DAISUKE KOYAMA
| Department of Computer and Network Engineering | Assistant Professor |
| Cluster I (Informatics and Computer Engineering) | Assistant Professor |
Researcher Information
Research Keyword
Field Of Study
Educational Background
Research Activity Information
Paper
- On volumetric locking in a hybrid symmetric interior penalty method for nearly incompressible linear elasticity on polygonal meshes
Daisuke Koyama; Fumio Kikuchi
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, SPRINGER JAPAN KK, 34, 2, 373-406, Aug. 2017, Peer-reviwed, A hybrid version of a symmetric interior penalty method for nearly incompressible linear elasticity is investigated. When a lifting term is used in the method, the method can be free of volumetric locking. On the other hand, when the lifting term is not used, an interior penalty parameter has to be taken to be of order lambda, the first Lam, parameter, as lambda tends to infinity, in order to guarantee the coercivity of the bilinear form in the method. Taking the interior penalty parameter to be of order lambda leads to volumetric locking phenomena when piecewise linear functions are employed to compute approximate solutions.
Scientific journal, English - Volume locking phenomena arising in a hybrid symmetric interior penalty method with continuous numerical traces
Daisuke Koyama; Fumio Kikuchi
Lecture Notes in Computational Science and Engineering, Springer Verlag, 116, 361-369, 2017, Peer-reviwed, A hybrid version of the symmetric interior penalty (HSIP) method is considered for linear elasticity problems for nearly incompressible materials. When the 1 conforming finite element method is applied to such problems, volume locking phenomena occur. Discontinuous Galerkin (DG) methods are known as a remedy for the locking. The HSIP method has two unknowns which are approximations for the displacement and its trace on the skeleton. The latter is often called the numerical trace. The HSIP method with the discontinuous numerical trace is free from locking. On the other hand, it is numerically observed that the HSIP method with the continuous numerical trace causes volume locking phenomena when the 1 elements are employed for the two unknowns. The numerical fact is mathematically proved in this paper.
International conference proceedings, English - An a priori error estimate of the Dirichlet-to-Neumann finite element method for multiple scattering problems
Daisuke Koyama
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, KINOKUNIYA CO LTD, 31, 1, 165-192, 2014, Peer-reviwed, The multiple Dirichlet-to-Neumann (DtN) boundary condition has been derived by Grote and Kirsch (J Comput Phys 201:630-650, 2004) to numerically solve multiple scattering problems. An a priori error estimate is established for finite element methods applied to the Helmholtz problem with the multiple DtN boundary condition. The error estimates account for the effects of truncation of infinite Fourier series representing the multiple DtN boundary condition as well as of discretization of the finite element method.
Scientific journal, English - Strong L^p convergence associated with Rellich-type discrete compactness for discontinuous Galerkin FEM
Fumio Kikuchi; Daisuke Koyama
JSIAM Letters, 6, 25-28, 2014, Peer-reviwed
Scientific journal, English - Preface
Daisuke Koyama; Choi-Hong Lai; Nobito Yamamoto
Journal of Algorithms & Computational Technology, Mathematical Modelling and Numerical Analysis of Science and Engineering Problems, 7, 3, i--ii, Sep. 2013
Scientific journal, English - Error Analysis of the DtN Finite Element Method for the Linear Water Wave Scattering Problem due to Stationary Bodies
Daisuke Koyama; Hideyuki Seto
Transactions of the Japan Society for Industrial and Applied Mathematics, The Japan Society for Industrial and Applied Mathematics, 22, 4, 341--382-382, Dec. 2012, Peer-reviwed, An a priori error estimate of the DtN (Drichlet-to-Neumann) finite element method for the linear water wave scattering problem due to bodies without forward speed in a 3D infinite water region with finite depth is established. The estimate accounts for the effects of truncation of infinite Fourier series representing the DtN boundary condition as well as of discretization of the finite element method. To estimate the error due to the truncation, several properties of the Hankel functions and the modihed Bessel functions are demonstrated.
Scientific journal, Japanese - A Parallel Schwarz Method for Multiple Scattering Problems
Daisuke Koyama
DOMAIN DECOMPOSITION METHODS IN SCIENCE AND ENGINEERING XIX, SPRINGER-VERLAG BERLIN, 78, 351-358, 2011, Peer-reviwed
International conference proceedings, English - Well-posedness of the Helmholtz problem with the multiple DtN boundary condition
Daisuke Koyama
Advances in Mathematical Sciences and Applications, 20, 2, 349--370-370, 2010, Peer-reviwed
Scientific journal, English - Superconvergence of a finite element method for the Webster equation
Xiong; Zhi Guang; Kako, Takashi; Koyama, Daisuke
Numer. Math. J. Chinese Univ., 32, 2, 106--117, 2010, Peer-reviwed
Scientific journal, English - Error estimates of the finite element method for the exterior Helmholtz problem with a modified DtN boundary condition
Daisuke Koyama
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, ELSEVIER SCIENCE BV, 232, 1, 109-121, Oct. 2009, Peer-reviwed, A priori error estimates in the H(1)- and L(2)-norms are established for the finite element method applied to the exterior Helmholtz problem, with modified Dirichlet-to-Neumann (MDtN) boundary condition. The error estimates include the effect of truncation of the MDtN boundary condition as well as that of discretization of the finite element method. The error estimate in the L(2)-norm is sharper than that obtained by the author [D. Koyama, Error estimates of the DtN finite element method for the exterior Helmholtz problem, J. Comput. Appl. Math. 200 (1) (2007) 21-31] for the truncated DtN boundary condition. (C) 2008 Elsevier B.V. All rights reserved.
Scientific journal, English - Error estimates of the DtN finite element method for the exterior Helmholtz problem
Daisuke Koyama
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, ELSEVIER SCIENCE BV, 200, 1, 21-31, Mar. 2007, Peer-reviwed, A priori error estimates are established for the DtN (Dirichlet-to-Neumann) finite element method applied to the exterior Helmholtz problem. The error estimates include the effect of truncation of the DtN boundary condition as well as that of the finite element discretization. A property of the Hankel functions which plays an important role in the proof of the error estimates is introduced. (c) 2005 Elsevier B.V. All rights reserved.
Scientific journal, English - Computational algorithm for the constrain matrix arising in a fictitious domain method
Daisuke Koyama
Transactions of the Japan Society for Industrial and Applied Mathematics, The Japan Society for Industrial and Applied Mathematics, 15, 4, 571-587, Dec. 2005, Peer-reviwed, A fictitious domain method via Lagrange multipliers for solving three-dimensional Dirichlet problems is considered. A computation algorithm for the constraint matrix in discrete problems of the arising saddle-point problem is presented, in which a triangulation algorithm for the intersection of a tetrahedron and a triangle plays an essential role. First such a triangulation algorithm is designed so that it does not generate any degenerate triangles on the assumption that the precision in computation is infinite. Next its simplified algorithm is presented; it can generate degenerate triangles even if it is implemented in precise arithmetic. These two algorithms are compared through numerical experiments.
Scientific journal, Japanese - Well-posedness of the wave equation with an artificial boundary condition
D. Koyama
Advances in Mathematical Sciences and Applications, 15, 2, 545-558, Oct. 2005, Peer-reviwed
Scientific journal, English - 外部Helmholtz問題で生じる線型方程式に対する前処理つきCOCG法の応用
柿原正伸; 小山大介; 藤野清次
日本計算工学会論文集, 日本計算工学会, No.20050022, 95-103, Jul. 2005, Peer-reviwed
Scientific journal, Japanese - A mixed-type finite element approximation for radiation problems using fictitious domain method
HM Nasir; T Kako; D Koyama
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, ELSEVIER SCIENCE BV, 152, 1-2, 377-392, Mar. 2003, Peer-reviwed, In the finite element approximation of the exterior Helmholtz problem, we propose an approximation method to implement the DtN mapping formulated as a pseudo-differential operator on a computational artificial boundary. The method is then combined with the fictitious domain method. Our method directly gives an approximation matrix for the sesqui-linear form for the DtN mapping. The eigenvalues of the approximation matrix are simplified to a closed form and can be computed efficiently by using a continued fraction formula. Solution outside the computational domain and the far-field solution can also be computed efficiently by expressing them as operations of pseudo-differential operators. An inner artificial DtN boundary condition is also implemented by our method. We prove the convergence of the solution of our method and compare the performance with the standard finite element approximation based on the Fourier series expansion of the DtN operator. The efficiency of our method is demonstrated through numerical examples. (C) 2002 Elsevier Science B.V. All rights reserved.
Scientific journal, English - A controllability method with an artificial boundary condition for the exterior Helmholtz problem
D Koyama
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, KINOKUNIYA CO LTD, 20, 1, 117-145, Feb. 2003, Peer-reviwed, The exterior Helmholtz problem is solved by a controllability method with a new artificial boundary condition for a time-periodic wave equation. The condition uses the Dirichlet-to-Neumann operator associated with the Helmholtz problem. A semi-discrete problem is derived for the time-periodic wave equation, and a necessary and sufficient condition is proved for the uniqueness of the discrete problem. A typical example where the condition is satisfied is shown. Some numerical examples are also presented.
Scientific journal, English - 3次元Helmholtz問題への仮想領域法の応用
小山大介
京都大学数理解析研究所研究集会「微分方程式の数値解法と線形計算」(発表2002.11.20), Nov. 2002
Japanese - An artificial boundary condition for the numerical computation of scattering waves
D. Koyama
Domain Decomposition Methods in Science and Engineering, Proceedings of 12th International Conference on Domain Decomposition Methods, Chiba, Japan, October 25-29, 1999, Edited by T. Chan, T. Kako, H. Kawarada and O. Pironneau, DDM.org, Printed in Japan, 401-409, 2001, Peer-reviwed
International conference proceedings, English - Finite element analysis for the eigenvalue problem of the linear water wave in a water region with a reentrant corner
Daisuke Koyama; Katsuhiko Tanimoto; Teruo Ushijima
Japan Journal of Industrial and Applied Mathematics, Kinokuniya Co. Ltd, 15, 3, 395-422, 1998, Peer-reviwed, We consider the eigenvalue problem of the linear water wave in a water region with a reentrant corner. When approximate solutions of the problem are obtained by means of standard finite element methods, it often happens that the rates of convergence for the approximate solutions are slow. To improve the behavior of the rates of convergence, we propose a numerical method. Our method is the following. Using a nonlocal boundary condition which is imposed on an artificial boundary, we reduce the original problem to a problem on a subdomain which has no reentrant corner. Then the finite element method is applied to the reduced problem in order to obtain approximate solutions. We state our theoretical results concerning the error estimates for the approximate eigenvalues and eigenvectors, and present some of our numerical results, which are consistent with the theoretical results.
Scientific journal, English - A finite element computation for the flow around a wing in 2-dimensional perfect fluid
T. Ushijima; D. Yokomatsu; D. Koyama
Proceedings of Third China-Japan Joint Seminar on Numerical Mathematics, held in Dalian, Chaina, August 26-30, 1996, Edited by Z.-C. Shi and M. Mori, Science Press, Beijing/New York,1998, 148-158, 1998
International conference proceedings, English
Books and other publications
Lectures, oral presentations, etc.
- An a priori difference estimate between the IP method and the HJ method for the biharmonic problem
小山大介
Oral presentation, Japanese, 日本数学会2022年度秋季総合分科会応用数学分科会, Domestic conference
15 Sep. 2022 - 重調和問題に対する内部ペナルティ法で生ずる行列の条件数の評価
小山大介
Oral presentation, Japanese, 日本数学会2021 年度秋季総合分科会応用数学分科会
17 Sep. 2021 - 重調和問題に対するある混合型非適合有限要素法への内部ペナルティ法の適用
小山大介
Oral presentation, Japanese, 日本数学会 ２０１８ 年会 応用数学分科会
20 Mar. 2018 - Hybrid discontinuous Galerkin methods for nearly incompressible elasticity problems
Daisuke Koyama
Public discourse, English, 東京大学 数値解析セミナー
28 Nov. 2017 - 板曲げ問題に対する内部ペナルティ法を用いた混合型有限要素法
小山大介
Oral presentation, Japanese, 日本応用数理学会 2017年度年会
08 Sep. 2017 - Volume locking effects in hybrid DGs for nearly incompressible elasticity
Daisuke Koyama
Others, English, College of Science DOMAS seminar Spring 2017 series, College of Science, Sultan Qaboos University
16 Mar. 2017 - 重調和方程式に対するある混合型有限要素スキームに基づくHDG法
小山大介
Oral presentation, Japanese, 日本応用数理学会 ２０１６年度年会, Domestic conference
12 Sep. 2016 - ハイブリッド型DGFEMで生ずる体積ロッキング現象について
小山 大介; 菊地 文雄; 伊原 翔
Oral presentation, Japanese, 日本応用数理学会2015年度年会
11 Sep. 2015 - A Locking-free Hybrid DGFEM for Nearly Incompressible Materials
Daisuke Koyama; Fumio Kikuchi; Sho Ihara
Oral presentation, English, 23rd International Conference on Domain Decomposition Methods
08 Jul. 2015 - On the robustness of a hybridized DGFEM for nearly incompressible elasticity
小山大介; 菊地文雄
Oral presentation, Japanese, 日本数学会2015年度年会応用数学分科会講演アブストラクト
24 Mar. 2015 - A locking-free hybrid DGFEM for linear elasticity
Daisuke Koyama
Oral presentation, English, 最適化・数値解析ワークショップ(2015), 劉雪峰，田中環, 新潟大学, Domestic conference
15 Feb. 2015 - ハイブリッド型DGFEMによる平面弾性問題の数値計算
小山大介; 菊地文雄
Oral presentation, Japanese, 日本応用数理学会2014年度年会 研究部会OS:科学技術計算と数値解析（２）
04 Sep. 2014 - 平面弾性問題に対するリフティング項付きハイブリッド型DGFEM
小山大介; 菊地文雄
Oral presentation, Japanese, 第10回 日本応用数理学会 研究部会連合発表会 科学技術計算と数値解析 研究部会
19 Mar. 2014 - 円外領域におけるHelmholtz問題に対する最適化Schwarz法
小山大介
Others, Japanese, RIMS研究集会「応用数理と計算科学における理論と応用の融合」, RIMS研究集会「応用数理と計算科学における理論と応用の融合」
Oct. 2013 - An Optimized Schwarz Method for Exterior Helmholtz Problems
Daisuke Koyama
Others, English, 22nd International Conference on Domain Decomposition Methods, 22nd International Conference on Domain Decomposition Methods
Sep. 2013 - Korn's inequality for a hybridized discontinuous Galerkin FEM with lifting operator
小山大介; 菊地文雄
Oral presentation, Japanese, 日本数学会2013年度秋季総合分科会 応用数学分科会講演アブストラクト(発表2013.9.27),日本数学会2013年度秋季総合分科会 応用数学分科会
Sep. 2013 - An optimized Schwarz method for acoustic radiation problems
Daisuke Koyama
Oral presentation, Japanese, 日本数学会,2012年度秋季総合分科会 応用数学分科会
Sep. 2012 - 多重DtN有限要素法の事前誤差評価
小山大介
Oral presentation, Japanese, 日本数学会2009年度秋季総合分科会 応用数学分科会講演アブストラクト(発表2009.9.27)
Sep. 2009 - A parallel algorithm for multiple scattering problems
Daisuke KOYAMA
Others, English, The 19th International Conference on Domain Decomposition Methods, The 19th International Conference on Domain Decomposition Methods
Aug. 2009 - 多重DtN境界条件が課されたHelmholtz問題の一意可解性
小山大介
Others, Japanese, 第4回「計算科学研究ステーション」研究集会, 電気通信大学計算科学研究ステーション
Mar. 2009 - 船のまわりの水面波動問題に対するDtN有限要素法の事前誤差評価
小山大介; 瀬戸秀幸
Oral presentation, Japanese, 日本応用数理学会 2008年度年会 講演予稿集,2008年度日本応用数理学会年会
Sep. 2008 - 船のまわりの水面波動問題に対するDtN有限要素法の事前誤差評価の導出について
小山大介
Others, Japanese, 第3回「計算科学研究ステーション」研究集会, 電気通信大学計算科学研究ステーション
Mar. 2008 - ３次元水面波動問題に対するDtN有限要素法の事前誤差評価
小山大介; 瀬戸秀幸
Oral presentation, Japanese, 日本応用数理学会 2007年度年会講演予稿集,日本応用数理学会 2007年度年会
Sep. 2007 - 無限領域における水面波動問題に対するDtN有限要素法
Daisuke Koyama; Hideyuki Seto
Others, Japanese, 第２回「計算科学研究ステーション」研究集会, 電気通信大学 計算科学研究ステーション
Mar. 2007 - 外部Helmholtz問題に対する修正DtN境界条件を用いた有限要素法の誤差評価
小山大介
Others, Japanese, 「計算科学研究ステーション」研究集会, 電気通信大学計算科学研究ステーション
Mar. 2006 - 仮想領域法において生ずる制約行列の計算法に関する一考察
小山大介
Oral presentation, Japanese, 日本応用数理学会,日本応用数理学会2005年度年会講演予稿集
Sep. 2005 - Helmholtz 方程式の波数に応じたCOCG法の前処理について
柿原正伸; 小山大介; 藤野清次
Oral presentation, Japanese, 日本応用数理学会2004年度年会講演予稿集
Sep. 2004 - 外部 Helmholtz 問題に適用した DtN 有限要素法に対する誤差解析
小山大介
Oral presentation, Japanese, 日本応用数理学会2004年度年会講演予稿集
Sep. 2004 - 外部 Helmholtz 問題に対する DtN 有限要素法の事前誤差評価
小山大介
Oral presentation, Japanese, 日本数学会2004年度秋季総合分科会 応用数学分科会講演アブストラクト
Sep. 2004 - Application of a fictitious domain method to 3D Helmholtz problems
D. Koyama
Others, English, 京都大学数理解析研究所講究録
May 2003 - 3次元 Helmholtz 問題の仮想領域法によって得られる近似解の収束について
小山大介
Oral presentation, Japanese, 日本数学会2002年度秋季総合分科会 応用数学分科会講演アブストラクト(発表2002.9.29)
Sep. 2002 - 3次元外部 Helmholtz 問題に対する数値計算法
小山大介
Oral presentation, Japanese, 第51回理論応用力学講演会 講演論文集 NCTAM 2002(発表2002.1.24).
Jan. 2002 - Helmholtz 方程式の3次元外部問題に対する数値計算
小山大介; 牛島照夫
Oral presentation, Japanese, 日本応用数理学会2001年度年会講演予稿集(発表2001.10.8)
Oct. 2001 - 波動方程式に対するある人工境界条件とその応用について
小山大介
Public discourse, Japanese, 京都大学偏微分方程式火曜セミナー
30 May 2000 - A time-dependent numerical algorithm for the Helmholtz equation
小山大介
Others, English, RIMS研究集会「偏微分方程式の数値解法とその周辺」 (数理解析研究所講究録1145)，（発表1999.11.17）
Apr. 2000 - Helmholtz方程式に対するある時間依存型数値解法の数学的考察
小山大介
Oral presentation, Japanese, 日本応用数理学会1999年度年会講演予稿集，(発表1999.10.5)
Oct. 1999 - An artificial boundary condition for the numerical computation of scattering waves
KOYAMA, Daisuke
Oral presentation, English, 12th International Conference on Domain Decomposition Methods（DD12），Book of Abstracts , held in Chiba，October 25-29，1999
Oct. 1999 - Helmholtz方程式のある数値解法に対する人工境界条件
小山大介
Oral presentation, Japanese, 日本応用数理学会平成10年度年会講演予稿集，(1998.9.13)
13 Sep. 1998 - ポアッソンソンバーを利用したヘルムホルツ方程式のある数値解法
小山大介
Others, Japanese, 文部省科学研究費基盤研究（B）展開研究「ポアッソンソルバーの現代化」研究打ち合わせ会，(1998.9.17)
Sep. 1998 - Helmholtz方程式に対する領域分割法
小山大介
Others, Japanese, 統計数理研究所共同研究リポート110 「核融合研究における数値解析手法と最適化」
Mar. 1998 - Klein-Gordon 方程式に対する人工境界条件
小山大介
Oral presentation, Japanese, 日本応用数理学会平成９年度年会講演予稿集， (発表1997.10.2)
Oct. 1997 - 非有界領域における波動方程式の有限要素計算
小山大介
Others, Japanese, 1996 年度ＭＨＤ研究集会「核融合研究における数値解析手法と最適化」 (発表1996.11.26)
Nov. 1996 - ３次元軸対称外部領域におけるポアッソン方程式の有限要素解析
小山大介; 牛島照夫
Oral presentation, Japanese, 日本応用数理学会平成８年度年会講演予稿集，(発表1996.9.26)
Sep. 1996 - 軸対称外部領域におけるポアッソン方程式の有限要素計算
小山大介; 牛島照夫
Others, Japanese, 応用数学合同研究集会報告集， (発表1995.12.19)
Dec. 1995 - 翼まわり流れに対するクッタの条件の数値計算におけるとりあつかい
牛島照夫; 横松大作; 小山大介
Others, Japanese, 応用数学合同研究集会報告集， (発表1995.12.21)
Dec. 1995 - 柱状領域におけるポアッソン方程式に対する非局所境界条件を用いた領域簡約法
小山大介; 牛島照夫
Others, Japanese, 1995 年度ＭＨＤ研究集会「ＭＨＤ数理モデルによる核融合計算と最適設計」 (発表1995.11.22)
Nov. 1995 - ３次元ポアッソン方程式の領域分割計算―非局所境界条件の適用―
小山大介; 牛島照夫
Oral presentation, Japanese, 日本応用数理学会平成７年度年会講演予稿集， (発表1995.9.19)
Sep. 1995 - A finite element method for 2-dimensional potential flow around a body with fractional order error estimate
USHIJIMA; Teruo, KOYAMA; Daisuke, YAN; Li-xiang
Others, English, International Congress on Industrial and Applied Mathematics 95 (発表1995.7.3)
Jul. 1995 - A numerical method for 2-D potential flow around a body with fractional order error estimate
USHIJIMA; Teruo, KOYAMA; Daisuke, YAN; Li-xiang
Others, English, International Conference on Parallel Algorithm for Scientific and Engineering Computations, (発表1995.5.24)
May 1995 - スチェクロ固有値問題と領域分割法
牛島照夫; 小山大介; 横松大作; 顔立祥
Others, Japanese, 応用数学合同研究集会報告集， (発表1994.12.21)
Dec. 1994 - 凹角を持つ水域における水の波 線形固有値問題に対する一数値計算法 ―非局所境界条件の導入―
小山大介; 谷本勝彦; 牛島照夫
Others, Japanese, 統計数理研究所共同研究リポート７２「ＭＨＤ数理モデ ルによる核融合計算と最適設計」， (発表1994.11.25)
Nov. 1994 - 水の波 線形固有値問題の有限要素近似における角の取り扱いについて
小山大介; 谷本勝彦; 牛島照夫
Oral presentation, Japanese, 日本応用数理学会平成６年度年会講演予稿集， (発表1994.9.20)
Sep. 1994 - 水の波 線形固有値問題に対する角の特異性を考慮した有限要素解析
小山大介; 谷本勝彦; 牛島照夫
Others, Japanese, 研究集会「偏微分方程式 数値解析の最近の発展」 (発表1994.7.13)
Jul. 1994 - 凹角のある水域における水の波 線形固有値問題の有限要素解析
小山大介; 谷本勝彦; 牛島照夫
Others, Japanese, 第２３回数値解析シンポジウム講演予稿集，(発表1994.6.8)
Jun. 1994 - スチェクロフ固有値問題と数値計算
牛島照夫; 小山大介; 横松大作; 谷本勝彦
Others, Japanese, 応用数学合同研究集会 報告集, (発表1993.12 pp.149--154.21)
Dec. 1993 - ラプラス方程式の有限要素近似における角の取り扱いについて
小山大介; 加古孝; 牛島照夫
Oral presentation, Japanese, 日本数学会1993年度年会応用数学分科会 講演アブストラクト, (発表1993.3.28)
Mar. 1993 - 角を持つ領域におけるラプラス方程式の一数値計算法
小山大介; 加古孝; 牛島照夫
Others, Japanese, 応用数学合同研究集会 報告集, (発表1992.12.24)
Dec. 1992 - 角を持つ領域におけるラプラス方程式の一数値解法
小山大介; 加古孝; 牛島照夫
Others, Japanese, 核融合科学研究所共同研究集会 「MHD数値計算の基礎研究」講演論文集, (発表1992.11.25)
Nov. 1992
Courses
- Theory of Analytic Functions
Apr. 2018 - Present
Tokyo University of Science - Numerical Mathematics 1
Apr. 2018 - Present
Tokyo University of Science - 有限要素法
Oct. 2008 - Mar. 2014
早稲田大学大学院基幹理工学研究科 - 情報領域演習第一
電気通信大学 - 情報・通信演習1
電気通信大学 - 情報数理工学実験第一・コンピュータサイエンス実験第一
電気通信大学 - 情報領域演習第二
The University of Electro-Communications - 総合コミュニケーション科学
The University of Electro-Communications - 先端工学基礎課程 情報・メディア・通信（ＩＭＣ）輪講A
The University of Electro-Communications - 先端工学基礎課程輪講
電気通信大学 - 情報工学演習第一
The University of Electro-Communications - 情報工学演習第二
The University of Electro-Communications
Research Themes
- 非適合要素を用いた混合型有限要素法への内部ペナルティ法の適用
01 Apr. 2019 - 31 Mar. 2022 - Study on numerical methods of wave propagation phenomena and its applications to information and energy transmission problems
KAKO Takashi; IMAMURA Toshiyuki; KOYAMA Daisuke
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), Transmissions of information or energy can be performed by use of the wave propagation phenomena. In this study we treated the information transmission by spoken language and electromagnetic radiation with various frequencies from antennas. We developed the methods to reduce the problem in unbounded region into the one in a bounded region using two techniques and then discretized the problems by FEM or FDM. We also developed similar methods for energy propagation phenomena such as those in elasticity or in electromagnetism and applied the method to several problems in seismology or electromagnetic wave heating phenomena in MRI., 21540116
2009 - 2011 - 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 - Study of Numerical Methods for Wave Propagation Phenomena in Unbounded Region and its Applications
KAKO Takashi; USHIJIMA Teruo; YOSHIDA Toshinobu; KOYAMA Daisuke; ZHANG Shao-liang; SUITO 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), The purpose of this research project is to develop the approximation methods for wave propagation problems in unbounded region and as its applications we study the numerical simulation of voice generation. We formulate the problem as the exterior Helmholtz equation, and reduce the problem to the one in a bounded region by introducing the artificial boundary condition on an artificial boundary. We developed the numerical methods for this problem based on the finite element discretization method and study the application problems including the voice generation. The results of the head investigator Kako are the followings. He found out the variational formula of the complex eigenvalues with respect to the deformation of vocal tract. The eigenvalues are related to the formants of frequency response function that is important for voice generation. He then developed the algorithm for designing the shape of vocal tract by use of the variational formula, and validated the algorithm through numerical simulations. He also studied the application of the Finite Difference Time Domain method to the acoustic problem and obtained several basic results. For the voice problem, Yoshida developed the method to obtain the mapping from the articulation parameters to the phonetic transmission characteristics by use of the neural networks. Suito studied the shape optimization problem for minimizing the reflection of the wave propagating in a tubular region with spatially changing impedance parameters and obtained unusual numerical results. Related to the numerical methods for the wave problem, Koyama studied the three dimensional Helmholtz problem by use of the fictitious domain method and derived the a priori error estimates for the approximation, and investigated the validity by some numerical experiences. Ushijima studied the Helmholtz problem by the collocation method based on the fundamental solutions and obtained a sufficient condition for the exponential convergence of the approximate solution and tried to validate of the theoretical results by multi-precision arithmetic computation. As for the numerical methods for solving large linear equations appearing in the application problems including the Helmholtz equation, Zhang studied the fast and efficient iteration methods. Imamura developed the automatic tuning techniques with high actuary and stability in the implementation for the parallel computation methods for the large linear systems., 14540106
2002 - 2004 - Finite Element Methods for Huge Domain and Domain Decomposition Methods with Related Topics
USHIJIMA Teruo; TAKEDA Tatsuoki; KAKO Takashi; YAMAMOTO Nobito; TABATA Masahisa; FUJIMA Shoiti
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, The University of Electro-Communications, Grant-in-Aid for Scientific Research (B), 1.Main Results Obtained in the Joint Works around the Head Investigator : Demonstration of the possibility for determination of the mapping of wing through finite element computation. Error estimate for the solutions of FSM(=Fundamental Solution Method)approximate problems to reduced wave problems in a domain exterior to a disc. Confirmation of the effectiveness of an FEM-FSM combined method applied to 2D exterior reduced wave problem, and its application to linear water wave problems in an exterior water region with constant water depth, where the abbreviation FEM stands for Finite Element Method. 2.Remarkable Progress Obtained in the Works by Investigators : (1)Establishment of a method solving linear systems determining discrete vector potentials(by J.Watanabe). (2)Application of multi layer neural networks to various types of inverse problems(in computer tomography, in data assimilation, in parameter evaluation, in time series prediction)(by T.Takeda). (3)Application of finite element analysis for stationary wave transmission phenomena in unbounded domains to the problem of voice generation with successfully captured formants(by T.Kako). (4)Development of a new method for determination of upper bounds for error estimation constants appeared in finite element computation of Poisson equations in non-convex polygonal domains(by N.Yamamoto). (5)Theoretical study on the effect of stationary non homogeneous spatial structure to qualitative properties of solutions in the case of non-linear reaction-diffusion equations through numerical simulation and asymptotic analysis(by K.Nakamura). (6)Mathematical and numerically experimental analysis of characteristic futures of approximation methods for various types of partial differential equations obtained through Runge-Kutta type formulas(by T.Koto). (7)Overcome of the difficulties in finite element numerical solution methods in flow problems through upwinding technique and approximation way of characteristic curves(by M.Tabata). (8)Finite element analysis of non-stationary field of eddy current based on moving coordinate system(by H.Kanayama). (9)Flux free finite element method applied to two phase fluid problems(by K Ohmori). (10)Parallel computation through mortar domain decomposition method(by S.Fujima). (11)Purely theoretical analysis and numerical analysis of numerical instability problems arising with association of steep change of phenomena, in such as shock waves(by H.aiso). 3.Invitation of Foreign Cooperative Researcher : (1)Professor Han Hou-de of Applied Mathematics Department, Tsinghua University, Beijing, China from July 26 to August 16,2002. (2)Professor Yu De-hao of Institute of Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, China from September 12 to October 3,2004. 4.Research Meetings : (1)Yokohama Research Meeting was held an KKR Hotel Port Pear Yokohama from January 8 to 10,2003. (2)Chofu Research Meeting was held at the University of Electro-Communications from February 19 to 20,2004. (3)Chofu Symposium 2005 was held at the University of Electro-Communication from February 17 to 19,2005., 14340031
2002 - 2004 - CT image reconstruction method for small amount of projection data and differential equation solution method by neural network
TAKEDA Tatsuoki; WATANABE Jiro; KAKO Takashi; USHIJIMA Teruo; FUKUHARA Makoto; KOYAMA Daisuke
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), By using squared residuals of a differential equation for the object function of a neural network we can solve the differential equation as the network itself becomes the solution after training. We investigated this method by applying it to Navier-Stokes equation, Poisson equation, Lorenz equation and so on, and obtained satisfactory results. We found that similar method is applied to CT image reconstruction problem with small amount of projection data. We applied it to model CT image reconstruction problem where an integral equation is solved and obtained satisfactory results. By generalizing the form of the object function this method can be applied to very wide range of problems. Defining the object function by the squared residuals of differential equations, integral equations, and algebraic equations multiplied by some appropriate penalty coefficients various kinds of problems can be solved owing to the excellent expressivity of the multi-layer neural network comparatively easily. One of the important application is the solution of data assimilation problem which is very important in the field of the meteorological and oceanological numerical simulations. We have also performed model numerical experiment of the data assimilation and obtained satisfactory results. This method is also applicable to the generalized Abel inversion which appears in various scientific and engineering researches. For comparing the new method with the conventional standard methods we studied these methods. As the mathematical basis of the CT image reconstruction we studied the inverse Radon transform. As for the decay Radon transform we derived an inverse formula, which we proved mathematically and numerically. We studied the Poisson equation and the Helmholtz equation in the infinite domain. We introduced an artificial boundary condition and studied the validity of the condition mathematically and numerically., 11650065
1999 - 2000 - Finite Element Method for Huge Domains and Related Topics
USHIJIMA Teruo; KATO Toshiyuki; KATO Takashi; TAKEDA Tatsunoki; FUKUHARA Makoto; KOYAMA Daisuke
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), 1. Main Results Obtained in the Joint Works around the Head Investigator : (1) Discretization method through charge simulation method for Steklov operator associated with Laplace problems in exterior domain of a disc. An FEM-CSM (Finite Element Method - Charge Simulation Method) combined method for 2D exterior Laplace problems was proposed in 1998 and its mathematical analysis has been studied during whole the term of project. Relation between continuous and discrete fourier coefficients, which is a key for the study, has been investigated. (2) Confirmation of the effectiveness of the FEM-FSM combined method through numerical computation (jointly with Masuda, S.). (3) Determination of the conformal mapping of wing through precise finite element computation for the potential function and stream function. (4) Proposal of the fundamental solution method (FSM, in short) for the determination of Steklov operator associated with the reduced wave problems in exterior domain of a disc. 2. Remarkable Progress Obtained in the Works by Investigators : (1) Numerical method for partial differential equations through neural network. Boundary condition fitting with the use of shape factor in the form of approximate function. Neural network solver for MHD equilibrium equation and Napier-Stokes equation. Acceleration of the neural net solution method with the use of Gauss-Newton method. (Obtained by Takeda and Fukuhara) (2) An iterative method for Helmholtz equation in domain decomposition computation. Numerical analysis and computation of the wave propagation in a bounded domain with open boundary portion connected with exterior infinite region. Proof of stability and convergence for Newmark's method for second order problem (obtained by Kako, T.). (3) Stability analysis for Runge-Kutta method through linear system theory. Stability analysis for Runge-Kutta method applied to delay-differential equations (obtained by Koto). (4) Mathematical justification for a wave equation method solving exterior Helmholtz problems. Proposal and justification of a new artificial boundary condition to the wave equation solver for exterior Helmholtz problem (obtained by Koyama). 3. Keeping the UEC-NA-Seminar (University of Electro-Communications Numerical Analysis Seminar). In each academic year of 1998 and 1999, 14 seminars were held in the Friday morning, generally. Within seminars, talks given by Professor Kamitani, A. of Yamagata University, Professor Sakajo, T. of Nagoya University, Professor Yamamoto, N. of then Kyushu university, Professor Matsuo, T. of Nagoya University, Professor Kanayama, H. of Kyushu University were supported by this grant. In addition to these regular seminar, special one-day and two-day workshops were held to discuss the subject of the project and related topics., 10640108
1998 - 1999 - 振動・波動現象の数理解析と数値解析
加古 孝; 小山 大介; 大西 勇; 田吉 隆夫; 牛島 照夫; 渡辺 二郎
日本学術振興会, 科学研究費助成事業, 電気通信大学, 一般研究(C), 本研究では、磁気流体波、音波、弾性波などの振動・波動現象を始めとする自然現象を、偏微分方程式の初期値境界値問題あるいはスペクトル固有値問題として定式化し、有限要素法を用いた数値計算アルゴリズムを与え、その妥当性の数学的解析と実際の数値計算結果の検討を行うことを研究目標とした。 研究を進めるに当たっては、研究者の個別研究に基礎をおきつつ、研究の相互交流にも力を注いだ。特に、週一開催された「数値解析研究会」や統計数理研究所主催の「MHD研究会」を始めとする年間を通しての各種の研究会での相互交流につとめた。以下、個別の研究実績について述べる。 1.抵抗性線形化磁気流体作用素のスペクトル近似と、系の時間発展問題の関連につき研究し、その過程でNewmarkのβ法について興味有る事実を見いだした(加古、千葉)。 2.構造体と音場の連成振動における固有値問題の解析的性質の解明と、それを利用した有限要素近似を研究し、近似スキームの収束証明と誤差評価を得た(加古、田吉、DENG Li)。 3.散乱問題の高次放射条件を利用した数値解析手法の研究を進め、領域分割法による反復計算法の有効性を理論的に明らかにすると共に、有限要素法による近似計算を実行し有効性を確認した(加古、劉)。 4.無限領域等の特異性を持つ領域における数値計算法の開発を行い、完全流体における一様流中の物体回り流れの数値計算法を考案し、流体中の振動・波動計算の基礎を築いた(小山、牛島)。 5.移流拡散問題の差分近似の安定性と近似誤差評価を研究し、散逸と分散が同時に存在する系の数値計算法に対し新たな知見を加えた(名古屋、牛島)。 6.計算機トモグラフィーにおけるラドン変換の、フィルター補正逆投影法で高周波成分を考慮した新しい計算法を考案し、数値実験と誤差解析を行った(室屋、渡辺: Numerical analysis of a reconstruction algorithm in computed tomography, Journal of Inverse and Ill posed Problem に投稿中)。 7.高分子二相分離問題の数学的解析に取り組み、モデルの妥当性を明らかにした(大西)。, 07640286
1995 - 1995 - 微分方程式の解の構造の解析とその応用
加古 孝; 小山 大介; 小藤 俊幸; 海津 聡; 牛島 照夫; 渡辺 二郎
日本学術振興会, 科学研究費助成事業, 電気通信大学, 一般研究(C), 本研究では、微分方程式の解の構造の解析と、そこで得られる情報を適切に考慮した数値計算法の開発と妥当性の数学的検証に取り組み、いくつかの成果が得られた。研究を進めるに当たっては、各分担者が独自に分担課題の研究を進めると共に、関係する研究者との研究連絡、研究交流を行った。特に、電気通信大学で定期的に開催された数値解析研究会での研究交流と、日中数値数学セミナーにおける、中国からの参加者を交えた研究交流に力を注いだ。以下、個別の研究実績について述べる。 1.磁気流体作用素のスペクトルの絶対連続性についての性質と抵抗性作用素の特異極限について、作用素解析、WKB法、有限要素計算の各方向から研究を進めた(千葉文浩、加古孝)。また、物体による散乱問題の高次放射条件を用いた有限要素計算を行い有効性の確認を行った(劉小進、加古孝)。さらに、音場・構造体連成系において現れる標準的ではない固有値問題の数理解析と、有限要素計算法の定式化と数値解析を行った(DENG Li、加古孝)。 2.角(カド)のある2次元図形の定義関数を、ラドン変換から再構成する問題で、計算値の収束と角(カド)における角(カク)の大きさの関係を明らかにした(渡辺二郎、室屋泰三)。 3.水の表面波の線形化解析におけるモード解析手法の妥当性を明らかにした(牛島照夫、小山大介)。スチュクロフ作用素を利用した計算法と数値解析で成果を得た(牛島照夫、小山大介、加古孝)。移流拡散問題に対し、ε-安定性の概念を導入し、その有効性を検証した(牛島照夫、名古屋靖一郎)。 4.非圧縮性粘性流体の分岐問題に係わる固有値問題の定式化と有限要素計算を実行した(海津聡、富森叡)。 5.遅延連立微分方程式に対する陰的ルンゲ・クッタ法の安定性を解析し、新たな知見を得た(小藤俊幸)。, 06640295
1994 - 1994
