List of Papers
Research Papers (refereed)
- 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]
- 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)
- 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
- 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]
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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
- 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]
- 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]
- 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
- 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]
- 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]
- 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
- 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]
- 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]
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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.
- 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
- 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
- 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
- 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
- H. Notsu. Differentiation, finite difference, and numerical analysis. Sugaku Seminar, June, 2024, pp.36-41. Link
- H. Notsu and K. Futai. Mathematical sciences in flow simulation (2). Sugaku Seminar, May, 2019, pp.81-85. Link
- H. Notsu. Mathematical sciences in flow simulation (1). Sugaku Seminar, April, 2019, pp.68-72. Link
- 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
- 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
- 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)
- 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.
- 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)
- Kanazawa University achievement award (功労表彰). H. Notsu. JST CREST project. March 18, 2022.
- 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