Networks of interconnected resistors, springs and beams, or pores are standard models of studying scalar and vector transport processes in heterogeneous materials and media, such as fluid flow in porous media, and conduction, deformations, and electric and dielectric breakdown in heterogeneous solids. The computation time and required memory are two limiting factors that hinder the scalability of the computations to very large sizes. We present a dual approach, based on the use of a combination of the central processing units (CPUs) and graphics processing units (GPUs), to simulation of flow, transport, and similar problems using the network models. A mixed-precision algorithm, together with the conjugate-gradient method is implemented on a single GPU solver. The efficiency of the method is tested with a variety of cases, including pore- and random-resistor network models in which the conductances are long-range correlated, and also contain percolation disorder. Both isotropic and anisotropic networks are considered. To put the method to a stringent test, the long-range correlations are generated by a fractional Brownian motion (FBM), which we generate by a message-passing interface method. For all the cases studied an overall speed-up factor of about one order of magnitude or better is obtained, which increases with the size of the network. Even the critical slow-down in networks near the percolation threshold does not decrease the speed-up significantly. We also obtain approximate but accurate bounds for the permeability anisotropy $K_x/K_y$ for stratified porous media.
A new format for storing sparse matrices is proposed for efficient sparse matrix-vector (SpMV) product calculation on modern graphics processing units (GPUs). This format extends the standard compressed row storage (CRS) format and can be quickly converted to and from it. Computational performance of two SpMV kernels for the new format is determined for over 130 sparse matrices on Fermi-class and Kepler-class GPUs and compared with that of five existing generic algorithms and industrial implementations, including Nvidia cuSparse CSR and HYB kernels. We found the speedup of up to $\approx 60%$ …
Most relatively modern desktop or even laptop computers contain a graphics card useful for more than showing colors on a screen. In this paper, we make a case for why you should learn enough about GPU (graphics processing unit) computing to use as an accelerator or even replacement to your CPU code. We include an example of our own as a case study to show what can be realistically expected.
In this paper, the OpenACC heterogeneous parallel programming model is successfully applied to modification and acceleration of the three-dimensional Tokamak magnetohydrodynamical code (CLTx). Through combination of OpenACC and MPI technologies, CLTx is further parallelized by using multiple-GPUs. Significant speedup ratios are achieved on NVIDIA TITAN Xp and TITAN V GPUs, respectively, with very few modifications of CLTx. Furthermore, the validity of the double precision calculations on the above-mentioned two graphics cards has also been strictly verified with m/n=2/1 resistive tearing mode …
We present a novel implementation of the modal discontinuous Galerkin (DG) method for hyperbolic conservation laws in two dimensions on graphics processing units (GPUs) using NVIDIA's Compute Unified Device Architecture (CUDA). Both flexible and highly accurate, DG methods accommodate parallel architectures well as their discontinuous nature produces element-local approximations. High performance scientific computing suits GPUs well, as these powerful, massively parallel, cost-effective devices have recently included support for double-precision floating point numbers. Computed examples for Eu…
We discuss the application of graphical processing units (GPUs) to accelerate real-space density functional theory (DFT) calculations. To make our implementation efficient, we have developed a scheme to expose the data parallelism available in the DFT approach; this is applied to the different procedures required for a real-space DFT calculation. We present results for current-generation GPUs from AMD and Nvidia, which show that our scheme, implemented in the free code Octopus, can reach a sustained performance of up to 90 GFlops for a single GPU, representing a significant speed-up when compa…
We present an algorithm for neighbor search in molecular simulations on graphics processing units (GPUs) based on bounding volume hierarchies (BVHs). The BVH is compressed into a low-precision, quantized representation to increase the BVH traversal speed compared to a previous implementation. We find that neighbor search using the quantized BVH is roughly two to four times faster than current state-of-the-art methods using uniform grids (cell lists) for a suite of benchmarks for common molecular simulation models. Based on the benchmark results, we recommend using the BVH instead of a single c…
The progress made in accelerating simulations of fluid flow using GPUs, and the challenges that remain, are surveyed. The review first provides an introduction to GPU computing and programming, and discusses various considerations for improved performance. Case studies comparing the performance of CPU- and GPU- based solvers for the Laplace and incompressible Navier-Stokes equations are performed in order to demonstrate the potential improvement even with simple codes. Recent efforts to accelerate CFD simulations using GPUs are reviewed for laminar, turbulent, and reactive flow solvers. Also, …
We discuss the advantages of parallelization by multithreading on graphics processing units (GPUs) for parallel tempering Monte Carlo computer simulations of an exemplified bead-spring model for homopolymers. Since the sampling of a large ensemble of conformations is a prerequisite for the precise estimation of statistical quantities such as typical indicators for conformational transitions like the peak structure of the specific heat, the advantage of a strong increase in performance of Monte Carlo simulations cannot be overestimated. Employing multithreading and utilizing the massive power o…
Magnetohydrodynamic (MHD) simulations based on the ideal MHD equations have become a powerful tool for modeling phenomena in a wide range of applications including laboratory, astrophysical, and space plasmas. In general, high-resolution methods for solving the ideal MHD equations are computationally expensive and Beowulf clusters or even supercomputers are often used to run the codes that implemented these methods. With the advent of the Compute Unified Device Architecture (CUDA), modern graphics processing units (GPUs) provide an alternative approach to parallel computing for scientific simu…
Solving the shallow water equations efficiently is critical to the study of natural hazards induced by tsunami and storm surge, since it provides more response time in an early warning system and allows more runs to be done for probabilistic assessment where thousands of runs may be required. Using Adaptive Mesh Refinement (AMR) speeds up the process by greatly reducing computational demands, while accelerating the code using the Graphics Processing Unit (GPU) does so through using faster hardware. Combining both, we present an efficient CUDA implementation of GeoClaw, an open source Godunov-t…
This paper introduces the Sheffield Magnetohydrodynamics Algorithm Using GPUs (SMAUG+), an advanced numerical code for solving magnetohydrodynamic (MHD) problems, using multi-GPU systems. Multi-GPU systems facilitate the development of accelerated codes and enable us to investigate larger model sizes and/or more detailed computational domain resolutions. This is a significant advancement over the parent single-GPU MHD code, SMAUG (Griffiths, M., Fedun, V., and Erdélyi, R. (2015). A fast MHD code for gravitationally stratified media using graphical processing units: SMAUG. Journal of Astrophysi…
Graphics Processing Units (GPUs) can speed up the numerical solution of various problems in astrophysics including the dynamical evolution of stellar systems; the performance gain can be more than a factor 100 compared to using a Central Processing Unit only. In this work I describe some strategies to speed up the classical $N$-body problem using GPUs. I show some features of the $N$-body code HiGPUs as template code. In this context, I also give some hints on the parallel implementation of a regularization method and I introduce the code HiGPUs-R. Although the main application of this work co…
This paper presents a Graphics Processing Units (GPUs) implementation of the Semiclassical Initial Value Representation (SC-IVR) propagator for vibrational molecular spectroscopy calculations. The time-averaging formulation of the SC-IVR for power spectrum calculations is employed. Details about the GPU implementation of the semiclassical code are provided. Four molecules with an increasing number of atoms are considered and the GPU-calculated vibrational frequencies perfectly match the benchmark values. The computational time scaling of two GPUs (NVIDIA Tesla C2075 and Kepler K20) respectivel…
The Random Phase Approximation (RPA) for correlation energy in the grid-based projector augmented wave (gpaw) code is accelerated by porting to the Graphics Processing Unit (GPU) architecture. The acceleration is achieved by grouping independent vectors/matrices and transforming the implementation from being memory bound to being computation/latency bound. With this approach, both the CPU and GPU implementations have been enhanced. We tested the GPU implementation on a few representative systems: molecules (O2), bulk solids (Li2O and MoO3) and molecules adsorbed on metal surfaces (N2/Ru(0001) …
In recent years graphical processing units (GPUs) have become a powerful tool in scientific computing. Their potential to speed up highly parallel applications brings the power of high performance computing to a wider range of users. However, programming these devices and integrating their use in existing applications is still a challenging task. In this paper we examined the potential of GPUs for two different applications. The first application, created at Paul Scherrer Institut (PSI), is used for parameter fitting during data analysis of muSR (muon spin rotation, relaxation and resonance) e…
We present our implementation of the RHMC algorithm for staggered fermions on Graphics Processing Units using the NVIDIA CUDA programming language. While previous studies exclusively deal with the Dirac matrix inversion problem, our code performs the complete MD trajectory on the GPU. After pointing out the main bottlenecks and how to circumvent them, we discuss the performance of our code.
Graphical processing units (GPUs) promise to revolutionize scientific computing in the near future. Already, they allow almost real-time integration of simplified numerical models of cardiac tissue dynamics. However, the integration methods that have been developed so far are typically of low order and use single precision arithmetics. In this work, we describe numerical implementation of double precision integrators required by, e.g., matrix-free Newton-Krylov solvers and compare several higher order, fully explicit numerical methods using finite-difference discretization of a range of models…
We present a new method for numerical hydrodynamics which uses a multidimensional generalisation of the Roe solver and operates on an unstructured triangular mesh. The main advantage over traditional methods based on Riemann solvers, which commonly use one-dimensional flux estimates as building blocks for a multidimensional integration, is its inherently multidimensional nature, and as a consequence its ability to recognise multidimensional stationary states that are not hydrostatic. A second novelty is the focus on Graphics Processing Units (GPUs). By tailoring the algorithms specifically to …
In this paper, we demonstrate the efficiency of using semi-Lagrangian discontinuous Galerkin methods to solve the drift-kinetic equation using graphic processing units (GPUs). In this setting we propose a second order splitting scheme and a 2d semi-Lagrangian scheme in the poloidal plane. The resulting method is able to conserve mass up to machine precision, allows us to take large time steps due to the absence of a CFL condition and provides local data dependency which is essential to obtain good performance on state-of-the art high-performance computing systems. We report simulations of a dr…
Particle-in-cell (PIC) simulations with Monte-Carlo collisions are used in plasma science to explore a variety of kinetic effects. One major problem is the long run-time of such simulations. Even on modern computer systems, PIC codes take a considerable amount of time for convergence. Most of the computations can be massively parallelized, since particles behave independently of each other within one time step. Current graphics processing units (GPUs) offer an attractive means for execution of the parallelized code. In this contribution we show a one-dimensional PIC code running on Nvidia GPUs…
This paper presents a generalised and efficient wall boundary treatment in the smoothed particle hydrodynamics (SPH) method for 3-D complex and arbitrary geometries with single- and multi-phase flows to be executed on graphics processing units (GPUs). Using a force balance between the wall and fluid particles with a novel penalty method, a pressure boundary condition is applied on the wall dummy particles which effectively prevents non-physical particle penetration into the wall boundaries also in highly violent impacts and multi-phase flows with high density ratios. A new density reinitialisa…
We report on our implementation of the RHMC algorithm for the simulation of lattice QCD with two staggered flavors on Graphics Processing Units, using the NVIDIA CUDA programming language. The main feature of our code is that the GPU is not used just as an accelerator, but instead the whole Molecular Dynamics trajectory is performed on it. After pointing out the main bottlenecks and how to circumvent them, we discuss the obtained performances. We present some preliminary results regarding OpenCL and multiGPU extensions of our code and discuss future perspectives.
Modern graphics processing units (GPUs) provide impressive computing resources, which can be accessed conveniently through the CUDA programming interface. We describe how GPUs can be used to considerably speed up molecular dynamics (MD) simulations for system sizes ranging up to about 1 million particles. Particular emphasis is put on the numerical long-time stability in terms of energy and momentum conservation, and caveats on limited floating-point precision are issued. Strict energy conservation over 10^8 MD steps is obtained by double-single emulation of the floating-point arithmetic in ac…
We present a CUDA accelerated implementation of the Characteristic/Scan Conversion algorithm to generate narrow band signed distance fields in logically Cartesian grids. We outline an approach of task and data management on GPUs based on an input of a closed triangulated surface with the aim of reducing pre-processing and mesh-generation times. The work demonstrates a fast signed distance field generation of triangulated surfaces with tens of thousands to several million features in high resolution domains. We present improvements to the robustness of the original algorithm and an overview of …
The performance potential for simulating quantum electron transport on graphical processing units (GPUs) is studied. Using graphene ribbons of realistic sizes as an example it is shown that GPUs provide significant speed-ups in comparison to central processing units as the transverse dimension of the ribbon grows. The recursive Green's function algorithm is employed and implementation details on GPUs are discussed. Calculated conductances were found to accumulate significant numerical error due to single-precision floating-point arithmetic at energies close to the charge neutrality point of th…
Restricted solid on solid surface growth models can be mapped onto binary lattice gases. We show that efficient simulation algorithms can be realized on GPUs either by CUDA or by OpenCL programming. We consider a deposition/evaporation model following Kardar-Parisi-Zhang growth in 1+1 dimensions related to the Asymmetric Simple Exclusion Process and show that for sizes, that fit into the shared memory of GPUs one can achieve the maximum parallelization speedup ~ x100 for a Quadro FX 5800 graphics card with respect to a single CPU of 2.67 GHz). This permits us to study the effect of quenched co…
We describe the use of Graphics Processing Units (GPUs) for speeding up the code NBODY6 which is widely used for direct $N$-body simulations. Over the years, the $N^2$ nature of the direct force calculation has proved a barrier for extending the particle number. Following an early introduction of force polynomials and individual time-steps, the calculation cost was first reduced by the introduction of a neighbour scheme. After a decade of GRAPE computers which speeded up the force calculation further, we are now in the era of GPUs where relatively small hardware systems are highly cost-effecti…
We have developed a numerical framework for a full solution of the relativistic Boltzmann equations for the quark-gluon matter using the multiple Graphics Processing Units (GPUs) on distributed clusters. Including all the $2 \to 2$ scattering processes of 3-flavor quarks and gluons, we compute the time evolution of distribution functions in both coordinate and momentum spaces for the cases of pure gluons, quarks and the mixture of quarks and gluons. By introducing a symmetrical sampling method on GPUs which ensures the particle number conservation, our framework is able to perform the space-ti…
We introduce ClimateMachine, a new open-source atmosphere modeling framework using the Julia language to be performance portable on central processing units (CPUs) and graphics processing units (GPUs). ClimateMachine uses a common framework both for coarser-resolution global simulations and for high-resolution, limited-area large-eddy simulations (LES). Here, we demonstrate the LES configuration of the atmosphere model in canonical benchmark cases and atmospheric flows, using an energy-conserving nodal discontinuous-Galerkin (DG) discretization of the governing equations. Resolution dependence…
We present an approach to molecular-dynamics simulations of ferrofluids on graphics processing units (GPUs). Our numerical scheme is based on a GPU-oriented modification of the Barnes-Hut (BH) algorithm designed to increase the parallelism of computations. For an ensemble consisting of one million of ferromagnetic particles, the performance of the proposed algorithm on a Tesla M2050 GPU demonstrated a computational-time speed-up of four order of magnitude compared to the performance of the sequential All-Pairs (AP) algorithm on a single-core CPU, and two order of magnitude compared to the perf…
We test the performances of two different approaches to the computation of forces for molecular dynamics simulations on Graphics Processing Units. A "vertex-based" approach, where a computing thread is started per particle, is compared to a newly proposed "edge-based" approach, where a thread is started per each potentially non-zero interaction. We find that the former is more efficient for systems with many simple interactions per particle, while the latter is more efficient if the system has more complicated interactions or fewer of them. By comparing computation times on more and less recen…
We report the first CUDA graphics-processing-unit (GPU) implementation of the polymer field-theoretic simulation framework for determining fully fluctuating expectation values of equilibrium properties for periodic and select aperiodic polymer systems. Our implementation is suitable both for self-consistent field theory (mean-field) solutions of the field equations, and for fully fluctuating simulations using the complex Langevin approach. Running on NVIDIA Tesla T20 series GPUs, we find double-precision speedups of up to 30x compared to single-core serial calculations on a recent reference CP…
Monte Carlo simulations of the transport of protons in human tissue have been deployed on graphics processing units (GPUs) with impressive results. To provide a more complete treatment of non-elastic nuclear interactions in these simulations, we developed a fast intranuclear cascade-evaporation simulation for the GPU. This can be used to model non-elastic proton collisions on any therapeutically relevant nuclei at incident energies between 20 and 250 MeV. Predictions are in good agreement with Geant4.9.6p2. It takes approximately 2 s to calculate $1\times 10^6$ 200 MeV proton-$^{16}$O interact…
The high arithmetic performance and intrinsic parallelism of recent graphical processing units (GPUs) can offer a technological edge for molecular dynamics simulations. ACEMD is a production-class bio-molecular dynamics (MD) simulation program designed specifically for GPUs which is able to achieve supercomputing scale performance of 40 nanoseconds/day for all-atom protein systems with over 23,000 atoms. We illustrate the characteristics of the code, its validation and performance. We also run a microsecond-long trajectory for an all-atom molecular system in explicit TIP3P water on a single wo…
A new flow solver scalable on multiple Graphics Processing Units (GPUs) for direct numerical simulation of wall-bounded incompressible flow is presented. This solver utilizes a previously reported work (J. Comp. Physics, vol. 352 (2018), pp.246-264) which proposes a semi-implicit fractional-step method on a single GPU. Extension of this work to accommodate multiple GPUs becomes inefficient when global transpose is used in the Alternating Direction Implicit (ADI) and Fourier-transform-based direct methods. A new strategy for designing an efficient multi-GPU solver is described to completely rem…
Detailed analysis of efficiency and pollutant emission characteristics of practical turbulent combustion devices using complex combustion kinetics often depend on the interactions between the combustion chemistry involving both gasses species and soot, and turbulent flow characteristics. Modeling of such combustion system often requires the use of chemical kinetic mechanisms with hundreds of species and thousands of reactions. Perfectly stirred reactors (PSR) are idealized reactor environments, where the reacting species have high rate of stirring, and the combustion products are uniformly dis…
Lattice spin models are useful for studying critical phenomena and allow the extraction of equilibrium and dynamical properties. Simulations of such systems are usually based on Monte Carlo (MC) techniques, and the main difficulty is often the large computational effort needed when approaching critical points. In this work, it is shown how such simulations can be accelerated with the use of NVIDIA graphics processing units (GPUs) using the CUDA programming architecture. We have developed two different algorithms for lattice spin models, the first useful for equilibrium properties near a second…
We outline how auxiliary-field quantum Monte Carlo (AFQMC) can leverage graphical processing units (GPUs) to accelerate the simulation of solid state sytems. By exploiting conservation of crystal momentum in the one- and two-electron integrals we show how to efficiently formulate the algorithm to best utilize current GPU architectures. We provide a detailed description of different optimization strategies and profile our implementation relative to standard approaches, demonstrating a factor of 40 speed up over a CPU implementation. With this increase in computational power we demonstrate the a…
We assess the performance of the hybrid Open Accelerator (OpenACC) and Message Passing Interface (MPI) approach for multi-graphics processing units (GPUs) accelerated thermal lattice Boltzmann (LB) simulation. The OpenACC accelerates computation on a single GPU, and the MPI synchronizes the information between multiple GPUs. With a single GPU, the two-dimension (2D) simulation achieved 1.93 billion lattice updates per second (GLUPS) with a grid number of $8193^{2}$, and the three-dimension (3D) simulation achieved 1.04 GLUPS with a grid number of $385^{3}$, which is more than 76% of the theore…
