I'll overview the past, present, and future of the GRAPE project, which started as the effort to design and develop specialized hardware for gravitational N-body problem. The current hardware, GRAPE-DR, has an architecture quite different from previous GRAPEs, in the sense that it is a collection of small, but programmable processors, while previous GRAPEs had hardwired pipelines. I'll discuss pros and cons of these two approaches, comparisons with other accelerators and future directions.

Graphics Processing Units (GPUs) offer a new way to accelerate numerical calculations by means of on-board massive parallelisation. We discuss two examples of GPU implementation relevant for cosmological simulations, an N-Body Particle-mesh solver and a radiative transfer code. The latter has also been ported on multi-GPU clusters. The range of acceleration (x30-x80) achieved here offer bright perspective for large scale simulations driven by GPUs.

GAMER is a GPU-accelerated Adaptive-MEsh-Refinement code for astrophysical simulations. In this work, two further extensions of the code are reported. First, we have implemented the MUSCL-Hancock method with the Roe's Riemann solver for the hydrodynamic evolution, by which the accuracy, overall performance and the GPU versus CPU speed-up factor are improved. Second, we have implemented the out-of-core computation, which utilizes the large storage space of multiple hard disks as the additional run-time virtual memory and permits an extremely large problem to be solved in a relatively small-size GPU cluster. The communication overhead associated with the data transfer between the parallel hard disks and the main memory is carefully reduced by overlapping it with the CPU/GPU computations.

According to a Top500.org compilation, large computer systems have been doubling in sustained speed every 1.14 years for the last 17 years. If this rapid growth continues, we will have computers by 2020 that can execute an Exaflop (1018) per second. Storage is also improving in cost and density at an exponential rate. Several innovations that will accompany this growth are reviewed here, including shrinkage of basic circuit components on Silicon, three-dimensional integration, and Phase Change Memory. Further growth will require new technologies, most notably those surrounding the basic building block of computers, the Field Effect Transistor. Implications of these changes for the types of problems that can be solved are briefly discussed.

We developed a fast numerical scheme for solving ambipolar diffusion MHD equations with the strong coupling approximation, which can be written as the ideal MHD equations with an additional ambipolar diffusion term in the induction equation. The mass, momentum, magnetic fluxes due to the ideal MHD equations can be easily calculated by any Godunov-type schemes. Additional magnetic fluxes due to the ambipolar diffusion term are added in the magnetic fluxes, because of two same spatial gradients operated on the advection fluxes and the ambipolar diffusion term. In this way, we easily kept divergence-free magnetic fields using the constraint transport scheme. In order to overcome a small time step imposed by ambipolar diffusion, we used the super time stepping method. The resultant scheme is fast and robust enough to do the long term evolution of star formation simulations. We also proposed that the decay of alfen by ambipolar diffusion be a good test problem for our codes.

Ambipolar diffusion (AD) is a key process in molecular clouds (MCs). Non-ideal MHD turbulence simulations are technically very challenging because of the large Alfvén speed of ions in weakly ionized clouds. Using the Heavy-Ion Approximation method (Li, McKee & Klein 2006), we have carried out two-fluid simulations of AD in isothermal, turbulent boxes at a resolution of 5123, to investigate the effect of AD on the weakly ionized turbulence in MCs. Our simulation results show that the neutral gas component of the two-fluid system gradually transforms from an ideal MHD turbulence system to near a pure hydrodynamic turbulence system within the standard AD regime, in which the neutrals and ions are coupled over a flow time. The change of the turbulent state has a profound effect on the weakly ionized MCs.

We implemented sink particles in the Adaptive Mesh Refinement (AMR) code FLASH to model the gravitational collapse and accretion in turbulent molecular clouds and cores. Sink particles are frequently used to measure properties of star formation in numerical simulations, such as the star formation rate and efficiency, and the mass distribution of stars. We show that only using a density threshold for sink particle creation is insufficient in case of supersonic flows, because the density can exceed the threshold in strong shocks that do not necessarily lead to local collapse. Additional physical collapse indicators have to be considered. We apply our AMR sink particle module to the formation of a star cluster, and compare it to a Smoothed Particle Hydrodynamics (SPH) code with sink particles. Our comparison shows encouraging agreement of gas and sink particle properties between the AMR and SPH code.

We present the first results of a large suite of convergence tests between Adaptive Mesh Refinement (AMR) Finite Difference Hydrodynamics and Smoothed Particle Hydrodynamics (SPH) simulations of the non-linear thin shell instability and the Kelvin-Helmholtz instability. We find that the two methods converge in the limit of high resolution and accuracy. AMR and SPH simulations of the non-linear thin shell instability converge with each other with standard algorithms and parameters. The Kelvin-Helmholtz instability in SPH requires both an artificial conductivity term and a kernel with larger compact support and more neighbours (e.g. the quintic kernel) in order converge with AMR. For purely hydrodynamical problems, SPH simulations take an order of magnitude longer than the grid code when converged.

Radiative Transfer (RT) is considered to be one of the four Grand Challenges in Computational Astrophysics aside of Astrophysical Fluid Dynamics, N-Body Problems in Astrophysics, and Relativistic Astrophysics. The high dimensionality (7D instead of 4D for MHD) and the underlying integro-differential transport equation have forced coders to implement approximative RT methods in order to fit spectra and images or to treat RT in their HD and MHD codes.

The central role of RT in star formation (SF) is based on several facts: a) The dense dusty gas in SF regions alters the radiation substantially making SF one of the most complex applications of RT. b) Radiation transports energy within the object and is therefore an essential part of any dynamical SF model. c) RT calculations tell us which of the processes/structures are visible at what wavelength by which telescope/instrument. Hence, RT is the central tool to analyze simulation results or to explore the scientific capabilities of planned instruments. d) With inverse RT, we can obtain the 1D-3D density and temperature structure from observations, completely decoupled from any (M)HD modeling (and the approximations made within).

In this review, we summarize the main difficulties and the currently used computational techniques to calculate the RT in SF regions. Recent applications of 3D continuum RT in molecular clouds and disks around young massive stars are discussed to illustrate the capabilities and limits of current RT modeling.

Information of astronomical objects is obtained mainly through their radiation. Thus, the radiative transfer problem has a central role in all astrophysical research. Basic radiative transfer analysis or more complex modeling is needed both to interpret observations and to make predictions on the basis of numerical models. In this paper I will discuss radiative transfer in the context of interstellar molecular clouds where the main scientific questions involve the structure and evolution of the clouds and the star formation process. The studies rely on the analysis of spectral line and dust continuum observations. After a discussion of the corresponding radiative transfer methods, I will examine some of the current challenges in the field. Finally, I will present three studies where radiative transfer modeling pays a central role: the polarized dust emission, the Zeeman effect in emission lines, and the continuum emission from dense cloud cores.

Submillimeter observations are a key for answering many of the big questions in modern-day astrophysics, such as how stars and planets form, how galaxies evolve, and how material cycles through stars and the interstellar medium. With the upcoming large submillimeter facilities ALMA and Herschel a new window will open to study these questions. ARTIST is a project funded in context of the European ASTRONET program with the aim of developing a next generation model suite for comprehensive multi-dimensional radiative transfer calculations of the dust and line emission, as well as their polarization, to help interpret observations with these groundbreaking facilities.

The determination of prestellar core structure is often based on observations of (sub)millimeter dust continuum. However, recently the Spitzer Space Telescope provided us with IR images of many objects not only in emission but also in absorption. We developed a technique to reconstruct the density and temperature distributions of protostellar objects based on radiation transfer (RT) simulations both in mm and IR wavelengths. Best-fit model parameters are obtained with the genetic algorithm. We apply the method to two cores of Infrared Dark Clouds and show that their observations are better reproduced by a model with an embedded heating source despite the lack of 70 μm emission in one of these cores. Thus, the starless nature of massive cores can only be established with the careful case-by-case RT modeling.

I review the progress of SPH calculations for modelling galaxies, and resolving gas dynamics on GMC scales. SPH calculations first investigated the response of isothermal gas to a spiral potential, in the absence of self gravity and magnetic fields. Surprisingly though, even these simple calculations displayed substructure along the spiral arms. Numerical tests indicate that this substructure is still present at high resolution (100 million particles, ~10 pc), and is independent of the initial particle distribution. One interpretation of the formation of substructure is that smaller clouds can agglomerate into more massive GMCs via dissipative collisions. More recent calculations have investigated how other processes, such as the thermodynamics of the ISM, and self gravity affect this simple picture. Further research has focused on developing models with a more realistic spiral structure, either by including stars, or incorporating a tidal interaction.

Star formation depends on the available gaseous “fuel” as well as galactic environment, with higher specific star formation rates where gas is predominantly molecular and where stellar (and dark matter) densities are higher. The partition of gas into different thermal components must itself depend on the star formation rate, since a steady state distribution requires a balance between heating (largely from stellar UV for the atomic component) and cooling. In this presentation, I discuss a simple thermal and dynamical equilibrium model for the star formation rate in disk galaxies, where the basic inputs are the total surface density of gas and the volume density of stars and dark matter, averaged over ~kpc scales. Galactic environment is important because the vertical gravity of the stars and dark matter compress gas toward the midplane, helping to establish the pressure, and hence the cooling rate. In equilibrium, the star formation rate must evolve until the gas heating rate is high enough to balance this cooling rate and maintain the pressure imposed by the local gravitational field. In addition to discussing the formulation of this equilibrium model, I review the current status of numerical simulations of multiphase disks, focusing on measurements of quantities that characterize the mean properties of the diffuse ISM. Based on simulations, turbulence levels in the diffuse ISM appear relatively insensitive to local disk conditions and energetic driving rates, consistent with observations. It remains to be determined, both from observations and simulations, how mass exchange processes control the ratio of cold-to-warm gas in the atomic ISM.

This brief review emphasizes the wide range of environments where interaction induced star formation occurs. In these environments we can study the numerous elaborations of a few basic physical processes, including: gravitational instability, accretion and large-scale shocks.

We studied the formation process of star clusters using high-resolution N-body/smoothed particle hydrodynamics simulations of colliding galaxies. The total number of particles is 1.2×108 for our high resolution run. The gravitational softening is 5 pc and we allow gas to cool down to ~10 K. During the first encounter of the collision, a giant filament consists of cold and dense gas found between the progenitors by shock compression. A vigorous starburst took place in the filament, resulting in the formation of star clusters. The mass of these star clusters ranges from 105−8M⊙. These star clusters formed hierarchically: at first small star clusters formed, and then they merged via gravity, resulting in larger star clusters.

The interstellar medium (ISM) in galaxies is multiphase and cloudy, with stars forming in the very dense, cold gas found in Giant Molecular Clouds (GMCs). Simulating the evolution of an entire galaxy, however, is a computational problem which covers many orders of magnitude, so many simulations cannot reach densities high enough or temperatures low enough to resolve this multiphase nature. Therefore, the formation of GMCs is not captured and the resulting gas distribution is smooth, contrary to observations. We investigate how star formation (SF) proceeds in simulated galaxies when we obtain parsec-scale resolution and more successfully capture the multiphase ISM. Both major mergers and the accretion of cold gas via filaments are dominant contributors to a galaxy's total stellar budget and we examine SF at high resolution in both of these contexts.

Major progress has been made over the last few years in understanding hydrodynamical processes on cosmological scales, in particular how galaxies get their baryons. There is increasing recognition that a large part of the baryons accrete smoothly onto galaxies, and that internal evolution processes play a major role in shaping galaxies – mergers are not necessarily the dominant process. However, predictions from the various assembly mechanisms are still in large disagreement with the observed properties of galaxies in the nearby Universe. Small-scale processes have a major impact on the global evolution of galaxies over a Hubble time and the usual sub-grid models account for them in a far too uncertain way. Understanding when, where and at which rate galaxies formed their stars becomes crucial to understand the formation of galaxy populations. I discuss recent improvements and current limitations in “resolved” modeling of star formation, aiming at explicitly capturing star-forming instabilities, in cosmological and galaxy-sized simulations. Such models need to develop three-dimensional turbulence in the ISM, which requires parsec-scale resolution at redshift zero.

We report results from numerical simulations of star formation in the early universe that focus on the role of subsonic turbulence, and investigate whether it can induce fragmentation of the gas. We find that dense primordial gas is highly susceptible to fragmentation, even for rms turbulent velocity dispersions as low as 20% of the initial sound speed. The resulting fragments cover over two orders of magnitude in mass, ranging from ~0.1 M⊙ to ~40 M⊙. However, our results suggest that the details of the fragmentation depend on the local properties of the turbulent velocity field and hence we expect considerable variations in the resulting stellar mass spectrum in different halos.

Cosmological Adaptive Mesh Refinement simulations are used to study the specific star formation rate (sSFR=SSF/Ms) history and the stellar mass fraction, fs=Ms/MT, of small galaxies, total masses MT between few × 1010 M⊙ to few ×1011 M⊙. Our results are compared with recent observational inferences that show the so-called “downsizing in sSFR” phenomenon: the less massive the galaxy, the higher on average is its sSFR, a trend seen at least since z ~ 1. The simulations are not able to reproduce this phenomenon, in particular the high inferred values of sSFR, as well as the low values of fs constrained from observations. The effects of resolution and sub-grid physics on the SFR and fs of galaxies are discussed.