Hisayasu Kuroda

Analytical and numerical study on the nonequilibrium relaxation by the simplified Fokker–Planck equation

Nonequilibrium relaxation by the simplified Fokker–Planck equation is studied by calculating the relaxation of Grad’s moments. From calculated relaxation of moments, we propose two simplified Fokker–Planck-type equations. For the quantitative validation of nonequilibrium relaxation by using the simplified Fokker–Planck-type equations, we solve a rarefied shock layer problem. To study the stronger diffusion of the distribution function than the simplified Fokker–Planck-type equation, we consider diffusion of the distribution function due to the gain term of the Boltzmann equation, because the Boltzmann equation can be described by a partial differential equation with higher-order terms than the simplified Fokker–Planck equation. The effect of the gain term of the Boltzmann equation is discussed based on comparisons with our proposed Bhatnagar–Gross–Krook equation with velocity-dependent collision frequency.

Knowledge Discovery in Auto-tuning Parallel Numerical Library

This paper proposes the parallel numerical library called ILIB which realises auto-tuning facilities with selectable calculation kernels, communication methods between processors, and various number of unrolling for loop expansion. This auto-tuning methodology has advantage not only in usability of library but also in performance of library. In fact, results of the performance evaluation show that the auto-tuning or auto-correction feature for the parameters is a crucial technique to attain high performance. A set of parameters which are auto-selected by this auto-tuning methodology gives us several kinds of important knowledge for highly efficient program production. These kinds of knowledge will help us to develop some other high-performance programs, in general.

Formulation and numerical analysis of diatomic molecular dissociation using Boltzmann kinetic equation

The direct description of chemical reactions by the Boltzmann equation still involves some difficulties in the kinetic theory. In this paper, we describe diatomic molecular dissociation due to transitions of vibrational quantum states resulting from inelastic collisions. These can be described by the Wang Chang-Uhlenbeck (WCU) equation. To avoid direct evaluation of the strong nonlinear collision kernel of the WCU equation, we used a kinetic equation. For accurate description of the dissociation process, we describe improvements we made to the conventional inelastic collision model (the so-called Morse model). Combining this inelastic collision model with the gas mixture model by Oguchi, we formulated a model for representing diatomic molecular dissociations. We validated this model by simulating a hypersonic shock layer with diatomic molecular dissociation.

Numerical analysis of relativistic shock layer problem by using relativistic Boltzmann–kinetic equations

The relativistic shock layer problem was numerically analyzed by using two relativistic Boltzmannkinetic equations. One is Marle model, and the other is Anderson-Witting model. As with Marle model, the temperature of the gain term was determined from its relation with the dynamic pressure in the framework of 14-moments theory. From numerical results of the relativistic shock layer problem, behaviors of projected moments in the nonequilibrium region were clarified. Profiles of the heat flux given by Marle model and Anderson-Witting model were quite adverse to the profile of the heat flux approximated by Navier-Stokes-Fourier law. On the other hand, profiles of the heat flux given by Marle model and Anderson-Witting model were similar to the profile approximated by Navier-Stokes-Fourier law. Additionally we discuss the differences between Anderson-Witting model and Marle model by focusing on the fact that the relaxational rate of the distribution function depends on both flow velocity and molecular velocity for Anderson-Witting model, while it depends only on the molecular velocity for Marle model.

Fast Quadruple Precision Arithmetic Library on Parallel Computer SR11000/J2

In this paper, the fast quadruple precision arithmetic of four kinds of basic operations and multiply-add operations are introduced. The proposed methods provide a maximum speed-up factor of 5 times to gcc 4.1.1 with POWER 5+ processor used on parallel computer SR11000/J2. We also developed the fast quadruple precision vector library optimized on POWER 5 architecture. Quadruple precision numbers, which is 128 bit long double data type, are emulated with a pair of 64 bit double data type on POWER 5+ prosessor used on SR11000/J2 with Hitachi Optimizing Compiler and gcc 4.1.1. To avoid rounding errors in computing quadruple precision arithmetic operations, emulation needs high computational cost. The proposed methods focus on optimizing the number of registers and instruction latency.

Consideration of the vibrationally linked molecular dissociation model based on the kinetic theory

In recent year, the remarkable development of high performance computing gradually makes it possible to simulate hyper‐dimensional distribution function, which constitutes of Boltzmann equation or other model equations. Our interests exist in formulation of molecular dissociation process with distribution function including molecular quantum states, which needs higher dimensions in accordance with the number of quantum mode. In this paper, Boltzmann model equation is used and discussed primarily. For assurance of properties of Boltzmann model equation, various models are analyzed numerically. Additionally the mixture gaseous model by Oguti and inelastic collision model by Morse‐Holway is combined with and extended into the molecular dissociation formulation.

Parallel blocked sparse matrix-vector multiplication with dynamic parameter selection method

A blocking method is a popular optimization technique for sparse matrix-vector multiplication (SpMxV). In this paper, a new blocking method which generalizes the conventional two blocking methods and its application to the parallel environment are proposed. This paper also proposes a dynamic parameter selection method for blocked parallel SpMxV which automatically selects the parameter set according to the characteristics of the target matrix and machine in order to achieve high performance on various computational environments. The performance with dynamically selected parameter set is compared with the performance with generally-used fixed parameter sets for 12 types of sparse matrices on four parallel machines: including PentiumIII, Sparc II, MIPS R12000 and Itanium. The result shows that the performance with dynamically selected parameter set is the best in most cases.