、示される。, 05750064
1993 - 1993

SINC関数近似に基づく数値計算アルゴリズムの研究
杉原 正顯; 緒方 秀教; 室田 一雄; 森 正武
日本学術振興会, 科学研究費助成事業, 東京大学, 一般研究(C), SINC関数近似に基づく数値計算アルゴリズムに関連して1.〜3.に述べるような研究を行った. 1.SINC関数近似に基づく特異積分計算用DE公式(二重指数関数型公式)の研究と開発 特異性をもつ関数に対するSINC関数近似式を導き,それに基づいて特異積分の数値計算用二重指数関数型積分公式を導いた.この公式は,すでに提案されている(Bialecki等による)一重指数関数型積分公式に比べ,収束性が優れていることが理論,実験両面で証明された.またさらに,この公式が関数解析的視点から見て最適性をもっていることも理論的に証明された. 2.SINC関数近似に基づく2点境界値問題のDE変換(二重指数関数型変換)を用いた数値計算用アルゴリズムの研究と開発 SINC-Galerkin法を用いて,2点境界値問題の二重指数関数型変換に基づく数値計算用アルゴリズムを導いた.この公式もまた従来提案されている(Lund等による)一重指数関数型変換に基づくアルゴリズムに比べ,収束性が優れていることが実験で証明された(これらの方法の誤差に関する理論的解析は難しく,今のところ実験を通しての証明でしかない).ただし,我々の方法の場合,解くべき線形方程式の条件数が悪化するので,方程式を高精度で解く必要がある. 3.無限区間におけるLagrange補間公式の研究 SINC補間公式は,分点を等間隔にとった無限区間におけるLagrange補間公式である(このことは高橋秀俊によって指摘されている).より一般の分点をとった場合の無限区間におけるLagrange補間公式の一般的な性質を議論し,さらに,実用上重要と思われるベッセル関数の零点を分点にもつような公式について詳細に研究した., 05650063
1993 - 1993

JSIAM Letters
Peer review etc, Peer review, 05 Apr. 2023 - Present

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YouTubeチャンネル開設、数学・数値解析に関する話の動画を発信。
https://www.youtube.com/channel/UC_Vm1H9AB1631EutDaclA0A
2020 - 2020