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List of Papers

Research Papers (refereed)

  1. J.F.T. Rabago, L. Afraites and H. Notsu. Detecting immersed obstacle in Stokes fluid flow using the coupled complex boundary method. To appear in SIAM Journal on Control and Optimization. arXiv:2403.11819[math.OC]

  2. 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]

  3. 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)　

  4. 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

  5. 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]

  6. 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)

  7. 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)

  8. 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)

  9. 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)

  10. 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)

  11. 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)

  12. 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

  13. 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]

  14. 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]

  15. 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

  16. 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]

  17. 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]

  18. 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

  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 II: A linear scheme.   ESAIM: M2AN, Vol.51 (2017), pp.1663-1689.   doi:10.1051/m2an/2017032   arXiv:1603.01074[math.NA]

  20. 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]

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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

  30. 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

  31. 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

  32. 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

  33. 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

  34. 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

  35. 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

  36. 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

  37. 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

  38. 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