We study the simulation of stellar mergers, which requires complex simulations with high computational demands. We have developed Octo-Tiger, a finite volume grid-based hydrodynamics simulation code with Adaptive Mesh Refinement which is unique in conserving both linear and angular momentum to machine precision. To face the challenge of increasingly complex, diverse, and heterogeneous HPC systems, Octo-Tiger relies on high-level programming abstractions. We use HPX with its futurization capabilities to ensure scalability both between nodes and within, and present first results replacing MPI with libfabric achieving up to a 2.8x speedup. We extend Octo-Tiger to heterogeneous GPU-accelerated supercomputers, demonstrating node-level performance and portability. We show scalability up to full system runs on Piz Daint. For the scenario's maximum resolution, the compute-critical parts (hydrodynamics and gravity) achieve 68.1 parallel efficiency at 2048 nodes.
There are several studies that investigate the structure of mass loss in V1309 Scorpii through computer simulation. One approach to modeling this system is smoothed-particle hydrodynamics (SPH). Notable SPH applications include StarSmasher @cite_44 @cite_18 (a fork of StarCrash @cite_8 ) and an unpublished code developed by a collaboration of researchers from Princeton University, Columbia University, and Osaka University @cite_45 @cite_31 . An alternative approach is to use the finite volume method to simulate mass transfer. Examples of such applications include Athena @cite_38 @cite_57 and its rewrite named Athena++ @cite_19 @cite_9 @cite_6 . Lastly, Enzo @cite_20 is a project that implements finite volume hydrodynamics along with a collisionless N-body module that can be used to simulate binary systems where one component is taken to be a point mass. With the exception of SPH codes using direct summation for gravity, is unique among three-dimensional self-gravitating hydrodynamics codes in that it simultaneously conserves both linear and angular momentum to machine precision. SPH codes using direct summation for gravity are limited to only a few thousand particles, making the better choice for high resolution simulations.
@cite_38 @cite_18 @cite_8 @cite_9 @cite_6 @cite_44 @cite_57 @cite_19 @cite_45 @cite_31 @cite_20
20410181 2041945014 2040246849 2116091257 2167106676 2115513040 2066986143 2118972993 2021150171 2763929764 2810967842 2129152507 2100986500 2196561007 2024343295 1978656738 2170078675 2128539477 2065217711 2031810620
In this paper, we propose an interactive method based on Smoothed Particle Hydrodynamics (SPH) to simulate blood as a fluid with free surfaces. While SPH was originally designed to simulate astronomical objects, we gear the method towards fluid simulation by deriving the force density fields directly from the Navier-Stokes equation and by adding a term to model surface tension effects. In contrast to Eulerian grid-based approaches, the particle-based approach makes mass conservation equations and convection terms dispensable which reduces the complexity of the simulation. In addition, the particles can directly be used to render the surface of the fluid. Our method can be used in interactive surgical training systems with models of up to 3000 particles. We propose a new ghost fluid approach for free surface and solid boundary conditions in Smoothed Particle Hydrodynamics (SPH) liquid simulations. Prior methods either suffer from a spurious numerical surface tension artifact or drift away from the mass conservation constraint, and do not capture realistic cohesion of liquid to solids. Our Ghost SPH scheme resolves this with a new particle sampling algorithm to create a narrow layer of ghost particles in the surrounding air and solid, with careful extrapolation and treatment of fluid variables to reflect the boundary conditions. We also provide a new, simpler form of artificial viscosity based on XSPH. Examples demonstrate how the new approach captures real liquid behaviour previously unattainable by SPH with very little extra cost. This paper presents a new variational framework for various existing Smooth Particle Hydrodynamic (SPH) techniques and presents a new corrected SPH formulation. The linear and angular momentum preserving properties of SPH formulations are also discussed. The paper will show that in general in order to preserve angular momentum, the SPH equations must correctly evaluate the gradient of a linear velocity field. A corrected algorithm that combines kernel correction with gradient correction is presented. The paper will illustrate the theory presented with several examples relating to simple free surface flows. A new code for astrophysical magnetohydrodynamics (MHD) is described. The code has been designed to be easily extensible for use with static and adaptive mesh refinement. It combines higher order Godunov methods with the constrained transport (CT) technique to enforce the divergence-free constraint on the magnetic field. Discretization is based on cell-centered volume averages for mass, momentum, and energy, and face-centered area averages for the magnetic field. Novel features of the algorithm include (1) a consistent framework for computing the time- and edge-averaged electric fields used by CT to evolve the magnetic field from the time- and area-averaged Godunov fluxes, (2) the extension to MHD of spatial reconstruction schemes that involve a dimensionally split time advance, and (3) the extension to MHD of two different dimensionally unsplit integration methods. Implementation of the algorithm in both C and FORTRAN95 is detailed, including strategies for parallelization using domain decomposition. Results from a test suite which includes problems in one-, two-, and three-dimensions for both hydrodynamics and MHD are given, not only to demonstrate the fidelity of the algorithms, but also to enable comparisons to other methods. The source code is freely available for download on the web. This paper presents an algorithmic approach for improving the performance of many types of stochastic dynamical simulations. The approach is to redesign existing algorithms that use sparse matrix-vector products (SPMV) with single vectors to instead use a more efficient kernel, the generalized SPMV (GSPMV), which computes with multiple vectors simultaneously. In this paper, we show how to redesign a dynamical simulation to exploit GSPMV in way that is not initially obvious because only one vector is available at a time. We study the performance of GSPMV as a function of the number of vectors, and demonstrate the use of GSPMV in the Stokesian dynamics method for the simulation of the motion of macromolecules in the cell. Specifically, for our application, we find that with modern multicore Intel microprocessors in clusters of up to 64 nodes, we can typically multiply by 8 to 16 vectors in only twice the time required to multiply by a single vector. After redesigning the Stokesian dynamics algorithm to exploit GSPMV, we measure a 30 percent speedup in performance in single-node, data parallel simulations. In fluid simulation, enforcing incompressibility is crucial for realism; it is also computationally expensive. Recent work has improved efficiency, but still requires time-steps that are impractical for real-time applications. In this work we present an iterative density solver integrated into the Position Based Dynamics framework (PBD). By formulating and solving a set of positional constraints that enforce constant density, our method allows similar incompressibility and convergence to modern smoothed particle hydro-dynamic (SPH) solvers, but inherits the stability of the geometric, position based dynamics method, allowing large time steps suitable for real-time applications. We incorporate an artificial pressure term that improves particle distribution, creates surface tension, and lowers the neighborhood requirements of traditional SPH. Finally, we address the issue of energy loss by applying vorticity confinement as a velocity post process. We propose a momentum-conserving two-way coupling method of SPH fluids and arbitrary rigid objects based on hydrodynamic forces. Our approach samples the surface of rigid bodies with boundary particles that interact with the fluid, preventing deficiency issues and both spatial and temporal discontinuities. The problem of inhomogeneous boundary sampling is addressed by considering the relative contribution of a boundary particle to a physical quantity. This facilitates not only the initialization process but also allows the simulation of multiple dynamic objects. Thin structures consisting of only one layer or one line of boundary particles, and also non-manifold geometries can be handled without any additional treatment. We have integrated our approach into WCSPH and PCISPH, and demonstrate its stability and flexibility with several scenarios including multiphase flow. Abstract Since the seminal work of [Sussman, M, Smereka P, Osher S. A level set approach for computing solutions to incompressible two-phase flow. J Comput Phys 1994;114:146–59] on coupling the level set method of [Osher S, Sethian J. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J Comput Phys 1988;79:12–49] to the equations for two-phase incompressible flow, there has been a great deal of interest in this area. That work demonstrated the most powerful aspects of the level set method, i.e. automatic handling of topological changes such as merging and pinching, as well as robust geometric information such as normals and curvature. Interestingly, this work also demonstrated the largest weakness of the level set method, i.e. mass or information loss characteristic of most Eulerian capturing techniques. In fact, [Sussman M, Smereka P, Osher S. A level set approach for computing solutions to incompressible two-phase flow. J Comput Phys 1994;114:146–59] introduced a partial differential equation for battling this weakness, without which their work would not have been possible. In this paper, we discuss both historical and most recent works focused on improving the computational accuracy of the level set method focusing in part on applications related to incompressible flow due to both of its popularity and stringent accuracy requirements. Thus, we discuss higher order accurate numerical methods such as Hamilton–Jacobi WENO [Jiang G-S, Peng D. Weighted ENO schemes for Hamilton–Jacobi equations. SIAM J Sci Comput 2000;21:2126–43], methods for maintaining a signed distance function, hybrid methods such as the particle level set method [Enright D, Fedkiw R, Ferziger J, Mitchell I. A hybrid particle level set method for improved interface capturing. J Comput Phys 2002;183:83–116] and the coupled level set volume of fluid method [Sussman M, Puckett EG. A coupled level set and volume-of-fluid method for computing 3d and axisymmetric incompressible two-phase flows. J Comput Phys 2000;162:301–37], and adaptive gridding techniques such as the octree approach to free surface flows proposed in [Losasso F, Gibou F, Fedkiw R. Simulating water and smoke with an octree data structure, ACM Trans Graph (SIGGRAPH Proc) 2004;23:457–62]. Recent advances on human motion analysis have made the extraction of human skeleton structure feasible, even from single depth images. This structure has been proven quite informative for discriminating actions in a recognition scenario. In this context, we propose a local skeleton descriptor that encodes the relative position of joint quadruples. Such a coding implies a similarity normalisation transform that leads to a compact (6D) view-invariant skelet al feature, referred to as skelet al quad. Further, the use of a Fisher kernel representation is suggested to describe the skelet al quads contained in a (sub)action. A Gaussian mixture model is learnt from training data, so that the generation of any set of quads is encoded by its Fisher vector. Finally, a multi-level representation of Fisher vectors leads to an action description that roughly carries the order of sub-action within each action sequence. Efficient classification is here achieved by linear SVMs. The proposed action representation is tested on widely used datasets, MSRAction3D and HDM05. The experimental evaluation shows that the proposed method outperforms state-of-the-art algorithms that rely only on joints, while it competes with methods that combine joints with extra cues. Binary stars commonly pass through phases of direct interaction which result in the rapid loss of mass, energy, and angular momentum. Though crucial to understanding the fates of these systems, including their potential as gravitational wave sources, this short-lived phase is poorly understood and has thus far been unambiguously observed in only a single event, V1309 Sco. Here we show that the complex and previously-unexplained photometric behavior of V1309 Sco prior to its main outburst results naturally from the runaway loss of mass and angular momentum from the outer Lagrange point, which lasts for thousands of orbits prior to the final dynamical coalescence, much longer than predicted by contemporary models. This process enshrouds the binary in a "death spiral" outflow, which affects the amplitude and phase modulation of its light curve, and contributes to driving the system together. The total amount of mass lost during this gradual phase ( @math ) rivals the mass lost during the subsequent dynamical interaction phase, which has been the main focus of "common envelope" modeling so far. Analogous features in related transients suggest that this behavior is ubiquitous. Abstract Many current successful Person Re-Identification (ReID) methods train a model with the softmax loss function to classify images of different persons and obtain the feature vectors at the same time. However, the underlying feature embedding space is ignored. In this paper, we use a modified softmax function, termed Sphere Softmax, to solve the classification problem and learn a hypersphere manifold embedding simultaneously. A balanced sampling strategy is also introduced. Finally, we propose a convolutional neural network called SphereReID adopting Sphere Softmax and training a single model end-to-end with a new warming-up learning rate schedule on four challenging datasets including Market-1501, DukeMTMC-reID, CHHK-03, and CUHK-SYSU. Experimental results demonstrate that this single model outperforms the state-of-the-art methods on all four datasets without fine-tuning or re-ranking. For example, it achieves 94.4 rank-1 accuracy on Market-1501 and 83.9 rank-1 accuracy on DukeMTMC-reID. The code and trained weights of our model will be released. Abstract This paper reports large-scale direct numerical simulations of homogeneous-isotropic fluid turbulence, achieving sustained performance of 1.08 petaflop s on gpu hardware using single precision. The simulations use a vortex particle method to solve the Navier–Stokes equations, with a highly parallel fast multipole method ( fmm ) as numerical engine, and match the current record in mesh size for this application, a cube of 4096 3 computational points solved with a spectral method. The standard numerical approach used in this field is the pseudo-spectral method, relying on the fft algorithm as the numerical engine. The particle-based simulations presented in this paper quantitatively match the kinetic energy spectrum obtained with a pseudo-spectral method, using a trusted code. In terms of parallel performance, weak scaling results show the fmm -based vortex method achieving 74 parallel efficiency on 4096 processes (one gpu per mpi process, 3 gpu s per node of the tsubame -2.0 system). The fft -based spectral method is able to achieve just 14 parallel efficiency on the same number of mpi processes (using only cpu cores), due to the all-to-all communication pattern of the fft algorithm. The calculation time for one time step was 108 s for the vortex method and 154 s for the spectral method, under these conditions. Computing with 69 billion particles, this work exceeds by an order of magnitude the largest vortex-method calculations to date. Abstract The purpose of this study is to find a combination of optimal numerical algorithms for time-stepping and mode-splitting suitable for a high-resolution, free-surface, terrain-following coordinate oceanic model. Due to mathematical feedback between the baroclinic momentum and tracer equations and, similarly, between the barotropic momentum and continuity equations, it is advantageous to treat both modes so that, after a time step for the momentum equation, the computed velocities participate immediately in the computation of tracers and continuity, and vice versa, rather than advancing all equations for one time step simultaneously. This leads to a new family of time-stepping algorithms that combine forward–backward feedback with the best known synchronous algorithms, allowing an increased time step due to the enhanced internal stability without sacrificing its accuracy. Based on these algorithms we design a split-explicit hydrodynamic kernel for a realistic oceanic model, which addresses multiple numerical issues associated with mode splitting. This kernel utilizes consistent temporal averaging of the barotropic mode via a specially designed filter function to guarantee both exact conservation and constancy preservation properties for tracers and yields more accurate (up to second-order), resolved barotropic processes, while preventing aliasing of unresolved barotropic signals into the slow baroclinic motions. It has a more accurate mode-splitting due to redefined barotropic pressure-gradient terms to account for the local variations in density field, while maintaining the computational efficiency of a split model. It is naturally compatible with a variety of centered and upstream-biased high-order advection algorithms, and helps to mitigate computational cost of expensive physical parameterization of mixing processes and submodels. We study transients produced by equatorial disk-like outflows from catastrophically mass-losing binary stars with an asymptotic velocity and energy deposition rate near the inner edge which are proportional to the binary escape velocity v_esc. As a test case, we present the first smoothed-particle radiation-hydrodynamics calculations of the mass loss from the outer Lagrange point with realistic equation of state and opacities. The resulting spiral stream becomes unbound for binary mass ratios 0.06 < q < 0.8. For synchronous binaries with non-degenerate components, the spiral-stream arms merge at a radius of 10a, where a is the binary semi-major axis, and the accompanying shock thermalizes about 10 of the kinetic power of the outflow. The mass-losing binary outflows produce luminosities reaching up to 10^6 L_Sun and effective temperatures spanning 500 < T_eff < 6000 K, which is compatible with many of the class of recently-discovered red transients such as V838 Mon and V1309 Sco. Dust readily forms in the outflow, potentially in a catastrophic global cooling transition. The appearance of the transient is viewing angle-dependent due to vastly different optical depths parallel and perpendicular to the binary plane. We predict a correlation between the peak luminosity and the outflow velocity, which is roughly obeyed by the known red transients. Outflows from mass-losing binaries can produce luminous (10^5 L_Sun) and cool (T_eff < 1500 K) transients lasting a year or longer, as has potentially been detected by Spitzer surveys of nearby galaxies. We discuss the performance of direct summation codes used in the simulation of astrophysical stellar systems on highly distributed architectures. These codes compute the gravitational interaction among stars in an exact way and have an O(N^2) scaling with the number of particles. They can be applied to a variety of astrophysical problems, like the evolution of star clusters, the dynamics of black holes, the formation of planetary systems, and cosmological simulations. The simulation of realistic star clusters with sufficiently high accuracy cannot be performed on a single workstation but may be possible on parallel computers or grids. We have implemented two parallel schemes for a direct N-body code and we study their performance on general purpose parallel computers and large computational grids. We present the results of timing analyzes conducted on the different architectures and compare them with the predictions from theoretical models. We conclude that the simulation of star clusters with up to a million particles will be possible on large distributed computers in the next decade. Simulating entire galaxies however will in addition require new hybrid methods to speedup the calculation. We employ the inverse Boltzmann method to coarse-grain three commonly used three-site water models (TIP3P, SPC and SPC E) where one molecule is replaced with one coarse-grained particle with isotropic two-body interactions only. The shape of the coarse-grained potentials is dominated by the ratio of two lengths, which can be rationalized by the geometric constraints of the water clusters. It is shown that for simple two-body potentials either the radial distribution function or the geometrical packing can be optimized. In a similar way, as needed for multiscale methods, either the pressure or the compressibility can be fitted to the all atom liquid. In total, a speed-up by a factor of about 50 in computational time can be reached by this coarse-graining procedure. Effective unmixing of hyperspectral data cube under a noisy scenario has been a challenging research problem in remote sensing arena. A branch of existing hyperspectral unmixing algorithms is based on Craig's criterion, which states that the vertices of the minimum-volume simplex enclosing the hyperspectral data should yield high fidelity estimates of the endmember signatures associated with the data cloud. Recently, we have developed a minimum-volume enclosing simplex (MVES) algorithm based on Craig's criterion and validated that the MVES algorithm is very useful to unmix highly mixed hyperspectral data. However, the presence of noise in the observations expands the actual data cloud, and as a consequence, the endmember estimates obtained by applying Craig-criterion-based algorithms to the noisy data may no longer be in close proximity to the true endmember signatures. In this paper, we propose a robust MVES (RMVES) algorithm that accounts for the noise effects in the observations by employing chance constraints. These chance constraints in turn control the volume of the resulting simplex. Under the Gaussian noise assumption, the chance-constrained MVES problem can be formulated into a deterministic nonlinear program. The problem can then be conveniently handled by alternating optimization, in which each subproblem involved is handled by using sequential quadratic programming solvers. The proposed RMVES is compared with several existing benchmark algorithms, including its predecessor, the MVES algorithm. Monte Carlo simulations and real hyperspectral data experiments are presented to demonstrate the efficacy of the proposed RMVES algorithm. We present a performance model-driven framework for automated performance tuning (autotuning) of sparse matrix-vector multiply (SpMV) on systems accelerated by graphics processing units (GPU). Our study consists of two parts. First, we describe several carefully hand-tuned SpMV implementations for GPUs, identifying key GPU-specific performance limitations, enhancements, and tuning opportunities. These implementations, which include variants on classical blocked compressed sparse row (BCSR) and blocked ELLPACK (BELLPACK) storage formats, match or exceed state-of-the-art implementations. For instance, our best BELLPACK implementation achieves up to 29.0 Gflop s in single-precision and 15.7 Gflop s in double-precision on the NVIDIA T10P multiprocessor (C1060), enhancing prior state-of-the-art unblocked implementations (Bell and Garland, 2009) by up to 1.8× and 1.5× for single-and double-precision respectively. However, achieving this level of performance requires input matrix-dependent parameter tuning. Thus, in the second part of this study, we develop a performance model that can guide tuning. Like prior autotuning models for CPUs (e.g., Im, Yelick, and Vuduc, 2004), this model requires offline measurements and run-time estimation, but more directly models the structure of multithreaded vector processors like GPUs. We show that our model can identify the implementations that achieve within 15 of those found through exhaustive search. This paper is one of the few works in identification of a model of a Variable Mass Underwater Vehicles (VMUVs) with six degrees of freedom. Since, the mass of fuel changes during the operation, the mass and the center of mass of these vehicles also change and therefore the VMUV has nonlinear-time varying model. In order to obtain a model of the VMUV, an identification procedure is done by using an especial neural network. In this network, which is called the Volterra neural network, the basis functions are Volterra polynomials. Also, genetic algorithm (GA) is used with neural network to structure selection of these nonlinear polynomials. Computer simulations, Monte Carlo and cross-correlation analyses are done by considering admissible levels of noises in the underwater vehicles instrumentations (rate gyros) and the results show the efficiency of the presented approach. Abstract At the heart of this article will be the study of a branching Brownian motion (BBM) with killing , where individual particles move as Brownian motions with drift − ρ , perform dyadic branching at rate β and are killed on hitting the origin. Firstly, by considering properties of the right-most particle and the extinction probability, we will provide a probabilistic proof of the classical result that the ‘one-sided’ FKPP travelling-wave equation of speed − ρ with solutions f : [ 0 , ∞ ) → [ 0 , 1 ] satisfying f ( 0 ) = 1 and f ( ∞ ) = 0 has a unique solution with a particular asymptotic when ρ 2 β , and no solutions otherwise. Our analysis is in the spirit of the standard BBM studies of [S.C. Harris, Travelling-waves for the FKPP equation via probabilistic arguments, Proc. Roy. Soc. Edinburgh Sect. A 129 (3) (1999) 503–517] and [A.E. Kyprianou, Travelling wave solutions to the K-P-P equation: alternatives to Simon Harris' probabilistic analysis, Ann. Inst. H. Poincare Probab. Statist. 40 (1) (2004) 53–72] and includes an intuitive application of a change of measure inducing a spine decomposition that, as a by product, gives the new result that the asymptotic speed of the right-most particle in the killed BBM is 2 β − ρ on the survival set. Secondly, we introduce and discuss the convergence of an additive martingale for the killed BBM, W λ , that appears of fundamental importance as well as facilitating some new results on the almost-sure exponential growth rate of the number of particles of speed λ ∈ ( 0 , 2 β − ρ ) . Finally, we prove a new result for the asymptotic behaviour of the probability of finding the right-most particle with speed λ > 2 β − ρ . This result combined with Chauvin and Rouault's [B. Chauvin, A. Rouault, KPP equation and supercritical branching Brownian motion in the subcritical speed area. Application to spatial trees, Probab. Theory Related Fields 80 (2) (1988) 299–314] arguments for standard BBM readily yields an analogous Yaglom-type conditional limit theorem for the killed BBM and reveals W λ as the limiting Radon–Nikodým derivative when conditioning the right-most particle to travel at speed λ into the distant future.