Paraiso : An Automated Tuning Framework for Explicit Solvers of Partial Differential Equations

We propose Paraiso, a domain specific language embedded in functional programming language Haskell, for automated tuning of explicit solvers of partial differential equations (PDEs) on GPUs as well as multicore CPUs. In Paraiso, one can describe PDE solving algorithms succinctly using tensor equations notation. Hydrodynamic properties, interpolation methods and other building blocks are described in abstract, modular, re-usable and combinable forms, which lets us generate versatile solvers from little set of Paraiso source codes. We demonstrate Paraiso by implementing a compressive hydrodynamics solver. A single source code less than 500 lines can be used to generate solvers of arbitrary dimensions, for both multicore CPUs and GPUs. We demonstrate both manual annotation based tuning and evolutionary computing based automated tuning of the program.Comment: 52 pages, 14 figures, accepted for publications in Computational Science and Discover

Direct Simulations of Particle Acceleration in Fluctuating Electromagnetic Field across a Shock

We simulate the acceleration processes of collisionless particles in a shock structure with magnetohydrodynamical (MHD) fluctuations. The electromagnetic field is represented as a sum of MHD shock solution (\Mag_0, \Ele_0) and torsional Alfven modes spectra (\delta \Mag, \delta \Ele ). We represent fluctuation modes in logarithmic wavenumber space. Since the electromagnetic fields are represented analytically, our simulations can easily cover as large as eight orders of magnitude in resonant frequency, and do not suffer from spatial limitations of box size or grid spacing. We deterministically calculate the particle trajectories under the Lorenz force for time interval of up to ten years, with a time step of $\sim 0.5 \sec$. This is sufficient to resolve Larmor frequencies without a stochastic treatment. Simulations show that the efficiency of the first order Fermi acceleration can be parametrized by the fluctuation amplitude $\eta \equiv ^{\frac 1 2} {B_0}^{-1}$ . Convergence of the numerical results is shown by increasing the number of wave modes in Fourier space while fixing $\eta$. Efficiency of the first order Fermi acceleration has a maximum at $\eta \simeq 10^1$. The acceleration rate depends on the angle between the shock normal and \Mag_0, and is highest when the angle is zero. Our method will provide a convenient tool for comparing collisionless turbulence theories with, for example, observations of bipolar structure of super nova remnants (SNRs) and shell-like synchrotron-radiating structure.Comment: 11 pages, 4 figures, accepted for publication in The Astrophysical Journal letter

無衝突乱流加速の数値シミュレーション

1.背景 2.乱流衝撃波における粒子加速のシミュレーション 3.MHD乱流における粒子のコヒーレント加

INTERDEPENDENCE OF ELECTRIC DISCHARGE AND MAGNETOROTATIONAL INSTABILITY IN PROTOPLANETARY DISKS

We study how the magnetorotational instability (MRI) in protoplanetary disks is affected by the electric discharge caused by the electric field in the resistive magnetohydrodynamic. We performed three-dimensional shearing box simulations with various values of plasma beta and electrical breakdown models. We find that the MRI is self-sustaining in spite of the high resistivity. The instability gives rise to the large electric field that causes the electrical breakdown, and the breakdown maintains the high degree of ionization required for the instability. The condition for this self-sustained MRI is set by the balance between the energy supply from the shearing motion and the energy consumed by ohmic dissipation. We apply the condition to various disk models and study where the active, self-sustained, and dead zones of MRI are located. In the fiducial minimum-mass solar-nebula model, the newly found sustained zone occupies only a limited volume of the disk. In the late-phase gas-depleted disk models, however, the sustained zone occupies a larger volume of the disk