Computing On Graphics Processing Units Research Articles

Acceleration of computation speed for elastic wave simulation using a Graphic Processing Unit

Numerical simulation in exploration geophysics provides important insights into subsurface wave propagation phenomena. Although elastic wave simulations take longer to compute than acoustic simulations, an elastic simulator can construct more realistic wavefields including shear components. Therefore, it is suitable for exploration of the responses of elastic bodies. To overcome the long duration of the calculations, we use a Graphic Processing Unit (GPU) to accelerate the elastic wave simulation. Because a GPU has many processors and a wide memory bandwidth, we can use it in a parallelised computing architecture. The GPU board used in this study is an NVIDIA Tesla C1060, which has 240 processors and a 102 GB/s memory bandwidth. Despite the availability of a parallel computing architecture (CUDA), developed by NVIDIA, we must optimise the usage of the different types of memory on the GPU device, and the sequence of calculations, to obtain a significant speedup of the computation. In this study, we simulate two- (2D) and three-dimensional (3D) elastic wave propagation using the Finite-Difference Time-Domain (FDTD) method on GPUs. In the wave propagation simulation, we adopt the staggered-grid method, which is one of the conventional FD schemes, since this method can achieve sufficient accuracy for use in numerical modelling in geophysics. Our simulator optimises the usage of memory on the GPU device to reduce data access times, and uses faster memory as much as possible. This is a key factor in GPU computing. By using one GPU device and optimising its memory usage, we improved the computation time by more than 14 times in the 2D simulation, and over six times in the 3D simulation, compared with one CPU. Furthermore, by using three GPUs, we succeeded in accelerating the 3D simulation 10 times.

An Energy-Efficient Heterogeneous System for Embedded Learning and Classification

Embedded learning applications in automobiles, surveillance, robotics, and defense are computationally intensive, and process large amounts of real-time data. Systems for such workloads have to balance stringent performance constraints within limited power budgets. High performance computer processing units (CPUs) and graphics processing units (GPUs) cannot be used in an embedded platform due to power issues. In this letter, we propose a low power heterogeneous system consisting of an Atom processor supported by multiple accelerators that target these workloads, and seek to find if such a system can satisfy performance requirements in an energy-efficient manner. We build our low-power system using an Atom processor, an ION, a GPU, and a field-programmable gate array (FPGA)-based custom accelerator, and study its performance and power characteristics using four representative workloads. With such a system, we show an energy improvement of 42-85% over a server comprising a 2.27 GHz quadcore Xeon coupled to a 1.3 GHz 240 core Tesla GPU.

Redesigning combustion modeling algorithms for the Graphics Processing Unit (GPU): Chemical kinetic rate evaluation and ordinary differential equation integration

Detailed modeling of complex combustion kinetics remains challenging and often intractable, due to prohibitive computational costs incurred when solving the associated large kinetic mechanisms. The Graphics Processing Unit (GPU), originally designed for graphics rendering on computer and gaming systems, has recently emerged as a powerful, cost-effective supplement to the Central Processing Unit (CPU) for dramatically accelerating scientific computations. Complex scientific computations are now being performed on the GPU in several research fields, such as quantum chemistry, molecular dynamics, and atmospheric modeling. Here, we present methods for exploiting the highly parallel structure of GPUs for combustion modeling. This paper outlines simple algorithm revisions that can be applied to the majority of existing combustion modeling algorithms for GPU computations. Significant simulation acceleration and predictive capability enhancements were obtained by using these GPU-enhanced algorithms for reaction rate evaluation and in ODE integration. For the demonstrations, we implemented the rate evaluation revisions in CHEMKIN and the ODE integration revisions in DASAC and DVODE and we tested the performance for simulating constant-volume ignition using SENKIN. The simulations using the revised algorithms are more than an order of magnitude faster than the corresponding CPU-only simulations, even for a low-end (double-precision) graphics card. Additionally, the computational time scales less than quadratically with the number of chemical species in the kinetic mechanism when using the GPU, as compared to the super-quadratic scaling normally seen with CPU-only chemical kinetics computations; and the GPU-based revisions do not involve approximations to the detailed kinetics. An analysis of the growth rates of combustion mechanism sizes versus computational capabilities of CPUs and GPUs further reveals the important role that GPUs are expected to play in the future of combustion modeling. Finally, we briefly outline practical steps for effectively transitioning from CPU-only to GPU-enhanced combustion modeling.

GPU-based fast gamma index calculation

The γ-index dose comparison tool has been widely used to compare dose distributions in cancer radiotherapy. The accurate calculation of γ-index requires an exhaustive search of the closest Euclidean distance in the high-resolution dose-distance space. This is a computational intensive task when dealing with 3D dose distributions. In this work, we combine a geometric method (Ju et al 2008 Med. Phys. 35 879–87) with a radial pre-sorting technique (Wendling et al 2007 Med. Phys. 34 1647–54) and implement them on computer graphics processing units (GPUs). The developed GPU-based γ-index computational tool is evaluated on eight pairs of IMRT dose distributions. The γ-index calculations can be finished within a few seconds for all 3D testing cases on one single NVIDIA Tesla C1060 card, achieving 45–75× speedup compared to CPU computations conducted on an Intel Xeon 2.27 GHz processor. We further investigated the effect of various factors on both CPU and GPU computation time. The strategy of pre-sorting voxels based on their dose difference values speeds up the GPU calculation by about 2.7–5.5 times. For n-dimensional dose distributions, γ-index calculation time on CPU is proportional to the summation of γn over all voxels, while that on GPU is affected by γn distributions and is approximately proportional to the γn summation over all voxels. We found that increasing the resolution of dose distributions leads to a quadratic increase of computation time on CPU, while less-than-quadratic increase on GPU. The values of dose difference and distance-to-agreement criteria also have an impact on γ-index calculation time.

GPU accelerated biochemical network simulation.

Motivation: Mathematical modelling is central to systems and synthetic biology. Using simulations to calculate statistics or to explore parameter space is a common means for analysing these models and can be computationally intensive. However, in many cases, the simulations are easily parallelizable. Graphics processing units (GPUs) are capable of efficiently running highly parallel programs and outperform CPUs in terms of raw computing power. Despite their computational advantages, their adoption by the systems biology community is relatively slow, since differences in hardware architecture between GPUs and CPUs complicate the porting of existing code.Results: We present a Python package, cuda-sim, that provides highly parallelized algorithms for the repeated simulation of biochemical network models on NVIDIA CUDA GPUs. Algorithms are implemented for the three popular types of model formalisms: the LSODA algorithm for ODE integration, the Euler–Maruyama algorithm for SDE simulation and the Gillespie algorithm for MJP simulation. No knowledge of GPU computing is required from the user. Models can be specified in SBML format or provided as CUDA code. For running a large number of simulations in parallel, up to 360-fold decrease in simulation runtime is attained when compared to single CPU implementations.Availability: http://cuda-sim.sourceforge.net/Contact: christopher.barnes@imperial.ac.uk; m.stumpf@imperial.ac.ukSupplementary information: Supplementary data are available at Bioinformatics online.

FAST CALCULATION OF THE LOMB-SCARGLE PERIODOGRAM USING GRAPHICS PROCESSING UNITS

I introduce a new code for fast calculation of the Lomb-Scargle periodogram, that leverages the computing power of graphics processing units (GPUs). After establishing a background to the newly emergent field of GPU computing, I discuss the code design and narrate key parts of its source. Benchmarking calculations indicate no significant differences in accuracy compared to an equivalent CPU-based code. However, the differences in performance are pronounced; running on a low-end GPU, the code can match 8 CPU cores, and on a high-end GPU it is faster by a factor approaching thirty. Applications of the code include analysis of long photometric time series obtained by ongoing satellite missions and upcoming ground-based monitoring facilities; and Monte-Carlo simulation of periodogram statistical properties.

Accelerated multidimensional radiofrequency pulse design for parallel transmission using concurrent computation on multiple graphics processing units.

Multidimensional radiofrequency (RF) pulses are of current interest because of their promise for improving high-field imaging and for optimizing parallel transmission methods. One major drawback is that the computation time of numerically designed multidimensional RF pulses increases rapidly with their resolution and number of transmitters. This is critical because the construction of multidimensional RF pulses often needs to be in real time. The use of graphics processing units for computations is a recent approach for accelerating image reconstruction applications. We propose the use of graphics processing units for the design of multidimensional RF pulses including the utilization of parallel transmitters. Using a desktop computer with four NVIDIA Tesla C1060 computing processors, we found acceleration factors on the order of 20 for standard eight-transmitter two-dimensional spiral RF pulses with a 64 × 64 excitation resolution and a 10-μsec dwell time. We also show that even greater acceleration factors can be achieved for more complex RF pulses.

GPU accelerated lattice Boltzmann model for shallow water flow and mass transport

AbstractA lattice Boltzmann method (LBM) for solving the shallow water equations (SWEs) and the advection–dispersion equation is developed and implemented on graphics processing unit (GPU)‐based architectures. A generalized lattice Boltzmann equation (GLBE) with a multiple‐relaxation‐time (MRT) collision method is used to simulate shallow water flow. A two‐relaxation‐time (TRT) method with two speed‐of‐sound techniques is used to solve the advection–dispersion equation. The proposed LBM is implemented to an NVIDIA®Computing Processor in a single GPU workstation. GPU computing is performed using the Jacket GPU engine for MATLAB®and CUDA. In the numerical examples, the MRT‐LBM model and the TRT‐LBM model are verified and show excellent agreement to exact solutions. The MRT outperforms the single‐relaxation‐time (SRT) collision operator in terms of stability and accuracy when the SRT parameter is close to the stability limit of 0.5. Mass transport with velocity‐dependent dispersion in shallow water flow is simulated by combining the MRT‐LBM model and the TRT‐LBM model. GPU performance with CUDA code shows an order of magnitude higher than MATLAB‐Jacket code. Moreover, the GPU parallel performance increases as the grid size increases. The results indicate the promise of the GPU‐accelerated LBM for modeling mass transport phenomena in shallow water flows. Copyright © 2010 John Wiley & Sons, Ltd.

GPU acceleration for general conservation equations and its application to several engineering problems

Presented is a general method for conservation equations called SHLL (split HLL) applied using Graphics Processing Unit (GPU) acceleration. The SHLL method is a purely vector-split approximation of the classical HLL method (Harten et al., 1983 [1]) which assumes the presence of local wave propagation in the algebraic derivation of fluxes across cell surfaces. The conventional HLL flux expression terms are interface-split and wave propagation velocities estimated (where required) based on local conditions. Due to the highly local nature of the SHLL fluxes, the scheme is very efficiently applied to GPU computation since the flux, initialisation and update phases of the computation are all vectorized processes. The SHLL scheme is applied to GPU computating using Nvidia’s CUDA package. Numerical schemes are presented for solutions to the general transport (convection–diffusion) equation, Euler Equations and Shallow Water Equations with results presented for several benchmark gas and shallow water flow engineering problems. Computational times are compared between high-end GPU (Nvidia C1060) and CPU (Intel Xeon 3.0 GHz, 32 MB cache) systems with reported speedups of over 67 times when applied to two dimensional simulations with multi-million cell numbers.

Highly interactive computational steering for coupled 3D flow problems utilizing multiple GPUs

Most computational fluid dynamics (CFD) simulations require massive computational power which is usually provided by traditional High Performance Computing (HPC) environments. Although interactivity of the simulation process is highly appreciated by scientists and engineers, due to limitations of typical HPC environments, present CFD simulations are usually executed non interactively. A recent trend is to harness the parallel computational power of graphics processing units (GPUs) for general purpose applications. As an alternative to traditional massively parallel computing, GPU computing has also gained popularity in the CFD community, especially for its application to the lattice Boltzmann method (LBM). For instance, Tolke and others presented very efficient implementations of the LBM for 2D as well as 3D space (Toelke J, in Comput Visual Sci. (2008); Toelke J and Krafczk M, in Int J Comput Fluid Dyn 22(7): 443–456 (2008)). In this work we motivate the use of GPU computing to facilitate interactive CFD simulations. In our approach, the simulation is executed on multiple GPUs instead of traditional HPC environments, which allows the integration of the complete simulation process into a single desktop application. To demonstrate the feasibility of our approach, we show a fully bidirectional fluid-structure-interaction for self induced membrane oscillations in a turbulent flow. The efficiency of the approach allows a 3D simulation close to realtime.

PacketShader

We present PacketShader, a high-performance software router framework for general packet processing with Graphics Processing Unit (GPU) acceleration. PacketShader exploits the massively-parallel processing power of GPU to address the CPU bottleneck in current software routers. Combined with our high-performance packet I/O engine, PacketShader outperforms existing software routers by more than a factor of four, forwarding 64B IPv4 packets at 39 Gbps on a single commodity PC. We have implemented IPv4 and IPv6 forwarding, OpenFlow switching, and IPsec tunneling to demonstrate the flexibility and performance advantage of PacketShader. The evaluation results show that GPU brings significantly higher throughput over the CPU-only implementation, confirming the effectiveness of GPU for computation and memory-intensive operations in packet processing.

RMieS‐EMSC correction for infrared spectra of biological cells: Extension using full Mie theory and GPU computing

In the field of biomedical infrared spectroscopy it is often desirable to obtain spectra at the cellular level. Samples consisting of isolated single biological cells are particularly unsuited to such analysis since cells are strong scatterers of infrared radiation. Thus measured spectra consist of an absorption component often highly distorted by scattering effects. It is now known that the predominant contribution to the scattering is Resonant Mie Scattering (RMieS) and recently we have shown that this can be corrected for, using an iterative algorithm based on Extended Multiplicative Signal Correction (EMSC) and a Mie approximation formula. Here we present an iterative algorithm that applies full Mie scattering theory. In order to avoid noise accumulation in the iterative algorithm a curve-fitting step is implemented on the new reference spectrum. The new algorithm increases the computational time when run on an equivalent processor. Therefore parallel processing by a Graphics Processing Unit (GPU) was employed to reduce computation time. The optimised RMieS-EMSC algorithm is applied to an IR spectroscopy data set of cultured single isolated prostate cancer (PC-3) cells, where it is shown that spectral distortions from RMieS are removed.

GPU-accelerated molecular modeling coming of age

Graphics processing units (GPUs) have traditionally been used in molecular modeling solely for visualization of molecular structures and animation of trajectories resulting from molecular dynamics simulations. Modern GPUs have evolved into fully programmable, massively parallel co-processors that can now be exploited to accelerate many scientific computations, typically providing about one order of magnitude speedup over CPU code and in special cases providing speedups of two orders of magnitude. This paper surveys the development of molecular modeling algorithms that leverage GPU computing, the advances already made and remaining issues to be resolved, and the continuing evolution of GPU technology that promises to become even more useful to molecular modeling. Hardware acceleration with commodity GPUs is expected to benefit the overall computational biology community by bringing teraflops performance to desktop workstations and in some cases potentially changing what were formerly batch-mode computational jobs into interactive tasks.

Nonlinear optimization with a massively parallel Evolution Strategy–Pattern Search algorithm on graphics hardware

This paper presents a massively parallel Evolution Strategy–Pattern Search Optimization (ES–PS) algorithm with graphics hardware acceleration on bound constrained nonlinear continuous optimization problems. The algorithm was specifically designed for a graphic processing unit (GPU) hardware platform featuring ‘Single Instruction Multiple Thread’ (SIMT). Evolution Strategy is a population-based evolutionary algorithm for solving complex optimization problems. GPU computing is an emerging desktop parallel computing platform. The hybrid ES–PS optimization method was implemented in the GPU environment and compared to a similar implementation on Central Processing Units (CPU). Computational results indicated that GPU-accelerated SIMT–ES–PS method was orders of magnitude faster than the corresponding CPU implementation. The main contribution of this paper was the parallelization analysis and performance analysis of the hybrid ES–PS with GPU acceleration. The computational results demonstrated a promising direction for high speed optimization with desktop parallel computing on a personal computer (PC).

TH‐C‐BRA‐04: Radiation Therapy Dose Calculation Using Graphics Processing Units

Dose computation methods in radiotherapy have traditionally been developed for central processing units (CPUs). Methods used in radiation therapy treatment planning must balance clinical accuracy requirements with practical planning time limits. The first commercial 3D treatment planning systems in the early 1990s took between 5–30 minutes to compute a beam depending on the dose grid size and computation method. In the years that followed CPU performance increased with Moore's law and more reasonable dose computation speeds of several seconds to minutes were achieved. However in recent years CPUs have increased computing power with additional cores not clock speed. At the same time graphic processing units (GPUs) have evolved from fixed function devices into flexible general purpose hardware. Today general purpose GPU computing (GPGPU) has turned desktops into supercomputers and languages such as OpenCL CUDA (Compute Unified Device Architecture) Fortran CUDA C and DirectCompute have allowed for fast GPU program development.Currently convolution/superposition algorithms are the primary computation methods used in treatment planning systems due to their combination of reasonable performance and accuracy. Monte Carlo methods are becoming more prevalent but they still have performance problems. Porting these algorithms to the GPU promises to provide a several orders of magnitude performance increase; resulting in near real‐time convolution/superposition dose computation.The implementation of these algorithms on the many‐core architecture of the GPU poses several challenges and opportunities. The first concern is dividing the algorithm up into many separate parallel processes that can be run independently of one another. The second concern is memory access patterns; for example the manually caching via shared memory the avoidance of write on write conflicts and the maximization of memory bandwidth efficiency. The third concern is how to best leverage the specific processing capabilities of the GPU such as hardware exponentials.Several approaches to implementing dose computation algorithms on the GPU will be discussed. The performance increase in these newer algorithms provides new opportunities in the way we approach treatment planning — whether it be real time treatment planning or enabling dosimetric guidance to treatment delivery.Learning Objectives;1. To understand the architecture differences between CPU and GPU2. To understand approaches complications and advantages to implementing pencil beam convolution/superposition algorithm and Monte Carlo algorithms on the GPU3. To understand the implications of the performance gain on treatment planning processes

Multi-Scale, Integrative Model Development using High-Performance Computer Architectures

In the field of biophysical modeling, it has often been desirable to build models that can run in real-time on a standard desktop workstation, but this is becoming more difficult to achieve. The complexity of molecular model components is increasing. Models of protein kinetics are evolving into large Markov chains where there were once a handful of Hodgekin-Huxley gating variables or algebraic equations. Additionally, models are integrating more modules for many aspects of cellular regulation, greatly increasing the number of states and expanding the range of relevant timescales. These models achieve mechanistic accuracy at the cost of greatly increased computation. Approximations may be made to decrease simulation time, but with some sacrifice of simulation accuracy. A simplified model of cardiac excitation-contraction (EC) coupling such as the coupled L-type Ca2+ channel-Ryanodine Receptor (LCC-RyR) model can provide a reasonable facsimile of EC coupling gain by modeling only a single LCC-RyR pair per cardiac dyad, far less than what is observed experimentally. To produce more detailed output the number of channels modeled per dyad can be increased, leading to an exponential growth in the number of states and compute time.Increased computing power is becoming more readily available in the form of multi-core processors, cluster computing, and general purpose graphics processing units (GPUs.) As the cost of such advanced computation decreases, the added benefit of including the fully detailed biophysical mechanisms in these models outweighs the computational cost of maintaining the model's complexity. The methods used here show how implementation of the coupled LCC-RyR model on the parallel GPU architecture can lead to significant speedup in simulation time. Use of the GPU also provides a beneficial scaleup in performance as models comprised of more states can be simulated on a larger machine in less time.

Understanding GPU Programming for Statistical Computation: Studies in Massively Parallel Massive Mixtures

This article describes advances in statistical computation for large-scale data analysis in structured Bayesian mixture models via graphics processing unit (GPU) programming. The developments are partly motivated by computational challenges arising in fitting models of increasing heterogeneity to increasingly large datasets. An example context concerns common biological studies using high-throughput technologies generating many, very large datasets and requiring increasingly high-dimensional mixture models with large numbers of mixture components. We outline important strategies and processes for GPU computation in Bayesian simulation and optimization approaches, give examples of the benefits of GPU implementations in terms of processing speed and scale-up in ability to analyze large datasets, and provide a detailed, tutorial-style exposition that will benefit readers interested in developing GPU-based approaches in other statistical models. Novel, GPU-oriented approaches to modifying existing algorithms software design can lead to vast speed-up and, critically, enable statistical analyses that presently will not be performed due to compute time limitations in traditional computational environments. Supplemental materials are provided with all source code, example data, and details that will enable readers to implement and explore the GPU approach in this mixture modeling context.

Implementation and evaluation of various demons deformable image registration algorithms on a GPU

Online adaptive radiation therapy (ART) promises the ability to deliver an optimal treatment in response to daily patient anatomic variation. A major technical barrier for the clinical implementation of online ART is the requirement of rapid image segmentation. Deformable image registration (DIR) has been used as an automated segmentation method to transfer tumor/organ contours from the planning image to daily images. However, the current computational time of DIR is insufficient for online ART. In this work, this issue is addressed by using computer graphics processing units (GPUs). A gray-scale-based DIR algorithm called demons and five of its variants were implemented on GPUs using the compute unified device architecture (CUDA) programming environment. The spatial accuracy of these algorithms was evaluated over five sets of pulmonary 4D CT images with an average size of 256 × 256 × 100 and more than 1100 expert-determined landmark point pairs each. For all the testing scenarios presented in this paper, the GPU-based DIR computation required around 7 to 11 s to yield an average 3D error ranging from 1.5 to 1.8 mm. It is interesting to find out that the original passive force demons algorithms outperform subsequently proposed variants based on the combination of accuracy, efficiency and ease of implementation.

Computation of Troposphere Slant Delays on a GPU

The computation of ray-traced troposphere delays which can be utilized for space geodetic applications is a time-consuming effort when a large number of rays has to be calculated. On the other hand, computation time can be tremendously reduced when algorithms are capable of supporting parallel processing architectures. Thus, by the use of an off-the-shelf graphics processing unit (GPU), it is demonstrated that troposphere slant delays can be computed very efficiently, without loss of accuracy. An adopted ray-tracing algorithm is presented, and results from GPU computations are compared with those obtained from calculations on a standard personal computer's CPU.

GPU-based ultra-fast dose calculation using a finite size pencil beam model

Online adaptive radiation therapy (ART) is an attractive concept that promises the ability to deliver an optimal treatment in response to the inter-fraction variability in patient anatomy. However, it has yet to be realized due to technical limitations. Fast dose deposit coefficient calculation is a critical component of the online planning process that is required for plan optimization of intensity-modulated radiation therapy (IMRT). Computer graphics processing units (GPUs) are well suited to provide the requisite fast performance for the data-parallel nature of dose calculation. In this work, we develop a dose calculation engine based on a finite-size pencil beam (FSPB) algorithm and a GPU parallel computing framework. The developed framework can accommodate any FSPB model. We test our implementation in the case of a water phantom and the case of a prostate cancer patient with varying beamlet and voxel sizes. All testing scenarios achieved speedup ranging from 200 to 400 times when using a NVIDIA Tesla C1060 card in comparison with a 2.27 GHz Intel Xeon CPU. The computational time for calculating dose deposition coefficients for a nine-field prostate IMRT plan with this new framework is less than 1 s. This indicates that the GPU-based FSPB algorithm is well suited for online re-planning for adaptive radiotherapy.