Poincar integral invariant and conserved quantity of Toda lattice systems

Sasa, Narimasa

JSIAM Letters, 14, p.88 - 91, 2022/00

https://doi.org/10.14495/jsiaml.14.88

Calculus in higher dimension

Sasa, Narimasa

Suri Kagaku, 56(5), p.22 - 28, 2018/05

In accordance with the basic research for the material development, we develop a numerical scheme for large scale parallel numerical simulation of a quantum condensate. We give a simple explanation of calculus which constitutes the theoretical basis for the engineering. We explain some key concepts of calculus, including scalar and vector fields, integral theorem.

Poincar integral invariant and momentum conservation in symplectic time integration of Hamiltonian partial differential equations

Sasa, Narimasa

Journal of the Physical Society of Japan, 86(7), p.074006_1 - 074006_6, 2017/07

https://doi.org/10.7566/JPSJ.86.074006

The momentum conservation law is investigated in numerical time evolutions of discretized Hamiltonian partial differential equations using symplectic integrators. Our investigation is based on the equivalence between the total momentum and the Poincare integral invariant of the system following our previous work. By introducing a Fourier interpolation method that is a canonical transformation, the total momentum of the system is shown to be an exact conserved quantity if the Hamiltonian possesses a discrete translational invariance and aliasing errors do not appear in the time evolutions. In addition, we perform numerical simulations that demonstrate the validity of our theoretical results under several conditions. Consequently, all symplectic integrators for discretized Hamiltonian partial differential equations are shown to inherit the property of the simultaneous conservation of the total momentum and approximated energy.

Momentum conservation law in symplectic integrators for partial differential equations

Sasa, Narimasa

Journal of the Physical Society of Japan, 83(12), p.123003_1 - 123003_4, 2014/12

https://doi.org/10.7566/JPSJ.83.123003

The momentum conservation law in symplectic integrators for partial differential equations is investigated. We show that the total momentum expressed by an integral form gives a conserved quantity even though a spatially discretized system is considered. By showing the equivalence between the integral form of the total momentum and a sum of areas of projections of a hypersurface in the phase space of the system, the conservation of the total momentum in symplectic integrators is generally proven. We also discuss an approximation formula for the total momentum for use in numerical simulations of a spatially discretized system. As a result, all symplectic integrators for discretized partial differential equations are shown to possess a property of substantial conservation of the energy and total momentum in Hamiltonian systems.

Momentum conservation law in explicit symplectic integrators for a nonlinear Schrdinger-type equation

Sasa, Narimasa

Journal of the Physical Society of Japan, 82(5), p.053001_1 - 053001_4, 2013/05

https://doi.org/10.7566/JPSJ.82.053001

This paper discusses the momentum conservation law in a symplectic integrator for a nonlinear Schrdinger-type equation. We show that the total momentum, which is formally expressed by a polynomial of a discrete variable, is conserved under cyclic boundary conditions. We also perform numerical simulations to demonstrate the validity and numerical convergence of our expression for the total momentum. As a result, the symplectic integrator simultaneously satisfies the energy, density and momentum conservation laws.

Energy spectra of quantum turbulence; Large-scale simulation and modeling

Sasa, Narimasa; Kano, Takuma*; Machida, Masahiko; L'vov, V. S.*; Rudenko, O.*; Tsubota, Makoto*

Physical Review B, 84(5), p.054525_1 - 054525_6, 2011/08

https://doi.org/10.1103/PhysRevB.84.054525

In a 2048 simulation of quantum turbulence within the Gross-Pitaevskii equation, it is demonstrated that the large-scale motions have a classical Kolmogorov-1941 energy spectrum , followed by an energy accumulation with const at about the reciprocal mean intervortex distance. This behavior was predicted by the L'vov-Nazarenko-Rudenko bottleneck model of gradual eddy-wave crossover, further developed in the paper.

Review of research on simulation engineering in FY2005

Otani, Takayuki; Sasa, Narimasa; Shimizu, Futoshi; Suzuki, Yoshio

JAEA-Review 2007-009, 36 Pages, 2007/03

JAEA-Review-2007-009.pdf:2.74MB

Research on simulation engineering for nuclear applications has been performed at Center for Computational Science & e-Systems, Japan Atomic Energy Agency (CCSE/JAEA). We established the committee which does research evaluation and advice as the help of the research and development. This report describes the result of the evaluation of research on simulation engineering performed at CCSE/JAEA in FY2005.

Splitting scheme for the Ginzburg-Landau equation in superconductors

Sasa, Narimasa

Nihon Oyo Suri Gakkai Rombunshi, 14(2), p.91 - 98, 2004/06

Splitting scheme is applied to solve numerically the time dependent Ginzburg-Landau and Maxwell equations which describe superconducting state in materials. First and second order splitting schemes are constructed with spacial difference method by using the link variables. We perform various numerical experiments and compare numerical stability by changing order of the schemes.

Application of AMG to Ginzburg-Landau equation for superconductors

Sasa, Narimasa; Machida, Masahiko; Yamada, Susumu; Arakawa, Chuichi

Keisan Kogaku Koenkai Rombunshu, 7(1), p.171 - 172, 2002/05

Algebraic Multi Grid(AMG) is applied to solve the Ginzburg-Landau equations for Superconductors. The method effectively solves large scale linear algebraic equations. AMG is also applicable for systems with complex boundary condition in contrast with usual Geometrical Multi Grid.

Symplectic integrator for nonlinear partial differential equations

Sasa, Narimasa; Yoshida, Haruo*

Oyo Sugaku Godo Kenkyu Shukai Hokokushu, 4 Pages, 2000/12

no abstracts in English