Nowadays, heterogeneous on chip processors are the de facto standard in desktop and mobile platforms. This kind of chips are comprised of several CPU cores and one integrated accelerator as a GPU, a DSP or a FPGA. These heterogeneous chip architectures present new opportunities to improve overall applications performance and reduce energy consumption. This can be achieved by assigning part of the computations to the CPU cores and offloading other part to the accelerator. However, to fully exploit this type of architectures, the application workload has to be automatically distributed between both processors and it must be done by using the best granularity for each processor. These concerns are key to achieve an optimal performance, but it is specially challenging for irregular applications, whose computations can vary drastically during execution time. In this talk, we briefly introduce the different alternatives available in order to maximize resource utilization on heterogeneous chips, paying particular attention to energy consumption. We first tackle the HW side, summarizing the state-of-the-art regarding heterogeneous chips. Next, we delve into the SW part, presenting some of the programming models that can be used to exploit heterogeneous systems composed of several cores and GPUs of FPGAs. Finally, we present our proposals to optimize the parallel_for and pipeline templates so that the programmer can productively make the most out of heterogeneous systems.

In this talk we will comment about the progress in the development of the 4th-order PIRK method designed to integrate in time wave-like equations. This high-order method can be useful when more accuracy is needed but there are resolution restrictions like in the case of 3D simulations. Thanks to the particular structure of the considered equations and the efficient stability analysis done, 5-stages 4th-order PIRK method has been analized. We want to point out that, up to our knowledge, the derivation of available 4th-order methods with IMEX schemes is quite complex and their application restricted due to the inversion of operators.

Elliptic partial differential equations (ePDEs) appear in a wide variety of areas of mathematics, physics and engineering. Typically, ePDEs must be solved numerically, which sets an ever growing demand for efficient and highly parallel algorithms to tackle their computational solution. The Scheduled Relaxation Jacobi (SRJ) is apromising class of methods, atypical for combining simplicity andefficiency, that has been recently introduced for solving linearPoisson-like ePDEs. The SRJ methodology relies on computing the appropriate parameters of a multilevel approach with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances. The efficiency in the reduction of the residual increases with the number of levels employed in the algorithm. Applying the original methodology to compute the algorithm parameters with more than 5 levels notably hinders obtaining optimal SRJ algorithms, as the mixed (non-linear) algebraic-differential equations from which they result become notably stiff. Here we present a new methodology for obtaining the parameters of SRJ schemes that overcomes the limitations of the original algorithm and provide parameters for SRJ schemes with up to 15 levels and resolutions of up to 2^15 points per dimension, allowing for acceleration factors larger than several hundreds with respect to the Jacobi method. Furthermore, we extend the original algorithm to apply it to certain systems of non-linear ePDEs.

An elementary model of (1+1)-dimensional general relativity, known as “R=T”, is set up so that a relativistic Euler system of self-gravitating gas coupled to a Liouville equation for the metric's conformal factor are deduced. The resulting Euler--Liouville system is simulated, by means of a locally inertial Godunov scheme. Well-balanced discretizations rely on the treatment of source terms at each interface of the grid, hence the metric's conformal factor remains flat in every computational cell. External field approximations are carried out, too: a Klein--Gordon equation is studied along with a Dirac one inside an hydrostatic gravitational field induced by a static, piecewise constant mass repartition. (The talk corresponds to the paper which was recently published in SIAM J. of Applied Math.)

The observation of several neutron stars with relatively low values of the surface magnetic field found in supernova remnants has led in recent years to controversial interpretations. A possible explanation is the slow rotation of the proto-neutron star at birth which is unable to amplify its magnetic field to typical pulsar levels. An alternative possibility, the hidden magnetic field scenario, seems to be favoured over the previous one due to the observation of three low magnetic field magnetars. This scenario considers the accretion of the fallback of the supernova debris onto the neutron star as the responsible for the observed low magnetic field. We have studied under which conditions the magnetic field of a neutron star can be buried into the crust due to an accreting fluid. We have considered a 1D calculation in general relativity to estimate the balance between the incoming accretion flow an the magnetosphere. Our study includes several models with different entropy, composition (including nuclear statistical equilibrium) and neutron star masses.

Using a self-consistent formalism to obtain the macroscopic structure of a compact object in strong magnetic fields from its microscopic Lagrangian, incorporating all relevant magnetic field effects and full general relativity, we compute equilibrium configurations of a magnetized white dwarf. This has interesting implications for the observations of super-Chandrasekhar mass white dwarfs, which pose a challenge to the use of type Ia supernovae as standard candles. The magnetic fields of white dwarfs distort their shape generating an anisotropic moment of inertia. A magnetized white dwarf that rotates obliquely relative to the symmetry axis has a time varying mass quadrupole moment and thus would emit gravitational radiation. We estimate the gravitational wave emission from such fast rotating magnetised white dwarfs.

We present a realistic numerical model for rotating superfluid neutron stars in a full general relativistic framework. Following the work initiated by Prix, Novak and Comer [1], we compute stationary axisymmetric configurations of neutron stars composed of two fluids, namely superfluid neutrons and charged particles (protons and electrons), which are free to rotate around a common axis with different rigid rotation rates. This system is described by a realistic equation of state derived from a relativistic mean field theory using DDH parametrization including (or not) delta mesons. Then, we apply this model to investigate pulsar glitches in a very simple way. From a series of equilibrium states of a neutron star, assuming total baryon mass and total angular momentum to be constant, we compute the evolution in time of the properties of the star during a glitch. To do so, we model a glitch as a transfer of angular momentum from one fluid to the other, through the action of mutual friction force [2]. This enables us to infer characteristic features relative to glitches, such as rise timescales, which could be compared to future accurate observations. [1] Prix, R., Novak, J. and Comer, G. L., Relativistic numerical models for stationary superfluid neutron stars, Phys. Rev. D 71, 2005. [2] Langlois, D., Sedrakian, D. M. and Carter, B., Differential rotation of relativistic superfluid in neutron stars, MNRAS 297, 1998. Comments: work done in collaboration with M. Oertel and J. Novak.

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Collapse and explosion of massive stars depends critically on the transport of neutrinos and their interaction with matter. In the case of very massive stars forming very compact proto-neutron stars, GR terms such as the gravitational redshift can cause important modifications of the neutrino emission. I am going to report on the most recent update including these terms approximately in the special-relativistic neutrino-MHD code Aenus/ALCAR and discuss the results for stars of 35 solar masses.

We will present an extension of the MPI-AMRVAC code in the General Relativistic Hydrodynamics (GRHD) framework. This code has an Adaptive Mesh Refinement (AMR) to model matter evolution in the vicinity of any kinds of compact object. We have tested it in the context of various types of boson stars where metrics are calculated by KADATH library (Grandclement 2010). We introduce new tests that can be used to validate GRHD codes devoted to boson star accretion flow studies. We will present as well the difference between spherical accretion on Black holes and Boson stars.

Gravitational waves (GW) emitted during core-collapse supernovae open a new window into the central engine of the explosion. The late collapse, core bounce, and the early postbounce dynamics of a rotating core leads to a characteristic GW signal. I will present our study of the dependence of the GW signal on total angular momentum and its distribution in the progenitor core by means of a large set of axisymmetric general-relativistic simulations, in which we systematically vary the initial angular momentum distribution in the core. We find that the precise distribution of angular momentum is relevant only for very rapidly rotating cores with T/|W|≳8% at bounce. We show that Advanced LIGO could measure the total angular momentum and its distribution for most rapidly rotating cores. We test our results for robustness against systematic uncertainties by utilizing a different equation of state of nuclear matter and variations in the electron fraction in the inner core. The results of these tests show that these uncertainties significantly reduce the accuracy with which the total angular momentum and its precollapse distribution can be inferred from observations.

The spin of a neutron star at birth may be impacted by the asymmetric character of the explosion of its massive progenitor. During the first second after bounce, the spiral mode of the Standing Accretion Shock Instability (SASI) is able to redistribute angular momentum and spin-up a neutron star born from a non-rotating progenitor. Our aim is to determine if this process is robust/systematic. We perform 2D numerical simulations of a simplified setup in cylindrical geometry, using the RAMSES code, to investigate whether the dynamics is dominated by a spiral or a sloshing mode. We show that the spiral mode prevails only if the ratio of the initial shock radius to the neutron star radius exceeds a critical value. The amount of angular momentum redistributed by a spiral mode is compared to analytical estimates in the linear regime. Numerical simulations of the non-linear regime reveal significant stochastic variations including a reversal of the direction of rotation of the accretion shock. Impact of the initial rotation of the progenitor regarding these results is also discussed.

The purpose of this talk is to give an overview on our recent work about the development of certain classes of incomplete Riemann solvers. The word ""incomplete"" means here that it is not necessary to know the complete eigenstructure of the system under study, but only some partial information about it (usually, a bound on the maximum wave speed). In particular, we will focus on the following points: * PVM and RVM methods. * Approximate Osher solvers. * A Jacobian-free implementation of PVM-Chebyshev methods. Numerical tests will be given for the ideal Euler and MHD equations, but it will become clear that the proposed framework can be applied to other systems as well (e.g., multilayer shallow water).

Many interesting astrophysical phenomena possess a large spread of length and time scales. This makes computational approaches very challenging. To overcome the computational limitations, delicate trade-offs between numerical resolution and fidelity to the physical conservation laws have to be committed. This puts great robustness requirements on the employed numerical methods. For instance, many systems of conservation laws used to model physical phenomena posses companion laws. These companion laws are generically fulfilled by analytical solutions to the original system of conservation laws. However, when the discretized equations are solved on a computer, these companion laws may not be fulfilled anymore. A prominent example is the divergence constraint on the magnetic field in magnetohydrodynamics. A seemingly trivial example is the preservation of steady states, such as hydrostatic equilibrium. Another, nearly omni present companion law in astrophysics, is the conservation of angular momentum. Methods that preserve discretely certain companion laws of the original system of conservation laws have been termed as structure preserving. We will illustrate some recent developments of such schemes. Their need will be motivated through several challenging astrophysical scenarios, including the simulation of convection in stellar interiors, magneto-rotationally driven core-collapse supernovae and compact binary merger.

Accretion on compact objects is commonly considered the most plausible mechanism to power up a list of astrophysical systems (such as AGNs, GRBs, X-Ray Binaries, etc. . .) and in particular magnetic fields are believed to play a major role in enabling the accretion process through the development of magnetic instabilities. We investigate the effects of a finite resistivity in a magnetized plasma orbiting around a rotating black hole in a fully covariant framework, providing a self-consistent closure for the Ohm law and performing 3D GRMHD simulations with a highly parallelized version of the ECHO code. We studied in particular the development of the Papaloizou-Pringle instability (PPI) and how it is affected by non-ideal effects, starting with different magnetic configurations and disk models. We also investigate the effects of a mean-field dynamo closure on axisymmetric disks, in order to address the question about the origin of the large-scale magnetic fields required in such systems: starting from a kinematic regime, we extend previous results to take into account a fully dynamical development of the magnetic field through a quenched $\alpha\Omega$-dynamo.

The magnetorotational instability (MRI) is one of the most promising agents amplifying the magnetic fields in a core-collapse supernova explosion. Combining theoretical analysis and numerical simulations, we investigate whether magnetic fields can be increased to dynamically relevant strengths. We find that a secondary shear flow instability (Kelvin-Helmholtz) developing on top of MRI structures terminates the MRI driven amplification when the magnetic field strength has grown only by a constant factor of about twenty.

Mergers of two neutron stars or a neutron star with a black hole are short but very energetic events in which the temperatures and densities are so high that neutrino interactions become dynamically relevant. This makes it necessary to separately solve radiation-transport equations for the neutrinos along with the hydrodynamics equations for the fluid. In the talk I will briefly describe the Alcar-Aenus code, which evolves the coupled neutrino-hydrodynamics equations, and discuss our recent simulations of neutrino-powered jets from neutron-star merger remnants.

The most popular scenario for core-collapse supernova explosions relies on the joint action of neutrino heating from the young neutron star and hydrodynamic instabilities like convection in the post-shock convection. We now see the advent of the first successful 3D simulations of these explosions using multi-group neutrino transport as required to accurately model neutrino heating and cooling. While it turned out harder to trigger shock revival in 3D than in axisymmetric 2D models, successful explosion models suggest that 3D effects can be helpful after shock revival for brining the simulations more in line with observed supernova explosion energies as I shall argue in this talk. I shall also outline feature of the parallel version of CoCoNuT employed for some of these simulations and discuss its performance on large HPC machines in Australia and Europe.