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List of Papers

Research Papers (refereed)

  1. K.S. Putri, T. Mizuochi, N. Kolbe, and H. Notsu. Error estimates for first- and second-order Lagrange-Galerkin moving mesh schemes for the one-dimensional convection-diffusion equation.   Journal of Scientific Computing, Vol.101:37, 2024.   doi:10.1007/s10915-024-02673-4 (OA)
    arXiv:2402.14691[math.NA]

  2. A. Rudiawan, A. Zak, M. Benes, M. Kimura and H. Notsu. An energy estimate and a stabilized Lagrange-Galerkin scheme for a multiphase flow model. Applied Mathematics Letters, Vol.153:109059, 2024.
    doi:10.1016/j.aml.2024.109059 (OA)　

  3. T.G. de Jong, N. Akashi, T. Taniguchi, H. Notsu, and K. Nakajima. Virtual reservoir acceleration for CPU and GPU: Case study for coupled spin-torque oscillator reservoir.   Machine Learning with New Compute Paradigms at NeurIPS 2023.   Link at OpenReview.net

  4. J.F.T. Rabago and H. Notsu. Numerical solution to a free boundary problem for the Stokes equation using the coupled complex boundary method in shape optimization settings.   Applied Mathematics and Optimization, Vol.89(2023), 2.
    doi:10.1007/s00245-023-10065-7   arXiv:2302.11828[math.OC]

  5. M.M. Rasid, M. Kimura, M.M. Murshed, E.R. Wijayanti, and H. Notsu.   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.   Mathematics, Vol.11(2023), 1633.   doi:10.3390/math11071633 (OA)

  6. K. Futai, N. Kolbe, H. Notsu and T. Suzuki.   A mass-preserving two-step Lagrange-Galerkin scheme for convection-diffusion problems.   Journal of Scientific Computing, Vol.92(2022), 37.   doi:10.1007/s10915-022-01885-w (OA)

  7. J.S.H. Simon and H. Notsu.   A shape design problem for the Navier-Stokes flow with a convective boundary condition.   Computational and Applied Mathematics, Vol.41(2022), 167.   doi:10.1007/s40314-022-01876-5 (OA)

  8. J.S.H. Simon and H. Notsu.   A shape optimization problem constrained with the Stokes equations to address maximization of vortices.   Evolution Equations and Control Theory, Vol.11(2022), pp.1873-1902.   doi:10.3934/eect.2022003 (OA)

  9. J.S.H. Simon and H. Notsu.   A convective boundary condition for the Navier-Stokes equations.   Applied Mathematics Letters, Vol.128(2022), 107876.   doi:10.1016/j.aml.2021.107876 (OA)

  10. D.O. Medeiros, H. Notsu and C.M. Oishi.   Second-order finite difference approximations of the upper-convected time derivative.   SIAM Journal on Numerical Analysis, Vol.59(2021), pp.2955-2988.
    doi:10.1137/20M1364990 (OA)

  11. K. Goto, K. Nakajima and H. Notsu.   Twin vortex computer in fluid flow.   New Journal of Physics, Vol.23(2021), 063051.   doi:10.1088/1367-2630/ac024d (OA)
    Press Release: English, Japanese1, Japanese2, Japanese3
    EurekAlert!, Asia Research News

  12. I. Wijaya and H. Notsu.   Stability estimates and a Lagrange-Galerkin scheme for a Navier-Stokes type model of flow in non-homogeneous porous media.
    Discrete & Continuous Dynamical Systems - S, Vol.14(2021), pp.1197-1212.   doi:10.3934/dcdss.2020234   arXiv:1901.09499[math.NA]

  13. M.M. Murshed, K. Futai, M. Kimura and H. Notsu.   Theoretical and numerical studies for energy estimates of the shallow water equations with a transmission boundary condition.   Discrete & Continuous Dynamical Systems - S, Vol.14(2021), pp.1063-1078.   doi:10.3934/dcdss.2020230   arXiv:1901.05725[math.NA]

  14. T. Taniguchi, N. Akashi, H. Notsu, M. Kimura, H. Tsukahara, K. Nakajima.   Chaos in nanomagnet via feedback current. Physical Review B, Vol.100(2019), 174425.   doi:10.1103/PhysRevB.100.174425   arXiv:1909.05315

  15. M. Kimura, K. Matsui, A. Muntean and H. Notsu.   Analysis of a projection method for the Stokes problem using an ε-Stokes approach.   Japan Journal of Industrial and Applied Mathematics, Vol.36 (2019), pp.959-985. doi:10.1007/s13160-019-00373-3   view-only page    arXiv:1812.10250[math.AP]

  16. M. Kimura, H. Notsu, Y. Tanaka and H. Yamamoto.   The gradient flow structure of an extended Maxwell viscoelastic model and a structure-preserving finite element scheme.   Journal of Scientific Computing, Vol.78 (2019), pp.1111-1131.   doi:10.1007/s10915-018-0799-2   view-only page    arXiv:1802.05566[math.NA]

  17. O. Fuchiwaki, Y. Tanaka, H. Notsu and T. Hyakutake.   Multi-axial non-contact in situ micromanipulation by steady streaming around two oscillating cylinders on holonomic miniature robots.   Microfluidics and Nanofluidics, Vol.22 (2018), 80.   doi:10.1007/s10404-018-2098-5   view-only page

  18. M. Lukáčová, H. Mizerová, H. Notsu and M. Tabata.   Numerical analysis of the Oseen-type Peterlin viscoelastic model by the stabilized Lagrange-Galerkin method, Part II: A linear scheme.   ESAIM: M2AN, Vol.51 (2017), pp.1663-1689.   doi:10.1051/m2an/2017032   arXiv:1603.01074[math.NA]

  19. M. Lukáčová, H. Mizerová, H. Notsu and M. Tabata.   Numerical analysis of the Oseen-type Peterlin viscoelastic model by the stabilized Lagrange-Galerkin method, Part I: A nonlinear scheme.   ESAIM: M2AN, Vol.51 (2017), pp.1637-1661.   doi:10.1051/m2an/2016078   arXiv:1603.01339[math.NA]

  20. M. Lukáčová, H. Notsu and B. She.   Energy dissipative characteristic schemes for the diffusive Oldroyd-B viscoelastic fluid.   International Journal for Numerical Methods in Fluids, Vol.81 (2016), pp.523-557.   doi:10.1002/fld.4195

  21. P.-Y. Hsu, H. Notsu and T. Yoneda.   A local analysis of the axisymmetric Navier-Stokes flow near a saddle point and no-slip flat boundary.   Journal of Fluid Mechanics, Vol.794 (2016), pp.444-459.   doi:10.1017/jfm.2016.174

  22. H. Notsu and M. Tabata.   Error estimates of a stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations.   ESAIM: M2AN, Vol.50 (2016), pp.361-380.   doi:10.1051/m2an/2015047

  23. H. Notsu and M. Tabata.   Error estimates of a pressure-stabilized characteristics finite element scheme for the Oseen equations.   Journal of Scientific Computing, Vol.65 (2015), pp.940-955.   doi:10.1007/s10915-015-9992-8

  24. M. Ogino, A. Takei, H. Notsu, S. Sugimoto, S. Yoshimura.   Performance evaluation of iterative methods for complex symmetric systems from high frequency electromagnetic field simulation.   Transaction of JSCES, Vol.2014 (2014), p.20140017.   doi:10.11421/jsces.2014.20140017

  25. H. Notsu and M. Kimura.   Symmetry and positive definiteness of the tensor-valued spring constant derived from P1-FEM for the equations of linear elasticity.   Networks and Heterogeneous Media, American Institute of Mathematical Sciences, Vol.9, No.4 (2014), pp.617-634.   doi:10.3934/nhm.2014.9.617

  26. H. Notsu, H. Rui and M. Tabata.   Development and L2-analysis of a single-step characteristics finite difference scheme of second order in time for convection-diffusion problems.   Journal of Algorithms & Computational Technology, Vol.7, No.3 (2013), pp.343-380.   doi:10.1260/1748-3018.7.3.343, Preprint version

  27. H. Notsu, D. Ueyama and M. Yamaguchi.   A self-organized mesh generator using pattern formation in a reaction-diffusion system.   Applied Mathematics Letters, Vol.26 (2013), pp.201-206.   doi:10.1016/j.aml.2012.08.012

  28. M. Tabata and H. Notsu.   Finite difference approximation requiring function values on non-grid points.   Transactions of the Japan Society for Industrial and Applied Mathematics, Vol.22, No.3 (2012), pp.171-179.   doi:10.11540/jsiamt.22.3_171

  29. Q. H. Yao, H. Kanayama, M. Ognio and H. Notsu.   Incomplete balancing domain decomposition for large scale 3-D non-stationary incompressible flow problems.   IOP Conference Series: Materials Science and Engineering, Vol.10, No.1 (2010), 012029.   doi:10.1088/1757-899X/10/1/012029

  30. Q. Yao, H. Kanayama, H. Notsu and M. Ogino.   Balancing domain decomposition for non-stationary incompressible flow problems using a characteristic-curve method.   Journal of Computational Science and Technology, Vol.4, No.2 (2010), Special Issue on Computational Mechanics Conference 2009 - JCST, pp.121-135.   doi:10.1299/jcst.4.121

  31. R. Miresmaeili, N. Saintier, H. Notsu, J.-M. Olive and H. Kanayama.   One-way coupled crystal plasticity-hydrogen diffusion simulation on artificial microstructure.   Journal of Computational Science and Technology, Vol.4, No.2 (2010), Special Issue on Computational Mechanics Conference 2009 - JCST, pp.105-120.   doi:10.1299/jcst.4.105

  32. S. Jimbo, M. Kimura and H. Notsu.   Exponential decay phenomenon of the principal eigenvalue of an elliptic operator with a large drift term of gradient type.   Asymptotic Analysis, Vol.65 (2009), pp.103-123.   doi:10.3233/asy-2009-0951

  33. H. Notsu and M. Tabata.   A single-step characteristic-curve finite element scheme of second order in time for the incompressible Navier-Stokes equations.   Journal of Scientific Computing, Vol.38, No.1 (2009), pp.1-14.   doi:10.1007/s10915-008-9217-5

  34. H. Notsu.   Numerical computations of cavity flow problems by a pressure stabilized characteristic-curve finite element scheme.   Transactions of the Japan Society for Computational Engineering and Science, Vol.2008:32.    doi:10.11421/jsces.2008.20080032

  35. H. Notsu and M. Tabata.   A combined finite element scheme with a pressure stabilization and a characteristic-curve method for the Navier-Stokes equations.   Transactions of the Japan Society for Industrial and Applied Mathematics, Vol.18, No.3 (2008), pp.427-445.   doi:10.11540/jsiamt.18.3_427

  36. M. Kimura and H. Notsu.   A level set method using the signed distance function.   Japan Journal of Industrial and Applied Mathematics, Vol.19, No.3 (2002), pp.415-446.   doi:10.1007/BF03167487

  37. M. Kimura and H. Notsu.   A level set method using a signed distance function for the mean curvature flow.   Transactions of the Japan Society for Industrial and Applied Mathematics, Vol.10, No.2 (2000), pp.101-118.   doi:10.11540/jsiamt.10.2_101


Proceedings

  1. I. Wijaya, M. Kimura, and H. Notsu.   A new Lagrange-Galerkin scheme for solving fluid flow in porous media.   IOP Conference Series: Journal of Physics: Conference Series, Vol.1245(2019), 012007.   doi:10.1088/1742-6596/1245/1/012007.

  2. H. Notsu and M. Tabata.   Stabilized Galerkin-characteristics finite element schemes for flow problems.   In P. Iványi and B.H.V. Topping (Eds), Proceedings of the Ninth International Conference on Engineering Computational Technology, Civil-Comp Press, Stirlingshire, UK, Paper 71 (13 pages), 2014.   doi:10.4203/ccp.105.71

  3. M. Ogino, A. Takei, H. Notsu, S. Sugimoto and S. Yoshimura.   Finite element analysis of high frequency electromagnetic fields using a domain decomposition method based on the COCR method.   Theoretical and Applied Mechanics Japan, Vol.61 (2013), pp.173-181.   doi:10.11345/nctam.61.173


Book chapters

  1. H. Notsu and M. Tabata.   Error estimates of a stabilized Lagrange-Galerkin scheme of second-order in time for the Navier-Stokes equations.   In Y. Shibata and Y. Suzuki (eds.), Mathematical Fluid Dynamics, Present and Future, pp.497-530, Springer, 2016.   doi:10.1007/978-4-431-56457-7_18

  2. H. Notsu and M. Tabata.   Stabilized Lagrange-Galerkin schemes of first- and second-order in time for the Navier-Stokes equations.   In Y. Bazilevs and K. Takizawa (eds.), Advances in Computational Fluid-Structure Interaction and Flow Simulation: New Methods and Challenging Computations, pp.331-343, Springer, 2016.   doi:10.1007/978-3-319-40827-9_26


Feature articles

  1. H. Notsu.   Differentiation, finite difference, and numerical analysis. Sugaku Seminar, June, 2024, pp.36-41.   Link

  2. H. Notsu and K. Futai.   Mathematical sciences in flow simulation (2).   Sugaku Seminar, May, 2019, pp.81-85.   Link

  3. H. Notsu.   Mathematical sciences in flow simulation (1).   Sugaku Seminar, April, 2019, pp.68-72.   Link

  4. H. Notsu.   Theory and practice of Lagrange-Galerkin methods.   Journal of the Japan Society for Computational Engineering and Science (JSCES), Vol.20, No.3 (2015), pp.21-24.   PDF


Report

  1. H. Notsu and M. Tabata.   Numerical computations of the two and three dimensional nonstationary Navier-Stokes equations by combined finite element schemes with a pressure stabilization and a characteristic-curve method of first and second order in time.   Zenkoku Kyodo Riyo System Koho, Vol.3, No.1 (2009), pp.12-21.   PDF


Book review

  1. H. Notsu.   The Japanese translation of "Computational Fluid–Structure Interaction: Methods and Applications (Wiley, 2013)" by Y. Tsugawa and K. Takizawa (Morikita, 2015).   JSIAM Online Magazine, J1512A (2016).   Link


Awards (research)

  1. Best Poster Award in 2010, JSIAM :   H. Notsu, M. Yamaguchi and D. Ueyama.   The development of a self-organized mesh generator.   JSIAM 2010 Annual Meeting (Sept. 6-9, 2010), Meiji Univ., Tokyo.

  2. Best Paper Award in 2003, JSIAM :   M. Kimura and H. Notsu.   A level set method using a signed distance function for the mean curvature flow.   Transactions of the Japan Society for Industrial and Applied Mathematics, Vol.10, No.2 (2000), pp.101-118.


Awards (others)

  1. Kanazawa University achievement award (功労表彰). H. Notsu. JST CREST project. March 18, 2022.
  2. Waseda University Teaching Award 2015 (Autumn): H. Notsu. Mathematics B2 (Calculus). November 24, 2016.


Thesis

  • Characteristic-Curve Finite Element Schemes for the Navier-Stokes Equations. March 26th, 2009.   PDF