均質化法の数値解析
キーワード：均質化法, 数値解析
2020.04.

粒子型解法の数値解析
キーワード：粒子法, 誤差解析
2011.04.

領域分割法を用いた電磁場問題の数値解析
キーワード：電磁場問題, 領域分割法, 有限要素法, 誤差解析
1999.04.

粘弾性流れ問題の数値解析
キーワード：粘弾性流れ問題, 有限要素法, 誤差解析
2009.04.

熱対流問題の数値解析とガラス溶融炉への応用
キーワード：熱対流問題, 有限要素法, 誤差解析, ガラス溶融炉
2002.03.

Navier-Stokes方程式の数値解析と抗力・揚力の数値計算への応用
キーワード：Navier-Stokes方程式, 有限要素法, 誤差解析, 抗力・揚力
1997.07.

移動境界問題の数値解析
キーワード：移動境界問題, 誤差評価
1994.04.

光の干渉・散乱問題の数値解析
キーワード：Maxwell方程式, Helmholtz方程式, 有限要素法, DtN写像, 誤差解析, ホログラフィー
2007.04.

Modeling and Simulation of Hierarchical and Heterogeneous Flow Systems with Applications to Materials Science (A3 Foresight Program)
2014.08～2019.03, 代表者：NISHIURA, Yasumasa, Tohoku University, Tohoku University (Japan), Peking University (China), Inha University (Korea).

ポストペタスケールシミュレーションのための階層分割型数値解法ライブラリ開発 (戦略的創造研究推進事業CREST ポストペタスケール高性能計算に資するシステムソフトウェア技術の創出)
2011.10～2016.03, 代表者：塩谷 隆二, 東洋大学, 東洋大学, 名古屋大学
地球シミュレータ, 次世代スパコン(京)などのスーパーコンピュータ上で超大規模な解析を可能とする, 汎用並列有限要素法解析システムADVENTURE（オープンソースソフトウェア）の開発及び公開を通し培ってきた, 大規模解析に極めて有効な手法である階層型領域分割法を, ポストペタスケールに向け, 大規模データ処理を扱うメッシュ生成や可視化処理部分に拡張することにより革新的技術開発を行い, 実用的超大規模シミュレーションの実現を目指します..

災害影響評価のための大規模マルチフィジックス・シミュレータの性能・機能強化 (学際大規模情報基盤共同利用・共同研究拠点)
2013.04～2015.03, 代表者：田上大助, 九州大学, 九州大学, 名古屋大学
数値シミュレーションによる自然災害の影響評価に基づいた防災・減災対策に寄与するために，高精度・高効率な大規模マルチフィジックス・シミュレータの構築を目指す．今年度は，地震および地震に伴って生じる津波が構造物に与える影響に着目し，波動・流れ・弾塑性の連成現象に対する高精度な数理モデル･シミュレーション手法の構築, 次世代並列計算機アーキテクチャにおける高効率な実装手法の確立の2点に重点を置く． .

災害影響評価のための大規模マルチフィジックス・シミュレータの高度・高性能化 (学際大規模情報基盤共同利用・共同研究拠点)
2012.04～2013.03, 代表者：田上大助, 九州大学, 九州大学, 名古屋大学
数値シミュレーションによる自然災害の影響評価に基づいた防災・減災対策に寄与するために，高精度・高効率な大規模マルチフィジックス・シミュレータの構築を目指す．今年度は，地震および地震に伴って生じる津波が構造物に与える影響に着目し，波動・流れ・弾塑性の連成現象に対する高精度な数理モデル･シミュレーション手法の構築, 次世代並列計算機アーキテクチャにおける高効率な実装手法の確立の2点に重点を置く． .

災害影響評価のための大規模マルチフィジックス・シミュレータの構築 (学際大規模情報基盤共同利用・共同研究拠点)
2011.04～2012.03, 代表者：田上大助, 九州大学, 九州大学, 名古屋大学
数値シミュレーションによる自然災害の影響評価に基づいた防災・減災対策に寄与するために，高精度・高効率な大規模マルチフィジックス・シミュレータの構築を目指す．今年度は，地震および地震に伴って生じる津波が構造物に与える影響に着目し，波動・流れ・弾塑性の連成現象に対する高精度な数理モデル･シミュレーション手法の構築, 次世代並列計算機アーキテクチャにおける高効率な実装手法の確立の2点に重点を置く． .

主要著書

主要原著論文

1.	TAGAMI, Daisuke, Numerical Stability of a Semi-Implicit Characteristic Time Integration of the Generalized Particle Method for Flow Problems, Proc. the 15th SPHERIC Int. Workshop, 2021.06.
2.	TAGAMI, Daisuke, Numerical analysis of the Navier–Stokes equations by a semi-implicit characteristic generalized particle methods, Proc. the 14th SPHERIC Int. Workshop, 53-58, 2019.06.
3.	IMOTO, Yusuke, TAGAMI, Daisuke, Truncation error estimates of approximate differential operators of a particle method based on the Voronoi decomposition, JSIAM Letters, 10.14495/jsiaml.9.69, 9, 69-72, 2017.10.
4.	TAGAMI, Daisuke, Mathematical analysis of characteristic generalized particle methods for convection-diffusion equations, Proc. the 12th SPHERIC Int. Workshop, 32-37, 2017.06.
5.	IMOTO, Yusuke, TAGAMI, Daisuke, A truncation error estimate of the interpolant of a particle method based on the Voronoi decomposition, JSIAM Letters, 10.14495/jsiaml.8.29, 8, 29-32, 2016.02.
6.	Shin-ichiro SUGIMOTO, Daisuke TAGAMI, Masao OGINO, Amane TAKEI, Hiroshi KANAYAMA, Improvement of convergence in time-harmonic Eddy current analysis with hierarchical domain decomposition method, Transaction of the Japan Society for Simulation Technology, 10.11308/tjsst.7.11, 7, 1, 11-17, 2015.04.
7.	TAGAMI, Daisuke and TABATA, Masahisa, Numerical computations of a melting glass convection in the furnace, Proceedings of The Seventh China-Japan Seminar on Numerical Mathematics, 149-160, 2006.12.
8.	TABATA, Masahisa and TAGAMI, Daisuke, Error estimates of finite element methods for nonstationary thermal convection problems with temperature-dependent coefficients, Numerische Mathematik, 10.1007/s00211-005-0589-2, 100, 2, 351-372, 2005.04.
9.	TAGAMI, Daisuke and ITOH, Hajime, A finite element analysis of thermal convection problems with the Joule heat, Japan Journal of Industrial and Applied Mathematics, 20, 2, 193-210, 2003.06.
10.	TABATA, Masahisa and TAGAMI, Daisuke, Error estimates for finite element approximations of drag and lift in nonstationary Navier-Stokes flows, Japan Journal of Industrial and Applied Mathematics, 17, 3, 371-389, 2000.10.
11.	TABATA, Masahisa and TAGAMI, Daisuke, A finite element analysis of a linearized problem of the Navier-Stokes equations with surface tension, SIAM Journal on Numerical Analysis, 10.1137/S0036142997329098, 38, 1, 40-57, 2000.06.

主要総説, 論評, 解説, 書評, 報告書等

主要学会発表等

1.	TAGAMI, Daisuke, Numerical Analysis of the Viscoelastic Flow Problems by a Semi-Implicit Characteristic Generalized Particle Methods, The 16th SPHERIC International Workshop (SPHERIC 2023), 2023.06.
2.	TAGAMI, Daisuke, Numerical Stability of a Semi-Implicit Characteristic Time Integration of the Generalized Particle Method for Flow Problems, The 15th SPHERIC International Workshop (SPHERIC 2021), 2021.06.
3.	TAGAMI, Daisuke, Numerical Analysis of a Balancing Domain Decomposition Method for Perturbed Magnetostatic Problems, 14th WCCM & ECCOMAS Conference 2020, 2021.01.
4.	TAGAMI, Daisuke, Numerical Analysis of the Navier--Stokes Equations by a Semi-Implicit Characteristic Generalized Particle Methods, The 14th SPHERIC International Workshop (SPHERIC 2019), 2019.06.
5.	TAGAMI, Daisuke, Numerical analysis of a generalized particle method for the convection-diffusion equation, International Congress of Mathematicians 2018 (ICM2018), 2018.08, Mathematical analysis of a characteristic generalized particle method is considered for convection-diffusion equations. The characteristic generalized particle method can keep particle distribusions at every time steps satisfying the regularity condition for unique solvability, stablities, and convergence. Therefore, error estimates of the characteristic generalized particle method are obtained. Moreover, some numerical results are shown..
6.	TAGAMI, Daisuke, Numerical analysis of thermal convection problems and its application to glass melting furnaces, The 7th China-Japan Joint Seminar for Computational Mathematics and Scientific Computing, 2004.08.
7.	TAGAMI, Daisuke and TABATA, Masahisa, A finite element computation of heat convection problems in the glass production furnace, International Workshops on Advances in Computational Mechanics, 2004.11.
8.	田上大助, 有限要素スキームを用いた流れ問題の数値計算と適用事例, 日本応用数理学会 3部会連携「応用数理セミナー」, 2009.12.
9.	田上大助, 流れ問題の有限要素計算と誤差評価, 明治大学グローバルCOEプログラム 現象数理学の形成と発展, 第8回現象数理若手シンポジウム ``航空機の数理 ---流体モデルと数値解析---'', 2011.01.
10.	田上 大助, 有限要素法を用いた流れ問題の数値解析 ---誤差評価から並列計算まで---, 日本数学会2012年度 秋季総合分科会 応用数学分科会, 2012.09.
11.	田上 大助 , 流れ問題に対する粒子型解法の数値解析へ向けて , CoMFoS14 , 2014.10.
12.	田上 大助, Oldroyd-B モデルを用いた粘弾性流れ問題に対する圧力安定化有限要素法に関するいくつかの考察, 京都大学数理解析 研究所研究集会 “現象解明に向けた 数値解析学の新展開”, 2015.11.
13.	TAGAMI, Daisuke, Error estimates of a generalized particle-based method for elliptic boundary value problems, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2015), 2015.09.
14.	TAGAMI, Daisuke, Finite element analysis of viscoelastic flow problems with application incorporating the Oldroyd-B model, IMI–La Trobe Joint Conference: Mathematics for Materials Science and Processing, 2016.02.
15.	TAGAMI, Daisuke, Some investigations into finite element methods for viscoelastic flow problems governed by Oldroyd-B models, Mathematical Analysis of Continuum Mechanics and Industrial Applications, 2015.11.
16.	田上 大助, 数値解析学から見た計算手法の高精度化・高効率化の取り組み , および物質・材料との連携展開, MI2 (情報統合型質・材料開発) と数学連携による新展開ワークショップ, 2016.02.
17.	TAGAMI, Daisuke, Some investigations of a generalized particle method for convection-diffusion equations, VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), 2016.06, A generalized particle method is considered for convection-diffusion equations. In Imoto--Tagami (2015), the generalized particle method has been introduced as a class of particle methods, which can describes Smoothed Particle Hydrodynamics (SPH), Moving Particle Semi-implicit (MPS), and others, and the truncation error estimate has been established. Moreover, in Imoto--Tagami (2015), error estimates of the generalized particle method for the Poisson equation and the heat equation have been established. Our goal is to establish of mathematical frameworks of particle methods, and this paper is regarded as the next step toward our goal. At this step, the particle motions is considered, which play a key role in practical computational fluid dynamics with particle methods. In general, the particle motions cause particle distributions unevenness and numerical schemes instability. To overcome this difficulties, the Lagrange--Galerkin characteristic starategy (see, for example, Pironneau (1980) and Notsu--Tabata (2015)), is introduced into numerical schemes. The Lagrange--Galerkin characteristic starategy does not require particle redistributions in our numerical scheme and solves numerical instabilities of the scheme. Some mathematical and numerical investigations are shown to confirm the effectiveness of our strategy..
18.	田上 大助, 材料科学に対する応用数学からの貢献, 日本応用数理学会2016年度年会, 2016.09, 講演者がこれまでに取り組んできた数値計算手法の数学的正当化についていくつかの実例を元に講演した..
19.	TAGAMI, Daisuke, Numerical analysis of a generalized particle-based method for convection-diffusion equations and its application, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2017), 2017.09.
20.	TAGAMI, Daisuke, Mathematical analysis of characteristic generalized particle methods for convection-diffusion equations, The 12th International SPHERIC Workshop, 2017.06.
21.	TAGAMI, Daisuke, A reduced iterative domain decomposition method for magnetic field problems with the gauge condition, KAUST Workshop on Computational Science and Engineering with High Performance Computers, 2017.05, An iterative Domain Decomposition Method (DDM) is appliedinto a mixed formulation of magnetic field problems, magnetostatic problems or eddy current problems, with the gauge condition. In case of the conventional one domain problems, magneticfield problems are often formulated by neglecting the gaugeconditions. However, when the formulation without any gaugeconditions was applied into iterative DDMs, iterativeprocedures diverge in case of large scale computationalmodels whose numbers of degrees of freedom (DOF) are largerthan 10^7. To overcome difficulties mentioned above, a gauge conditionis introduced via the Lagrange multiplier and magnetic fieldproblems are formulated by mixed variational problems. Moreover, an efficient reduced iterative procedure isestablished by means of the property of the Lagrangemultiplier that vanishes in the whole domain. Finally, some numerical results are shown in case ofultra-large computational models whose numbers of DOF are10^7--10^9..
22.	TAGAMI, Daisuke, An application of characteristic methods into a generalized particle method for convection-diffusion equations, Mathematical Analysis of Continuum Mechanics and Industrial Applications, 2016.10.
23.	TAGAMI, Daisuke, Some remarks on a time-explicit particle methods for flow problems, ANZIAM Conference 2018, 2018.02, We have recently obtained error estimates of a generalized particle method for convection-diffusion problems, and have now continued to estimate it for the incompressible Navier--Stokes equations. When introducing an implicit scheme in time based on the predictor-corrector strategy to particle methods for the incompressible Navier--Stokes equations, we need to solve the pressure Poisson equation at each time step. However, the pressure Poisson equation causes the increasing of computational costs, especially in case of huge computational models appearing in High-Performance Computing (HPC) fields.Therefore, many researchers in HPC fields introduce explicit schemes in time based on an equation of state of gas. In this talk, we regard one of such explicit schemes as a perturbation problem derived from the compressible Navier--Stokes equations, and give some remarks on the relations between them and the incompressible Navier--Stokes equations. Moreover, we show some numerical results by using a time-explicit particle methods for the incompressible Navier--Stokes equations..
24.	田上大助, 流れ問題に対する計算手法の数値解析 ―有限要素法と粒子法―, RIMS共同研究 (グループ型) “数理農学の基盤づくりに向けて”, 2018.01, 非圧縮粘性あるいは粘弾性流れ問題に対する有限要素法の正当性を数値解析によって数学的に保証する結果を紹介する. また近年, 我々が進めている粒子法の数値解析について, 用いる近似微分作用素の適合性に対する十分条件となるある正則条件の紹介や, 流れ場に従って運動する際に起こる粒子の不均一化を回避可能な移流拡散方程式に対する特性曲線一般化粒子法の誤差解析を紹介する. またこれらと関連する話題として, 管路を流れる粘弾性流体の数値計算に適用した例や, 生物群の個体運動において微視スケールと巨視スケールの接続に粒子法で用いる補間関数を利用した数理モデルについても紹介する..
25.	TAGAMI, Daisuke, Numerical analysis of a characteristic particle method for convection-diffusion equations, The 2016 Geometric Numerical Integration and its Applications, 2016.12, We present error estimates of a generalzied particle method for convection-diffusion equations. We also show some numerical results, which agree with theoretical ones..

1.

Ryuji Shioya (Toyo University), Hiroshi Kanayama (Kyushu University), Shin-ichiro Sugimoto (Tokyo University of Science, Suwa), Daisuke Tagami (Kyushu University), Amane Takei (University of Miyazaki), Masao Ogino (Nagoya University), et al., LexADV, 2014.05 LexADVの中でも, 特に電磁場問題の超大規模計算モデルに対する数値計算アルゴリズムの改良に貢献している. このアルゴリズムを利用したライブラリが公開されている., [URL], We have been developing an open source system software, ADVENTURE, which is a general-purpose parallel finite element analysis system and can simulate a large scale analysis model with supercomputer like the Earth Simulator or K-computer. In the system, HDDM (hierarchical domain decomposition method), which is a very effective technique to large-scale analysis, was developed. The aim of this project is to develop a numerical library based on HDDM that is extended to pre and post processing parts, including mesh generation and visualization of large scale data, for the Post Petascale simulation. .

所属学会名

学協会役員等への就任

学会大会・会議・シンポジウム等における役割

学術論文等の審査

海外渡航状況, 海外での教育研究歴

外国人研究者等の受入れ状況