Time Parallel Gravitational Collapse Simulation

This article demonstrates the applicability of the parallel-in-time method Parareal to the numerical solution of the Einstein gravity equations for the spherical collapse of a massless scalar eld. To account for the shrinking of the spatial domain in time, a tailored load balancing scheme is proposed and compared to load balancing based on number of time steps alone. The performance of Parareal is studied for both the sub-critical and black hole case; our experiments show that Parareal generates substantial speedup and, in the super-critical regime, can reproduce Choptuik's black hole mass scaling law

A Parallel Tree-SPH code for Galaxy Formation

We describe a new implementation of a parallel Tree-SPH code with the aim to simulate Galaxy Formation and Evolution. The code has been parallelized using SHMEM, a Cray proprietary library to handle communications between the 256 processors of the Silicon Graphics T3E massively parallel supercomputer hosted by the Cineca Supercomputing Center (Bologna, Italy). The code combines the Smoothed Particle Hydrodynamics (SPH) method to solve hydro-dynamical equations with the popular Barnes and Hut (1986) tree-code to perform gravity calculation with a NlogN scaling, and it is based on the scalar Tree-SPH code developed by Carraro et al(1998)[MNRAS 297, 1021]. Parallelization is achieved distributing particles along processors according to a work-load criterion. Benchmarks, in terms of load-balance and scalability, of the code are analyzed and critically discussed against the adiabatic collapse of an isothermal gas sphere test using 20,000 particles on 8 processors. The code results balanced at more that 95% level. Increasing the number of processors, the load-balance slightly worsens. The deviation from perfect scalability at increasing number of processors is almost negligible up to 32 processors. Finally we present a simulation of the formation of an X-ray galaxy cluster in a flat cold dark matter cosmology, using 200,000 particles and 32 processors, and compare our results with Evrard (1988) P3M-SPH simulations. Additionaly we have incorporated radiative cooling, star formation, feed-back from SNae of type II and Ia, stellar winds and UV flux from massive stars, and an algorithm to follow the chemical enrichment of the inter-stellar medium. Simulations with some of these ingredients are also presented.Comment: 19 pages, 14 figures, accepted for publication in MNRA

SAPPORO: A way to turn your graphics cards into a GRAPE-6

We present Sapporo, a library for performing high-precision gravitational N-body simulations on NVIDIA Graphical Processing Units (GPUs). Our library mimics the GRAPE-6 library, and N-body codes currently running on GRAPE-6 can switch to Sapporo by a simple relinking of the library. The precision of our library is comparable to that of GRAPE-6, even though internally the GPU hardware is limited to single precision arithmetics. This limitation is effectively overcome by emulating double precision for calculating the distance between particles. The performance loss of this operation is small (< 20%) compared to the advantage of being able to run at high precision. We tested the library using several GRAPE-6-enabled N-body codes, in particular with Starlab and phiGRAPE. We measured peak performance of 800 Gflop/s for running with 10^6 particles on a PC with four commercial G92 architecture GPUs (two GeForce 9800GX2). As a production test, we simulated a 32k Plummer model with equal mass stars well beyond core collapse. The simulation took 41 days, during which the mean performance was 113 Gflop/s. The GPU did not show any problems from running in a production environment for such an extended period of time.Comment: 13 pages, 9 figures, accepted to New Astronom

Can Nonlinear Hydromagnetic Waves Support a Self-Gravitating Cloud?

Using self-consistent magnetohydrodynamic (MHD) simulations, we explore the hypothesis that nonlinear MHD waves dominate the internal dynamics of galactic molecular clouds. We employ an isothermal equation of state and allow for self-gravity. We adopt ``slab-symmetry,'' which permits motions $\bf v_\perp$ and fields $\bf B_\perp$ perpendicular to the mean field, but permits gradients only parallel to the mean field. The Alfv\'en speed $v_A$ exceeds the sound speed $c_s$ by a factor $3-30$. We simulate the free decay of a spectrum of Alfv\'en waves, with and without self-gravity. We also perform simulations with and without self-gravity that include small-scale stochastic forcing. Our major results are as follows: (1) We confirm that fluctuating transverse fields inhibit the mean-field collapse of clouds when the energy in Alfv\'en- like disturbances remains comparable to the cloud's gravitational binding energy. (2) We characterize the turbulent energy spectrum and density structure in magnetically-dominated clouds. The spectra evolve to approximately $v_{\perp,\,k}^2\approx B_{\perp,\,k}^2/4\pi\rho\propto k^{-s}$ with $s\sim 2$, i.e. approximately consistent with a ``linewidth-size'' relation $\sigma_v(R) \propto R^{1/2}$. The simulations show large density contrasts, with high density regions confined in part by the fluctuating magnetic fields. (3) We evaluate the input power required to offset dissipation through shocks, as a function of $c_s/v_A$, the velocity dispersion $\sigma_v$, and the scale $\lambda$ of the forcing. In equilibrium, the volume dissipation rate is $5.5(c_s/v_a)^{1/2} (\lambda/L)^{-1/2}\times \rho \sigma_v^3/L$, for a cloud of linear size $L$ and density $\rho$. (4) Somewhat speculatively, we apply our results to a ``typical'' molecular cloud. The mechanical power input requiredComment: Accepted for publication in Ap.J. 47 pages, 13 postscript figures. Report also available at http://cfa-www.harvard.edu/~gammie/MHD.p