Waseda Institute for Advanced Study (WIAS)Waseda University


OKAWA, Hirotada


OKAWA, Hirotada


Ph.D. in Science


Assistant Professor


Research Topic

Development of numerical methods for nonlinear elliptic partial differential equations

Nonlinear elliptic partial differential equations appear in physics and engineering.  For instance, constructing initial data for a constrained system such as Maxwell and Einstein equations or preparing stationary fluid flows inside some boundary corresponds to solving nonlinear elliptic partial differential equations.  Numerical methods are  quite helpful when an analytic solution cannot be obtained, but the following issues should be resolved: (i) Transformation from Nonlinear elliptic partial differential equations to a set of nonlinear equations, (ii) Method to solve a set of nonlinear equations.  However, in particular, there is no perfect method for issue (ii).  The Newton method which is the only existing solver for a set of nonlinear equations is quite useful, while it fails when the initial guess is far from the solution.  Recently, we have proposed a new method for this issue.  I would like to apply it for nonlinear elliptic partial differential equations and construct useful numerical methods in practice.

Education and Academic Employment

2012.3 Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Ph.D. in Science
2012.4-2012.7 Research fellow at Yukawa Institute for Theoretical Physics
2012.8-2014.6 ERC fellow at Institute Superior Tecnico
2014.7-2019.3 HPCI researcher at Yukawa Institute for Theoretical Physics

Fields of Research Interests

Astrophysics, General Relativity, Numerical Analysis

Academic Publications
  • K.Fujisawa,H.Okawa,Y.Yamamoto,S.Yamada,”Effects of rotation and magnetic field on the revival of a stalled shock in supernova explosions“, Astrophysical J., 872, 155, Feb. 2019
  • K-I.Maeda, K.Okabayashi, H.Okawa,”Maximal efficiency of the collisional Penrose process with spinning particles”, Phys.Rev. D98, no.6, 064027, Sep. 2018
  • K.Aoki,K-i.Maeda,Y.Misonoh,H.Okawa,“Massive graviton geons”、Phys.Rev.、D97、no.4、044005、Feb. 2018
  • H.Nagakura,W.Iwakami,S.Furusawa,H.Okawa,A.Harada,K.Sumiyoshi,S.Yamada, H.Matsufuru,A.Imakura,“Simulations of core-collapse supernovae in spatial axisymmetry with full Boltzmann neutrino transport”、Astrophys.J.、854、no.2、136、Feb. 2018
  • K-i.Nakao,H.Okawa,K-i.Maeda,“Nonlinear collisional Penrose process: How much energy can a black hole release?”、PTEP、no.1、013E01、Jan. 2018
  • C-M.Yoo,T.Harada,H.Okawa,“3D simulation of spindle gravitational collapse of a collisionless particle system”、Class.Quant.Grav.34、no.10、105010、Apr. 2017
  • R.Hirai,H.Nagakura,H.Okawa,K,Fujisawa,“Hyperbolic self-gravity solver for large scale hydrodynamical simulations”、Phys.Rev.、D93、no.8、083006、Apr. 2016
  • H.Okawa,“Nonlinear evolutions of bosonic clouds around black holes”、Class.Quant.Grav.32、no.21、214003、Oct. 2015
  • H.Okawa,H.Witek,V.Cardoso,“Black holes and fundamental fields in Numerical Relativity:Initial data construction and evolution of bound states”、Phys.Rev.、D89、no.10、104032、May 2014
  • H.Okawa,“Initial conditions for Numerical Relativity – Introduction to numerical methods for solving elliptic PDEs”、Int.J.Mod.Phys.、A28、1340016、Aug. 2013
Other Interests

Football, Cooking

Affiliated Academic Organizations

The Physical Society of Japan


2010.3 Graduate award in Graduate School of Arts and Science, the University of Tokyo
2012.2 Poster award in GCOE symposium

Related articles

LIM, Hyunjung
AIZAWA, Toshiaki
XU, Alison
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