arXiv subjects

Naohito Nakasato

Publications and source records attributed to Naohito Nakasato.

At least 19 recordsLinked to original sources

arXiv2024

Evaluation of POSIT Arithmetic with Accelerators

We present an evaluation of 32-bit POSIT arithmetic through its implementation as accelerators on FPGAs and GPUs. POSIT, a floating-point number format, adaptively changes the size of its fractional part. We developed hardware designs for FPGAs and software for GPUs to accelerate linear algebra operations using Posit(32,2) arithmetic. Our FPGA- and GPU-based accelerators in Posit(32,2) arithmetic significantly accelerated the Cholesky and LU decomposition algorithms for dense matrices. In terms of numerical accuracy, Posit(32,2) arithmetic is approximately 0.5 - 1.0 digits more accurate than the standard 32-bit format, especially when the norm of the elements of the input matrix is close to 1. Evaluating power consumption, we observed that the power efficiency of the accelerators ranged between 0.043 - 0.076 Gflops/watts for the LU decomposition in Posit(32,2) arithmetic. The power efficiency of the latest GPUs as accelerators of Posit(32,2) arithmetic is better than that of the evaluated FPGA chip.

cs.DC↗

arXiv2023

Accelerating 128-bit Floating-Point Matrix Multiplication on FPGAs

General Matrix Multiplication (GEMM) is a fundamental operation widely used in scientific computations. Its performance and accuracy significantly impact the performance and accuracy of applications that depend on it. One such application is semidefinite programming (SDP), and it often requires binary128 or higher precision arithmetic to solve problems involving SDP stably. However, only some processors support binary128 arithmetic, which makes SDP solvers generally slow. In this study, we focused on accelerating GEMM with binary128 arithmetic on field-programmable gate arrays (FPGAs) to enable the flexible design of accelerators for the desired computations. Our binary128 GEMM designs on a recent high-performance FPGA achieved approximately 90GFlops, 147x faster than the computation executed on a recent CPU with 20 threads for large matrices. Using our binary128 GEMM design on the FPGA, we successfully accelerated two numerical applications: LU decomposition and SDP problems, for the first time.

cs.DC↗

arXiv2019

Double-Detonation Models for Type Ia Supernovae: Trigger of Detonation in Companion White Dwarfs and Signatures of Companions' Stripped-off Materials

We have studied double-detonation explosions in double-degenerate (DD) systems with different companion white dwarfs (WD) for modeling type Ia supernovae (SNe Ia) by means of high-resolution smoothed particle hydrodynamics (SPH) simulations. We have found that only the primary WDs explode in some of the DD systems, while the explosions of the primary WDs induce the explosions of the companion WDs in the other DD systems. The former case is so-called Dynamically-Driven Double-Degenerate Double-Detonation (D$^6$) explosion, or helium-ignited violent merger explosion. The supernova ejecta of the primary WDs strip materials from the companion WDs, whose mass is $\sim 10^{-3}M_\odot$. The stripped materials contain carbon and oxygen when the companion WDs are carbon-oxygen (CO) WDs with He shells $\lesssim 0.04M_\odot$. Since they contribute to low-velocity ejecta components as observationally interfered for iPTF14atg, D$^6$ explosions can be counterparts of sub-luminous SNe Ia. The stripped materials may contribute to low-velocity C seen in several SNe Ia. In the latter case, the companion WDs explode through He detonation if they are He WDs, and through double-detonation mechanism if they are CO WDs with He shells. We name these explosions "triple" and "quadruple" detonation (TD/QD) explosions after the number of detonations. The QD explosion may be counterparts of luminous SNe Ia, such as SN 1991T and SN 1999aa, since they yield a large amount of $^{56}$Ni, and their He-detonation products contribute to the early emissions accompanying such luminous SNe Ia. On the other hand, the TD explosion may not yield a sufficient amount of $^{56}$Ni to explain luminous SNe Ia.

astro-ph.HE↗

arXiv2018

Three-Dimensional Simulation of Double-Detonations in the Double-Degenerate Model for Type Ia Supernovae and Interaction of Ejecta with a Surviving White Dwarf Companion

We study the hydrodynamics and nucleosynthesis in the double-detonation model of Type Ia supernovae (SNe~Ia) and the interaction between the ejecta and a surviving white dwarf (WD) companion in the double-degenerate scenario. We set up a binary star system with $1.0M_\odot$ and $0.6M_\odot$ carbon-oxygen (CO) WDs, where the primary WD consists of a CO core and helium (He) shell with $0.95$ and $0.05M_\odot$, respectively. We follow the evolution of the binary star system from the initiation of a He detonation, ignition and propagation of a CO detonation, and the interaction of SN ejecta with the companion WD. The companion (or surviving) WD gets a flung-away velocity of $\sim 1700$~km~s$^{-1}$, and captures $^{56}$Ni of $\sim 0.03M_\odot$, and He of $3 \times 10^{-4}M_\odot$. Such He can be detected on the surface of surviving WDs. The SN ejecta contains a `companion-origin stream', and unburned materials stripped from the companion WD ($\sim 3 \cdot 10^{-3}M_\odot$), although the stream compositions would depend on the He shell mass of the companion WD. The ejecta has also a velocity shift of $\sim 1000$~km~s$^{-1}$ due to the binary motion of the exploding primary WD. These features would be prominent in nebular-phase spectra of oxygen emission lines from the unburned materials like SN~2010lp and iPTF14atg, and of blue- or red-shifted Fe-group emission lines from the velocity shift like a part of sub-luminous SNe~Ia. We expect SN~Ia counterparts to the D$^6$ model would leave these fingerprints for SN~Ia observations.

astro-ph.HE↗

arXiv2017

Does Explosive Nuclear Burning occur in Tidal Disruption Events of White Dwarfs by Intermediate Mass Black Holes ?

We investigate nucleosynthesis in tidal disruption events (TDEs) of white dwarfs (WDs) by intermediate mass black holes (IMBHs). We consider various types of WDs with different masses and compositions by means of 3 dimensional (3D) smoothed particle hydrodynamics (SPH) simulations. We model these WDs with different numbers of SPH particles, $N$, from a few $10^4$ to a few $10^7$, in order to check mass resolution convergence, where SPH simulations with $N>10^7$ (or a space resolution of several $10^6$ cm) have unprecedentedly high resolution in this kind of simulations. We find that nuclear reactions become less active with increasing $N$, and that these nuclear reactions are excited by spurious heating due to low resolution. Moreover, we find no shock wave generation. In order to investigate the reason for the absence of a shock wave, we additionally perform 1 dimensional (1D) SPH and mesh-based simulations with a space resolution ranging from $10^4$ to $10^7$ cm, using characteristic flow structure extracted from the 3D SPH simulations. We find shock waves in these 1D high-resolution simulations. One of these shock waves triggers a detonation wave. However, we have to be careful of the fact that, if the shock wave emerged at a bit outer region, it could not trigger the detonation wave due to low density. Note that the 1D initial conditions lack accuracy to precisely determine where a shock wave emerges. We need to perform 3D simulations with $\lesssim 10^6$ cm space resolution in order to conclude that WD TDEs become optical transients powered by radioactive nuclei.

astro-ph.HE↗

arXiv2016

The critical mass ratio of double white dwarf binaries for violent merger-induced Type Ia supernova explosions

Mergers of carbon-oxygen (CO) white dwarfs (WDs) are considered as one of the potential progenitors of type Ia supernovae (SNe Ia). Recent hydrodynamical simulations showed that the less massive (secondary) WD violently accretes onto the more massive (primary) one, carbon detonation occurs, the detonation wave propagates through the primary, and the primary finally explodes as a sub-Chandrasekhar mass SN Ia. Such an explosion mechanism is called the violent merger scenario. Based on the smoothed particle hydrodynamics (SPH) simulations of merging CO WDs, we derived more stringent critical mass ratio (qcr) leading to the violent merger scenario than the previous results. We conclude that this difference mainly comes from the differences in the initial condition, synchronously spinning of WDs or not. Using our new results, we estimated the brightness distribution of SNe Ia in the violent merger scenario and compared it with previous studies. We found that our new qcr does not significantly affect the brightness distribution. We present the direct outcome immediately following CO WD mergers for various primary masses and mass ratios. We also discussed the final fate of the central system of the bipolar planetary nebula Henize 2-428, which was recently suggested to be a double CO WD system whose total mass exceeds the Chandrasekhar-limiting mass, merging within the Hubble time. Even considering the uncertainties in the proposed binary parameters, we concluded that the final fate of this system is almost certainly a sub-Chandrasekhar mass SN Ia in the violent merger scenario.

astro-ph.HE↗

arXiv2015

A systematic study of carbon-oxygen white dwarf mergers: mass combinations for Type Ia supernovae

Mergers of two carbon-oxygen (CO) white dwarfs (WDs) have been considered as progenitors of Type Ia supernovae (SNe Ia). Based on smoothed particle hydrodynamics (SPH) simulations, previous studies claimed that mergers of CO WDs lead to an SN Ia explosion either in the dynamical merger phase or stationary rotating merger remnant phase. However, the mass range of CO WDs that lead to an SN Ia has not been clearly identified yet. In the present work, we perform systematic SPH merger simulations for the WD masses ranging from $0.5~M_{\odot}$ to $1.1~M_{\odot}$ with higher resolutions than the previous systematic surveys and examine whether or not carbon burning occurs dynamically or quiescently in each phase. We further study the possibility of SN Ia explosion and estimate the mass range of CO WDs that lead to an SN Ia. We found that when the both WDs are massive, i.e., in the mass range of $0.9~M_{\odot} {\le} M_{1,2} {\le} 1.1~M_{\odot}$, they can explode as an SN Ia in the merger phase. On the other hand, when the more massive WD is in the range of $0.7~M_{\odot} {\le} M_{1} {\le} 0.9~M_{\odot}$ and the total mass exceeds $1.38~M_{\odot}$, they can finally explode in the stationary rotating merger remnant phase. We estimate the contribution of CO WD mergers to the entire SN Ia rate in our galaxy to be of ${\lt} 9\%$. So, it might be difficult to explain all galactic SNe Ia by CO WD mergers.

astro-ph.HE↗

arXiv2015

Hydrodynamical evolution of merging carbon-oxygen white dwarfs: their pre-supernova structure and observational counterparts

We perform smoothed particle hydrodynamics (SPH) simulations for merging binary carbon-oxygen (CO) white dwarfs (WDs) with masses of $1.1$ and $1.0$ $M_\odot$, until the merger remnant reaches a dynamically steady state. Using these results, we assess whether the binary could induce a thermonuclear explosion, and whether the explosion could be observed as a type Ia supernova (SN Ia). We investigate three explosion mechanisms: a helium-ignition following the dynamical merger (`helium-ignited violent merger model'), a carbon-ignition (`carbon-ignited violent merger model'), and an explosion following the formation of the Chandrasekhar mass WD (`Chandrasekhar mass model'). An explosion of the helium-ignited violent merger model is possible, while we predict that the resulting SN ejecta are highly asymmetric since its companion star is fully intact at the time of the explosion. The carbon-ignited violent merger model can also lead to an explosion. However, the envelope of the exploding WD spreads out to $\sim 0.1R_\odot$; it is much larger than that inferred for SN 2011fe ($< 0.1R_\odot $) while much smaller than that for SN 2014J ($\sim 1R_\odot$). For the particular combination of the WD masses studied in this work, the Chandrasekhar mass model is not successful to lead to an SN Ia explosion. Besides these assessments, we investigate the evolution of unbound materials ejected through the merging process (`merger ejecta'), assuming a case where the SN Ia explosion is not triggered by the helium- or carbon-ignition during the merger. The merger ejecta interact with the surrounding interstellar medium, and form a shell. The shell has a bolometric luminosity of more than $2 \times 10^{35}$ ergs$^{-1}$ lasting for $\sim 2 \times 10^4$ yr. If this is the case, Milky Way should harbor about $10$ such shells at any given time.

astro-ph.HE↗

arXiv2014

A development of an accelerator board dedicated for multi-precision arithmetic operations and its application to Feynman loop integrals

Higher order corrections in perturbative quantum field theory are required for precise theoretical analysis to investigate new physics beyond the Standard Model. This indicates that we need to evaluate Feynman loop diagram with multi-loop integral which may require multi-precision calculation. We developed a dedicated accelerator system for multi-precision calculation (GRAPE9-MPX). We present performance results of our system for the case of Feynman two-loop box and three-loop selfenergy diagrams with multi-precision.

hep-ph↗

arXiv2014

GPU accelerated Hybrid Tree Algorithm for Collision-less N-body Simulations

We propose a hybrid tree algorithm for reducing calculation and communication cost of collision-less N-body simulations. The concept of our algorithm is that we split interaction force into two parts: hard-force from neighbor particles and soft-force from distant particles, and applying different time integration for the forces. For hard-force calculation, we can efficiently reduce the calculation and communication cost of the parallel tree code because we only need data of neighbor particles for this part. We implement the algorithm on GPU clusters to accelerate force calculation for both hard and soft force. As the result of implementing the algorithm on GPU clusters, we were able to reduce the communication cost and the total execution time to 40% and 80% of that of a normal tree algorithm, respectively. In addition, the reduction factor relative the normal tree algorithm is smaller for large number of processes, and we expect that the execution time can be ultimately reduced down to about 70% of the normal tree algorithm.

astro-ph.IM↗

arXiv2013

Type Ia Supernova Models and Progenitor Scenarios

We review some recent developments in theoretical studies on the connection between the progenitor systems of Type Ia supernovae (SNe Ia) and the explosion mechanisms. (1) DD-subCh: In the merging of double C+O white dwarfs (DD scenario), if the carbon detonation is induced near the white dwarf (WD) surface in the early dynamical phase, it could result in the (effectively) sub-Chandrasekhar mass explosion. (2) DD-Ch: If no surface C-detonation is ignited, the WD could grow until the Chandrasekhar mass is reached, but the outcome depends on whether the quiescent carbon shell burning is ignited and burns C+O into O+Ne+Mg. (3) SD-subCh: In the single degenerate (SD) scenario, if the He shell-flashes grow strong to induce a He detonation, it leads to the sub-Chandra explosion. (4) SD-Ch: If the He-shell flashes are not strong enough, they still produce interesting amount of Si and S near the surface of C+O WD before the explosion. In the Chandra mass explosion, the central density is high enough to produce electron capture elements, e.g., stable Ni-58. Observations of the emission lines of Ni in the nebular spectra provides useful diagnostics of the sub-Chandra vs. Chandra issue. The recent observations of relatively low velocity carbon near the surface of SNe Ia provide also interesting constraint on the explosion models.

astro-ph.SR↗

arXiv2012

Astrophysical Particle Simulations on Heterogeneous CPU-GPU Systems

A heterogeneous CPU-GPU node is getting popular in HPC clusters. We need to rethink algorithms and optimization techniques for such system depending on the relative performance of CPU vs. GPU. In this paper, we report a performance optimized particle simulation code "OTOO", that is based on the octree method, for heterogenous systems. Main applications of OTOO are astrophysical simulations such as N-body models and the evolution of a violent merger of stars. We propose optimal task split between CPU and GPU where GPU is only used to compute the calculation of the particle force. Also, we describe optimization techniques such as control of the force accuracy, vectorized tree walk, and work partitioning among multiple GPUs. We used OTOO for modeling a merger of two white dwarf stars and found that OTOO is powerful and practical to simulate the fate of the process.

astro-ph.IM↗

arXiv2011

Implementation of a Parallel Tree Method on a GPU

The kd-tree is a fundamental tool in computer science. Among other applications, the application of kd-tree search (by the tree method) to the fast evaluation of particle interactions and neighbor search is highly important, since the computational complexity of these problems is reduced from O(N^2) for a brute force method to O(N log N) for the tree method, where N is the number of particles. In this paper, we present a parallel implementation of the tree method running on a graphics processing unit (GPU). We present a detailed description of how we have implemented the tree method on a Cypress GPU. An optimization that we found important is localized particle ordering to effectively utilize cache memory. We present a number of test results and performance measurements. Our results show that the execution of the tree traversal in a force calculation on a GPU is practical and efficient.

astro-ph.IM↗

arXiv2011

Chemodynamical Simulations of the Milky Way Galaxy

We present chemodynamical simulations of a Milky Way-type galaxy using a self-consistent hydrodynamical code that includes supernova feedback and chemical enrichment, and predict the spatial distribution of elements from Oxygen to Zinc. In the simulated galaxy, the kinematical and chemical properties of the bulge, disk, and halo are consistent with the observations. The bulge formed from the assembly of subgalaxies at z>3, and has higher [alpha/Fe] ratios because of the small contribution from Type Ia Supernovae. The disk formed with a constant star formation over 13 Gyr, and shows a decreasing trend of [alpha/Fe] and increasing trends of [(Na,Al,Cu,Mn)/Fe] against [Fe/H]. However, the thick disk stars tend to have higher [alpha/Fe] and lower [Mn/Fe] than thin disk stars. We also predict the frequency distribution of elemental abundance ratios as functions of time and location, which can be directly compared with galactic archeology projects such as HERMES.

astro-ph.GA↗

arXiv2009

Fast Simulations of Gravitational Many-body Problem on RV770 GPU

The gravitational many-body problem is a problem concerning the movement of bodies, which are interacting through gravity. However, solving the gravitational many-body problem with a CPU takes a lot of time due to O(N^2) computational complexity. In this paper, we show how to speed-up the gravitational many-body problem by using GPU. After extensive optimizations, the peak performance obtained so far is about 1 Tflops.

astro-ph.IM↗

arXiv2007

Evolution of Collisionally Merged Massive Stars

We investigate the evolution of collisionally merged stars with mass of ~100 MSun which might be formed in dense star clusters. We assumed that massive stars with several tens Msun collide typically after ~1Myr of the formation of the cluster and performed hydrodynamical simulations of several collision events. Our simulations show that after the collisions, merged stars have extended envelopes and their radii are larger than those in the thermal equilibrium states and that their interiors are He-rich because of the stellar evolution of the progenitor stars. We also found that if the mass-ratio of merging stars is far from unity, the interior of the merger product is not well mixed and the elemental abundance is not homogeneous. We then followed the evolution of these collision products by a one dimensional stellar evolution code. After an initial contraction on the Kelvin-Helmholtz (thermal adjustment) timescale (~1000-10000 yr), the evolution of the merged stars traces that of single homogeneous stars with corresponding masses and abundances, while the initial contraction phase shows variations which depend on the mass ratio of the merged stars. We infer that, once runaway collisions have set in, subsequent collisions of the merged stars take place before mass loss by stellar winds becomes significant. Hence, stellar mass loss does not inhibit the formation of massive stars with mass of ~1000Msun.

astro-ph↗

arXiv2003

3-D Simulations of the Chemical and Dynamical Evolution of the Galactic Bulge

A three-dimensional hydrodynamical N-body model for the formation of the Galaxy is presented with special attention to the formation of the bulge component. Starting with cosmologically motivated initial conditions, we obtain a qualitatively similar stellar system to the Galaxy. Then we analyze the chemical and kinematic properties of the bulge stars in our model and find qualitative agreement with observational data. The early evolution of our model has revealed that most bulge stars form during the sub-galactic merger (merger component of the bulge stars). Because of the strong star burst induced by the merger, the metallicity distribution function of such stars becomes as wide as observed. We find that another group of the bulge stars forms later in the inner region of the disk (non-merger component of the bulge stars). Because of the difference in the formation epoch, the main source of iron for this group of stars is different from the merger component. Iron in the merger and non-merger components comes mainly from Type II and Type Ia supernovae, respectively. Since a Type Ia supernova ejects $\sim$ 10 times more iron than a Type II supernova, [Fe/H] of the non-merger component tends to be higher than that of the merger component, which widens the metallicity distribution function. From these results, we suggest that the Galactic bulge consists of two chemically different components; one has formed quickly through the sub-galactic clump merger in the proto-galaxy and the other has formed gradually in the inner disk.

astro-ph↗

arXiv2000

Metal Enrichment of The Primordial Interstellar Medium through 3-D Hydrodynamical Evolution of The First Supernova Remnant

The long-term evolution of supernova remnants (SNRs) in the primordial interstellar medium (ISM) with an inhomogeneous structure is calculated to investigate metal enrichment of the primordial gas. For this purpose, we have constructed a parallel 3-D hydrodynamics code incorporating the radiative cooling and self-gravity. The self-gravity and radiative cooling develop the inhomogeneous structure of the ISM from a small perturbation with a power-law spectrum. The resultant density ranges from 0.5 cm$^{-3}$ to 10$^6$ cm $^{-3}$. Calculations for a supernova (SN) with the progenitor mass of 20 solar mass are performed as the first step of a series of our study. It is found from the results that a single SN distributes some of newly synthesized heavy elements into a dense filament of the ISM with densities ranging from 100 to 10$^4$ cm$^{-3}$ depending on where the SN explodes. Thus, the metallicity [Mg/H] of the dense filaments polluted by the SN ejecta becomes $-2.7\pm0.5$. From these filaments, the first Population II stars will form. This value is in accordance with the previous analytical work (Shigeyama & Tsujimoto 1998) with accuracy of $\sim 0.3$ dex.

astro-ph↗