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last modified：2025/03/31
Professor Hirofumi Notsu
Faculty, Affiliation
Faculty of Mathematics and Physics, Institute of Science and Engineering
Professor
College and School Educational Field
Division of Mathematical and Physical Science, Graduate School of Natural Science and Technology
Division of Mathematical and Physical Sciences, Graduate School of Natural Science and Technology
School of Mathematics and Physics, College of Science and Engineering
Laboratory
H.Notsu Laboratory
Academic Background
【Degree】
Doctor of Mathematics
Career
Kanazawa University Faculty of Mathematics and Physics Professor(2019/04/01-)
Japan Science and Technology Agency (JST) PRESTO Researcher(2016/10/01-2020/03/31)
Kanazawa University Associate Professor(2016/04/01-2019/03/31)
Waseda University Associate Professor(2015/04-2016/03)
Waseda University Assistant Professor(2011/04-2015/03)
Meiji University Postdoctoral researcher(2010/04-2011/03)
AIST Postdoctoral researcher(2009/04-2010/03)
Year & Month of Birth
Academic Society
The Japan Society for Industrial and Applied Mathematics (JSIAM)
The Japan Society for Industrial and Applied Mathematics (JSIAM), Assoc. ed. Bull. JSIAM
The Mathematical Society of Japan (MSJ), Comm. mem. Div. Appl. Math.
The Japan Society for Industrial and Applied Mathematics (JSIAM), Assoc. ed. Trans. JSIAM
The Japan Society for Computational Engineering and Science (JSCES)
Award
○The best poster award of JSIAM(2010/09/07)
○The best paper award of JSIAM(2003/09/18)
Specialities
Numerical Analysis
Speciality Keywords
Numerical Analysis, the finite element method, flow problems
Research Themes
Numerical analysis of flow problems
Books
- H. Notsu and M. Tabata Mathematical Fluid Dynamics, Present and Future, Eds.: Y. Shibata and Y. Suzuki Springer 2016
- H. Notsu and M. Tabata Advances in Computational Fluid-Structure Interaction and Flow Simulation: New Methods and Challenging Computations, Eds.: Y. Bazilevs and K. Takizawa Springer 2016
Papers
- Detecting immersed obstacle in Stokes fluid flow using the coupled complex boundary method J.F.T. Rabago, L. Afraites, H. Notsu SIAM Journal on Control and Optimization 63 2 822-851 2025/03/20
- Error estimates for first- and second-order Lagrange-Galerkin moving mesh schemes for the one-dimensional convection-diffusion equation K.S. Putri, T. Mizuochi, N. Kolbe, H. Notsu Journal of Scientific Computing 101 37 2024/08/26
- An energy estimate and a stabilized Lagrange-Galerkin scheme for a multiphase flow model A. Rudiawan, A. Zak, M. Benes, M. Kimura and H. Notsu Applied Mathematics Letters 153 109059 2024/03/11
- Numerical solution to a free boundary problem for the Stokes equation using the coupled complex boundary method in shape optimization settings J.F.T. Rabago and H. Notsu Applied Mathematics and Optimization 89 2 2023/11/07
- Virtual reservoir acceleration for CPU and GPU: Case study for coupled spin-torque oscillator reservoir T.G. de Jong, N. Akashi, T. Taniguchi, H. Notsu, and K. Nakajima Machine Learning with New Compute Paradigms at NeurIPS 2023 2023/11/01
- A two-step Lagrange-Galerkin scheme for the shallow water equations with a transmission boundary condition and its application to the Bay of Bengal region—Part I: Flat bottom topography M.M. Rasid, M. Kimura, M.M. Murshed, E.R. Wijayanti, and H. Notsu Mathematics 11 1633 2023/03/28
- A mass-preserving two-step Lagrange-Galerkin scheme for convection-diffusion problems K. Futai, N. Kolbe, H. Notsu, T. Suzuki Journal of Scientific Computing 92 2 37 2022/06/25
- A shape design problem for the Navier-Stokes flow with a convective boundary condition J.S.H. Simon and H. Notsu Computational and Applied Mathematics 41 167 2022/05/06
- A shape optimization problem constrained with the Stokes equations to address maximization of vortices J.S.H. Simon, H. Notsu Evolution Equations and Control Theory 2022/01
- A convective boundary condition for the Navier-Stokes equations J.S.H. Simon, H. Notsu Applied Mathematics Letters 128 107876 2021/12/24
- Second-order finite difference approximations of the upper-convected time derivative D.D. Medeiros, H. Notsu, C.M. Oishi SIAM Journal on Numerical Analysis 59 6 2955-2988 2021/12/02
- Twin vortex computer in fluid flow K. Goto, K. Nakajima and H. Notsu. New Journal of Physics 23 063051 2021/06/17
- Stability estimates and a Lagrange-Galerkin scheme for a Navier-Stokes type model of flow in non-homogeneous porous media I. Wijaya, H. Notsu Discrete & Continuous Dynamical Systems - S 14 3 1197-1212 2021/03
- Theoretical and numerical studies for energy estimates of the shallow water equations with a transmission boundary condition M.M. Murshed, K. Futai, M. Kimura, H. Notsu Discrete & Continuous Dynamical Systems - S 14 3 1063-1078 2021/03
- The gradient flow structure of an extended Maxwell viscoelastic model and a structure-preserving finite element scheme M. Kimura, H. Notsu, Y. Tanaka and H. Yamamoto Journal of Scientific Computing 78 2 1111-1131 2019
- Chaos in nanomagnet via feedback current T. Taniguchi, N. Akashi, H. Notsu, M. Kimura, H. Tsukahara, K. Nakajima Physical Review B 100 174425 2019
- Multi-axial non-contact in situ micromanipulation by steady streaming around two oscillating cylinders on holonomic miniature robots O. Fuchiwaki, Y. Tanaka, H. Notsu and T. Hyakutake Microfluidics and Nanofluidics 22 80 2018
- Numerical analysis of the Oseen-type Peterlin viscoelastic model by the stabilized Lagrange-Galerkin method, Part II: A linear scheme. M. Lukacova-Medvidova, H. Mizerova, H. Notsu and M. Tabata ESAIM: M2AN 51 1663-1689 2017
- Numerical analysis of the Oseen-type Peterlin viscoelastic model by the stabilized Lagrange-Galerkin method, Part I: A nonlinear scheme M. Lukacova-Medvidova, H. Mizerova, H. Notsu, M. Tabata ESAIM: M2AN 51 1637-1661 2017
- A local analysis of the axisymmetric Navier–Stokes flow near a saddle point and no-slip flat boundary P.-Y. Hsu, H. Notsu and T. Yoneda Journal of Fluid Mechanics 794 444-459 2016
- Error estimates of a stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations H. Notsu and M. Tabata ESAIM: M2AN 50 361-380 2016
- Energy dissipative characteristic schemes for the diffusive Oldroyd-B viscoelastic fluid M. Lukáčová, H. Notsu and B. She International Journal for Numerical Methods in Fluids 81 523-557 2016
- Error estimates of a pressure-stabilized characteristics finite element scheme for the Oseen equations H. Notsu and M. Tabata Journal of Scientific Computing 65 940-955 2015
- Theory and practice of Lagrange-Galerkin methods H. Notsu Journal of the Japan Society for Computational Engineering and Science (JSCES) 20 3 21-24 2015
- Symmetry and positive definiteness of the tensor-valued spring constant derived from P1-FEM for the equations of linear elasticity H. Notsu and M. Kimura Networks and Heterogeneous Media 9 4 617-634 2014
- Performance evaluation of iterative methods for complex symmetric systems from high frequency electromagnetic field simulation M. Ogino, A. Takei, H. Notsu, S. Sugimoto and S. Yoshimura Transaction of JSCES 2014 20140017 2014
- Finite element analysis of high frequency electromagnetic fields using a domain decomposition method based on the COCR method M. Ogino, A. Takei, H. Notsu, S. Sugimoto and S. Yoshimura Theoretical and Applied Mechanics Japan 61 173-181 2013
- Development and L2-analysis of a single-step characteristics finite difference scheme of second order in time for convection-diffusion problems H. Notsu, H. Rui and M. Tabata Journal of Algorithms & Computational Technology 7 3 343-380 2013
- A self-organized mesh generator using pattern formation in a reaction-diffusion system H. Notsu, D. Ueyama and M. Yamaguchi Applied Mathematics Letters 26 201-206 2013
- Finite difference approximation requiring function values on non-grid points M. Tabata and H. Notsu Transactions of the Japan Society for Industrial and Applied Mathematics 22 3 171-179 2012
Conference Presentations
- 流体構造連成問題のための AMR を用いた数値シミュレーション手法の開発(conference：先魁シンポジウム「産学連携デジタルツインの社会実装」-二軸押出研究会-)(2024/12/05)
- An energy estimate and a stabilized Lagrange–Galerkin scheme for a multiphase flow model(conference：Workshop in Prague at Czech Academy of Sciences)(2024/11/26)
- Adaptive stabilized Lagrange–Galerkin methods: Theory and applications(conference：Tohoku University, AIMR Math Group Seminar)(2024/10/15)
- An adaptive pressure-stabilized Lagrange–Galerkin method for incompressible flow problems(conference：Mathematics of Shapes)(2024/08/31)
- An adaptive stabilized Lagrange–Galerkin method for incompressible flow problems(conference：AFSI 2024)(2024/08/20)
- A finite element scheme for a multiphase flow model(conference：Mathematical Society of Japan)(2024/03/20)
- Stabilized Lagrange-Galerkin schemes for viscous and viscoelastic flow problems(conference：Computational Mathematics and Applications Seminar)(2024/03/07)
- A mass-preserving two-step Lagrange-Galerkin scheme for convection-diffusion problems(conference：Seminar on Partial Differential Equations)(2023/10/31)
- Reservoir computing with fluid flows(conference：Advances in Computational Mechanics (ACM 2023))(2023/10/24)
- A Lagrangian moving mesh method(conference：Biwako Workshop on Mathematical Biology)(2023/08/17)
- A mass-preserving two-step Lagrange–Galerkin scheme for convection-diffusion problems(conference：RIMS 共同研究)(2022/10/12)
- Second-order finite difference approximations of the upper-convected time derivative(conference：WCCM-APCOM 2022)(2022/07/31)
- Twin vortex computer in fluid flow and a related topic(conference：RIMS Workshop)(2022/07/08)
- A second-order approximation of the upper-convected time derivative based on the generalized Lie derivative(conference：日本数学会2021年度秋期総合分科会)(2021/09/16)
- Twin vortex computer in fluid flow(conference：International Conference: Differential Equations for Data Science 2021 (DEDS2021))(2021/03/10)
- Vorticity maximization for a fluid with a nonlinear do-nothing boundary condition: A shape design approach(conference：第2回若手数学者交流会)(2021/03/14)
- Vorticity maximization of a linear fluid flow via volume and perimeter constrained shape optimization(conference：Czech-Japanese Seminar in Applied Mathematics (CJS2021))(2021/01/07)
- A mass-conservative Lagrange-Galerkin scheme of second-order in time for convection-diffusion problems(conference：Czech-Japanese Seminar in Applied Mathematics (CJS2021))(2021/01/07)
- Three dimensional numerical simulation of the Navier–Stokes equations in straight and curved cylindrical domains(conference：Czech-Japanese Seminar in Applied Mathematics (CJS2021))(2021/01/06)
- A Lagrangian moving mesh scheme for advection-diffusion equations(2020/12/19)
- An adaptive Lagrangian finite-volume method for convection-diffusion equations(conference：Czech-Japanese Seminar in Applied Mathematics (CJS2021))(2021/01/06)
- Development of an accurate Lagrange-Galerkin scheme with adaptive mesh refinement(conference：Extended Kanazawa Analysis Seminar)(2018/11/09)
- A mass-conservative Lagrange–Galerkin scheme of second-order in time with AMR for convection problems(conference：CJK2018: The Seventh China–Japan–Korea Joint Conference on Numerical Mathematics)(2018/08/21)
- Numerical analysis of Lagrange-Galerkin schemes for flow problems(conference：International Workshop on Computational Science 2018)(2018/06/30)
- A mass-conservative Lagrange–Galerkin scheme of second-order in time with adaptive mesh refinement for convection problems(conference：CoMFoS18)(2018/06/18)
- The gradient flow structure of the Maxwell viscoelastic model and a structure-preserving finite element scheme(conference：KSIAM 2018 Spring Conference)(2018/05/25)
- The gradient flow structure of the Maxwell viscoelastic model and a structure-preserving finite element scheme(conference：Conference on Mathematical Fluid Dynamics)(2018/05/08)
- Numerical analysis of the Oseen-type Peterlin viscoelastic model(conference：2018 A3 Fluid Mechanics Workshop)(2018/03/10)
- Numerical analysis and computation of viscoelastic models(conference：Numerical Analysis: Applications to Biomedical Problems and Foundations)(2018/02/21)
- Numerical analysis of viscoelastic models(conference：Mini-symposium on Complex Flows: Dynamics of Viscoelastic and Inertioelastic flows)(2018/01/20)
- A structure-preserving finite element scheme for the Maxwell model(conference：A3 Soft Matter Workshop)(2017/12/21)
- Numerical analysis of the Oseen-type Peterlin viscoelastic model(conference：The 42nd Sapporo Symposium on Partial Differential Equations)(2017/08/09)
- A Lagrange-Galerkin scheme for a diffusive Oldroyd-B viscoelastic fluid(conference：Second Joint Workshop of China-Japan-Korea A3 Foresight Program)(2015/11/27)
- Error estimates of Lagrange-Galerkin schemes for flow problems(conference：International Workshop on the Multi-Phase Flow; Analysis, Modeling and Numerics)(2015/11/11)
- Convergence analysis of stable and stabilized Lagrange-Galerkin schemes for natural convection problems(conference：Joint International Conference and Autumn School 2015)(2015/10/07)
- A stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations and its computation(conference：The 12th Hirschegg Workshop on Conservation Laws)(2015/09/17)
- Error estimates of stabilized Galerkin-characteristics finite element schemes for incompressible flow problems(conference：The 18th International Conference on Finite Elements in Flow Problems (FEF2015))(2015/03/17)
- Error estimates of Lagrange-Galerkin finite element schemes for natural convection problems(conference：The 11th Japanese-German International Workshop on Mathematical Fluid Dynamics)(2015/03/12)
- Linear and nonlinear schemes for an Oseen-type diffusive Peterlin model(conference：The 4th Workshop on Mathematical Analysis for Nonlinear Phenomena)(2016/02/13)
- Error estimates of a stabilized Lagrange-Galerkin scheme for an Oseen-type diffusive Peterlin model(conference：International Conference CoMFoS15: Mathematical Analysis of Continuum Mechanics and Industrial Applications)(2015/11/18)
- Error estimates of stabilized Lagrange-Galerkin finite element schemes for flow problems(conference：2015 A3 joint Workshop on Fluid Dynamics and Material Science)(2015/02/13)
- A stabilized Galerkin-characteristics finite element scheme for the Navier-Stokes equations and its applications(conference：Workshop: Numerical Methods and Analysis for Structures and Singularities in Fluids)(2014/12/09)
- A stabilized Galerkin-characteristics finite element scheme for the Navier-Stokes equations: theory, computations and applications(conference：International Conference on Mathematical Fluid Dynamics, Present and Future)(2014/11/14)
- Stabilized Galerkin-characteristics finite element schemes for flow problems(conference：The Ninth International Conference on Engineering Computational Technology (ECT 2014))(2014/09/05)
- A stabilized characteristics finite element scheme for three-dimensional flow problems(conference：The Fifth China-Japan-Korea Conference on Numerical Mathematics)(2014/08/27)
- Error estimates of a stabilized characteristics finite element scheme for the Navier-Stokes equations(conference：International Congress of Mathematicians (ICM 2014))(2014/08/19)
- Computation and numerical analysis of viscous and viscoelastic fluid flows(conference：Workshop on Numerical Methods and Analysis for Structures and Singularities in Fluids II)(2017/01/30)
Others
- Mathematical sciences in flow simulation (2) Hirofumi Notsu, Kouta Futai Sugaku Seminar 691 81--85 2019/04
- Mathematical sciences in flow simulation (1) Hirofumi Notsu Sugaku Seminar 690 68--72 2019/03
Arts and Fieldwork
Patent
Theme to the desired joint research
○Finite element analysis
Grant-in-Aid for Scientific Research
○Grant-in-Aid for Scientific Research (A)「New development of numerical analysis based on the space-time variational method」(2021-2025)
○Grant-in-Aid for Scientific Research (B)「Deepening and new development of mathematical study on cell adhesion」(2020-2024)
○「New trends of energy gradient flow: mathematical aspects and various phenomena and applications」(2020-2024)
○Grant-in-Aid for Scientific Research (B)「粘弾性流体に特有な渦の数理解析」(2018-2021)
○Grant-in-Aid for Challenging Exploratory Research「周期的定常流れに対する４次元流れ領域区分の定式化および数値解析法の提案」(2016-2017)
○Grant-in-Aid for Young Scientists (B)「Development of the characteristics finite element methods for non-Newtonian fluids」(2014-2017)
○Grant-in-Aid for Young Scientists (B)「Construction of the high-quality characteristics finite element method」(2011-2013)
Competitive research funding,Contribution
○Performance improvement of physical reservoir computing based on the theory of dynamical systems Japan Science and Technology Agency, CREST(2020-2025)
○Mathematical modeling, numerical analysis and simulation of three-dimensional free-surface polymeric fluids Japan Science and Technology Agency, PRESTO(2016-2019)
Collaborative research,Consignment study
Classes (Bachelors)
○Introduction to Numerical Analysis 1a(2017)
○Introduction to Numerical Analysis 1b(2017)
○Introduction to Numerical Analysis 2b(2017)
○Introduction to Numerical Analysis 2a(2017)
○Computational Science(2017)
○Analysis 3C(2017)
○Computational Science(2016)
○Introduction to Numerical Analysis 2(2016)
○Numerical Analysis(2016)
○Analysis 3C(2016)
○Introduction to Numerical Analysis 1(2016)
○Presentation and Debate (Freshman Seminar II)(2016)
○Freshman Seminar I(2016)
Classes (Graduate Schools)
○Applied Analysis a(2017)
○Exercise A(2017)
○Applied Analysis b(2017)
○Numerical Analysis of Flow Problems(2017)
○Numerical Analysis of Flow Problems(2017)
○Numerical Analysis of Flow Problems(2017)
○Numerical Analysis of Flow Problems(2017)
○Research Work A(2017)
○Seminar A(2017)
○Numerical Analysis of Flow Problems(2016)
○Applied Analysis a(2016)
○Applied Analysis b(2016)
○Exercise A(2016)
○Research Work A(2016)
○Seminar A(2016)