Graphics Processing Units Algorithm Research Articles

GPU-Accelerated Batch-ACPF Solution for N-1 Static Security Analysis

Graphics processing unit (GPU) has been applied successfully in many scientific computing realms due to its superior performances on float-pointing calculation and memory bandwidth, and has great potential in power system applications. The N-1 static security analysis (SSA) appears to be a candidate application in which massive alternating current power flow (ACPF) problems need to be solved. However, when applying existing GPU-accelerated algorithms to solve N-1 SSA problem, the degree of parallelism is limited because existing researches have been devoted to accelerating the solution of a single ACPF. This paper therefore proposes a GPU-accelerated solution that creates an additional layer of parallelism among batch ACPFs and consequently achieves a much higher level of overall parallelism. First, this paper establishes two basic principles for determining well-designed GPU algorithms, through which the limitation of GPU-accelerated sequential-ACPF solution is demonstrated. Next, being the first of its kind, this paper proposes a novel GPU-accelerated batch-QR solver, which packages massive number of QR tasks to formulate a new larger-scale problem and then achieves higher level of parallelism and better coalesced memory accesses. To further improve the efficiency of solving SSA, a GPU-accelerated batch-Jacobian-Matrix generating and contingency screening is developed and carefully optimized. Lastly, the complete process of the proposed GPU-accelerated batch-ACPF solution for SSA is presented. Case studies on an 8503-bus system show dramatic computation time reduction is achieved compared with all reported existing GPU-accelerated methods. In comparison to UMFPACK-library-based single-CPU counterpart using Intel Xeon E5-2620, the proposed GPU-accelerated SSA framework using NVIDIA K20C achieves up to 57.6 times speedup. It can even achieve four times speedup when compared to one of the fastest multi-core CPU parallel computing solution using KLU library. The proposed batch-solving method is practically very promising and lays a critical foundation for many other power system applications that need to deal with massive subtasks, such as Monte-Carlo simulation and probabilistic power flow.

A novel GPU-accelerated strategy for contingency screening of static security analysis

Graphics processing unit (GPU) has been applied successfully in many computation and memory intensive realms due to its superior performances in float-pointing calculation, memory bandwidth and power consumption, and has great potential in power system applications. Contingency screening is a major time consuming part of contingency analysis. In the absence of relevant existing research, this paper is the first of its kind to propose a novel GPU-accelerated algorithm for direct current (DC) contingency screening. Adapting actively unique characteristics of GPU software and hardware, the proposed GPU algorithm is optimized from four aspects: data transmission, parallel task allocation, memory access, and CUDA (Compute Unified Device Architecture) stream. Case studies on a 3012-bus system and 8503-bus system have shown that the GPU-accelerated algorithm, in compared with its counterpart CPU implementation, can achieve about 20 and 50 times speedup respectively. This highly promising performance has demonstrated that carefully designed performance tuning in conjunction with GPU programing architecture is imperative for a GPU-accelerated algorithm. The presented performance tuning strategies can be applicable to other GPU applications in power systems.

Efficient GPU algorithms for parallel decomposition of graphs into strongly connected and maximal end components

This article presents parallel algorithms for component decomposition of graph structures on general purpose graphics processing units (GPUs). In particular, we consider the problem of decomposing sparse graphs into strongly connected components, and decomposing graphs induced by stochastic games (such as Markov decision processes) into maximal end components. These problems are key ingredients of many (probabilistic) model-checking algorithms. We explain the main rationales behind our GPU-algorithms, and show a significant speed-up over the sequential (as well as existing parallel) counterparts in several case studies.

A new approach for second‐order perturbation theory

A new second-order perturbation theory (MP2) approach is presented for closed shell energy evaluations. The new algorithm has a significantly lower memory footprint, a lower FLOP (floating point operations) count, and a lower time to solution compared to previously implemented parallel MP2 methods in the GAMESS software package. Additionally, this algorithm features an adaptive approach for the disk/distributed memory storage of the MP2 amplitudes. The algorithm works well on a single workstation, small cluster, and large Cray cluster, and it allows one to perform large calculations with thousands of basis functions in a matter of hours on a single workstation. The same algorithm has been adapted for graphical processing unit (GPU) architecture. The performance of the new GPU algorithm is also discussed.

Efficient methods for implementation of multi-level nonrigid mass-preserving image registration on GPUs and multi-threaded CPUs

Background and objectiveFaster and more accurate methods for registration of images are important for research involved in conducting population-based studies that utilize medical imaging, as well as improvements for use in clinical applications. We present a novel computation- and memory-efficient multi-level method on graphics processing units (GPU) for performing registration of two computed tomography (CT) volumetric lung images. MethodsWe developed a computation- and memory-efficient Diffeomorphic Multi-level B-Spline Transform Composite (DMTC) method to implement nonrigid mass-preserving registration of two CT lung images on GPU. The framework consists of a hierarchy of B-Spline control grids of increasing resolution. A similarity criterion known as the sum of squared tissue volume difference (SSTVD) was adopted to preserve lung tissue mass. The use of SSTVD consists of the calculation of the tissue volume, the Jacobian, and their derivatives, which makes its implementation on GPU challenging due to memory constraints. The use of the DMTC method enabled reduced computation and memory storage of variables with minimal communication between GPU and Central Processing Unit (CPU) due to ability to pre-compute values. The method was assessed on six healthy human subjects. ResultsResultant GPU-generated displacement fields were compared against the previously validated CPU counterpart fields, showing good agreement with an average normalized root mean square error (nRMS) of 0.044±0.015. Runtime and performance speedup are compared between single-threaded CPU, multi-threaded CPU, and GPU algorithms. Best performance speedup occurs at the highest resolution in the GPU implementation for the SSTVD cost and cost gradient computations, with a speedup of 112 times that of the single-threaded CPU version and 11 times over the twelve-threaded version when considering average time per iteration using a Nvidia Tesla K20X GPU. ConclusionsThe proposed GPU-based DMTC method outperforms its multi-threaded CPU version in terms of runtime. Total registration time reduced runtime to 2.9min on the GPU version, compared to 12.8min on twelve-threaded CPU version and 112.5min on a single-threaded CPU. Furthermore, the GPU implementation discussed in this work can be adapted for use of other cost functions that require calculation of the first derivatives.

GPUSGD: A GPU‐accelerated stochastic gradient descent algorithm for matrix factorization

SummaryMatrix factorization is one of the leading techniques for many applications such as social network‐based recommendation systems. As of today, many parallel stochastic gradient descent (SGD) methods have been proposed to address the matrix factorization issue on shared‐memory (multi‐core) systems and distributed systems. However, these methods cannot be improved significantly on graphics processing unit (GPU) because the serious over‐writing problem and thread divergence may occur. The fundamental reason for such undesired results is that GPU is a parallel single instruction multiple data device, which only can greatly improve the applications with fine‐grained parallelism. In this paper, we propose an efficient GPU algorithm, named GPUSGD, to solve the matrix factorization problem based on SGD method. The major advantage of the proposed GPUSGD is that such method not only can handle the over‐writing problem but also can avoid the performance loss caused by the thread divergence. The experimental results show that GPUSGD performs much better in accelerating the matrix factorization compared with the existing state‐of‐the‐art parallel methods. To the best of our knowledge, this is the first work that develops a parallel SGD method to improve the matrix factorization on GPU. Copyright © 2015 John Wiley & Sons, Ltd.

Gappy Pattern Matching on GPUs for On-Demand Extraction of Hierarchical Translation Grammars

Grammars for machine translation can be materialized on demand by finding source phrases in an indexed parallel corpus and extracting their translations. This approach is limited in practical applications by the computational expense of online lookup and extraction. For phrase-based models, recent work has shown that on-demand grammar extraction can be greatly accelerated by parallelization on general purpose graphics processing units (GPUs), but these algorithms do not work for hierarchical models, which require matching patterns that contain gaps. We address this limitation by presenting a novel GPU algorithm for on-demand hierarchical grammar extraction that is at least an order of magnitude faster than a comparable CPU algorithm when processing large batches of sentences. In terms of end-to-end translation, with decoding on the CPU, we increase throughput by roughly two thirds on a standard MT evaluation dataset. The GPU necessary to achieve these improvements increases the cost of a server by about a third. We believe that GPU-based extraction of hierarchical grammars is an attractive proposition, particularly for MT applications that demand high throughput.

HEVC Encoding Optimization Using Multicore CPUs and GPUs

Although the High Efficiency Video Coding (HEVC) standard significantly improves the coding efficiency of video compression, it is unacceptable even in offline applications to spend several hours compressing 10 s of high-definition video. In this paper, we propose using a multicore central processing unit (CPU) and an off-the-shelf graphics processing unit (GPU) with 3072 streaming processors (SPs) for HEVC fast encoding, so that the speed optimization does not result in loss of coding efficiency. There are two key technical contributions in this paper. First, we propose an algorithm that is both parallel and fast for the GPU, which can utilize 3072 SPs in parallel to estimate the motion vector (MV) of every prediction unit (PU) in every combination of the coding unit (CU) and PU partitions. Furthermore, the proposed GPU algorithm can avoid coding efficiency loss caused by the lack of a MV predictor (MVP). Second, we propose a fast algorithm for the CPU, which can fully utilize the results from the GPU to significantly reduce the number of possible CU and PU partitions without any coding efficiency loss. Our experimental results show that compared with the reference software, we can encode high-resolution video that consumes 1.9% of the CPU time and 1.0% of the GPU time, with only a 1.4% rate increase.

A GPU Implementation of an Explicit Compact FDTD Algorithm with a Digital Impedance Filter for Room Acoustics Applications

In recent years, computational engineering has undergone great changes due to the development of the graphics processing unit (GPU) technology. For example, in room acoustics, the wave-based methods, that formerly were considered too expensive for 3-D impulse response simulations, are now chosen to exploit the parallel nature of GPU devices considerably reducing the execution time of the simulations. There exist contributions related to this topic that have explored the performance of different GPU algorithms; however, the computational analysis of a general explicit model that incorporates algorithms with different neighboring orders and a general frequency dependent impedance boundary model has not been properly developed. In this paper, we present a GPU implementation of a complete room acoustic model based on a family of explicit finite-difference time-domain (FDTD) algorithms. We first develop a strategy for implementing a frequency independent (FI) impedance model which is free from thread divergences and then, we extend the model adding a digital impedance filter (DIF) boundary subroutine able to compute the acoustic pressure of different nodes such as corners or edges without an additional performance penalty. Both implementations are validated and deeply analyzed by performing different 3-D numerical experiments. Finally, we define a performance metric which is able to objectively measure the computing throughput of a FDTD implementation using a simple number. The robustness of this metric allows us to compare algorithms even if these have been run in different GPU cards or have been formulated with other explicit models.

GPU acceleration of amplitude-preserved Q compensation prestack time migration

Amplitude-preserved Q compensation prestack time migration (Q migration) is a new method that evolved from prestack Kirchhoff time migration (PKTM). Five algorithms are developed for Q migration on graphics processing units (GPUs). First, the principle of Q migration is briefly introduced. Second, one parallel strategy, namely, imaging domain parallel strategy, is proposed to accelerate Q migration on a single GPU by developing GPU algorithm. Results show that the imaging domain parallel strategy with the corresponding algorithm is superior to the CPU algorithm in several aspects, i.e., faster computing speed, shorter computing time, and higher computational efficiency. Third, based on the imaging domain parallel strategy, two division methods, namely, seismic data division method and velocity data division method, are presented to optimize the performance of Q migration on multi-GPUs and four algorithms are implemented by using Message Passing Interface (MPI)+Compute Unified Device Architecture (CUDA) and multi-thread+CUDA. An optimal algorithm is determined by comparing the performance of four algorithms. Results demonstrate that the optimal algorithm has the shortest computing time, which is 3.85 times shorter than that of a single GPU when four GPUs are all involved in computation and 300 times shorter than that of a 4-core central processing unit (CPU). Finally, a parallel computing framework on GPU cluster is established, which consists of imaging domain parallel strategy, seismic data division method and MPI+CUDA. This framework is suitable for all prestack time migration (PSTM) methods and has a short computing time and high speedup ratio on GPU cluster.

On the performance of multi-GPU-based expert systems for acoustic localization involving massive microphone arrays

Sound source localization is an important topic in expert systems involving microphone arrays, such as automatic camera steering systems, human–machine interaction, video gaming or audio surveillance. The Steered Response Power with Phase Transform (SRP-PHAT) algorithm is a well-known approach for sound source localization due to its robust performance in noisy and reverberant environments. This algorithm analyzes the sound power captured by an acoustic beamformer on a defined spatial grid, estimating the source location as the point that maximizes the output power. Since localization accuracy can be improved by using high-resolution spatial grids and a high number of microphones, accurate acoustic localization systems require high computational power. Graphics Processing Units (GPUs) are highly parallel programmable co-processors that provide massive computation when the needed operations are properly parallelized. Emerging GPUs offer multiple parallelism levels; however, properly managing their computational resources becomes a very challenging task. In fact, management issues become even more difficult when multiple GPUs are involved, adding one more level of parallelism. In this paper, the performance of an acoustic source localization system using distributed microphones is analyzed over a massive multichannel processing framework in a multi-GPU system. The paper evaluates and points out the influence that the number of microphones and the available computational resources have in the overall system performance. Several acoustic environments are considered to show the impact that noise and reverberation have in the localization accuracy and how the use of massive microphone systems combined with parallelized GPU algorithms can help to mitigate substantially adverse acoustic effects. In this context, the proposed implementation is able to work in real time with high-resolution spatial grids and using up to 48 microphones. These results confirm the advantages of suitable GPU architectures in the development of real-time massive acoustic signal processing systems.

A new sparse matrix vector multiplication graphics processing unit algorithm designed for finite element problems

SummaryRecently, graphics processing units (GPUs) have been increasingly leveraged in a variety of scientific computing applications. However, architectural differences between CPUs and GPUs necessitate the development of algorithms that take advantage of GPU hardware. As sparse matrix vector (SPMV) multiplication operations are commonly used in finite element analysis, a new SPMV algorithm and several variations are developed for unstructured finite element meshes on GPUs. The effective bandwidth of current GPU algorithms and the newly proposed algorithms are measured and analyzed for 15 sparse matrices of varying sizes and varying sparsity structures. The effects of optimization and differences between the new GPU algorithm and its variants are then subsequently studied. Lastly, both new and current SPMV GPU algorithms are utilized in the GPU CG solver in GPU finite element simulations of the heart. These results are then compared against parallel PETSc finite element implementation results. The effective bandwidth tests indicate that the new algorithms compare very favorably with current algorithms for a wide variety of sparse matrices and can yield very notable benefits. GPU finite element simulation results demonstrate the benefit of using GPUs for finite element analysis and also show that the proposed algorithms can yield speedup factors up to 12‐fold for real finite element applications. Copyright © 2015 John Wiley & Sons, Ltd.

Prediction of Protein-Ligand Binding Sites for Cisplatin and Transplatin based on Hydrogen Bonds

Platinum compounds are very important to treatment of various malignant tumors. However, prediction of platinum-binding sites is very hard to be made. Nevertheless, hydrolysis of leaving groups bounded to platinum compounds plays an important role in delivering platinum to a target molecule. Herein, a study in silico provides an understanding of the molecular surface in atomic level of three-dimensional structure of cisplatin and transplatin and their binding-sites in order to offer some insights in drug designing. The goal of this work was to implement a new approach based on geometric and physicochemical parameters to find platinum-binding sites using parallel computing algorithms for graphics processing units (GPUs). These algorithms were tested and validated by analysing platinum-binding sites in five known proteins. The results indicated that these binding sites were predicted with significant success. In our analysis HexServer and PatchDock server did not find putative binding-sites for cisplatin and transplatin as we found for the five chosen proteins. Herein, we have shown that the present method have had a better prediction of platinum-binding site than HexServer and PatchDock methods.

A nonvoxel-based dose convolution/superposition algorithm optimized for scalable GPU architectures.

Real-time adaptive planning and treatment has been infeasible due in part to its high computational complexity. There have been many recent efforts to utilize graphics processing units (GPUs) to accelerate the computational performance and dose accuracy in radiation therapy. Data structure and memory access patterns are the key GPU factors that determine the computational performance and accuracy. In this paper, the authors present a nonvoxel-based (NVB) approach to maximize computational and memory access efficiency and throughput on the GPU. The proposed algorithm employs a ray-tracing mechanism to restructure the 3D data sets computed from the CT anatomy into a nonvoxel-based framework. In a process that takes only a few milliseconds of computing time, the algorithm restructured the data sets by ray-tracing through precalculated CT volumes to realign the coordinate system along the convolution direction, as defined by zenithal and azimuthal angles. During the ray-tracing step, the data were resampled according to radial sampling and parallel ray-spacing parameters making the algorithm independent of the original CT resolution. The nonvoxel-based algorithm presented in this paper also demonstrated a trade-off in computational performance and dose accuracy for different coordinate system configurations. In order to find the best balance between the computed speedup and the accuracy, the authors employed an exhaustive parameter search on all sampling parameters that defined the coordinate system configuration: zenithal, azimuthal, and radial sampling of the convolution algorithm, as well as the parallel ray spacing during ray tracing. The angular sampling parameters were varied between 4 and 48 discrete angles, while both radial sampling and parallel ray spacing were varied from 0.5 to 10 mm. The gamma distribution analysis method (γ) was used to compare the dose distributions using 2% and 2 mm dose difference and distance-to-agreement criteria, respectively. Accuracy was investigated using three distinct phantoms with varied geometries and heterogeneities and on a series of 14 segmented lung CT data sets. Performance gains were calculated using three 256 mm cube homogenous water phantoms, with isotropic voxel dimensions of 1, 2, and 4 mm. The nonvoxel-based GPU algorithm was independent of the data size and provided significant computational gains over the CPU algorithm for large CT data sizes. The parameter search analysis also showed that the ray combination of 8 zenithal and 8 azimuthal angles along with 1 mm radial sampling and 2 mm parallel ray spacing maintained dose accuracy with greater than 99% of voxels passing the γ test. Combining the acceleration obtained from GPU parallelization with the sampling optimization, the authors achieved a total performance improvement factor of >175 000 when compared to our voxel-based ground truth CPU benchmark and a factor of 20 compared with a voxel-based GPU dose convolution method. The nonvoxel-based convolution method yielded substantial performance improvements over a generic GPU implementation, while maintaining accuracy as compared to a CPU computed ground truth dose distribution. Such an algorithm can be a key contribution toward developing tools for adaptive radiation therapy systems.

4D MR phase and magnitude segmentations with GPU parallel computing

The increasing size and number of data sets of large four dimensional (three spatial, one temporal) magnetic resonance (MR) cardiac images necessitates efficient segmentation algorithms. Analysis of phase-contrast MR images yields cardiac flow information which can be manipulated to produce accurate segmentations of the aorta. Phase contrast segmentation algorithms are proposed that use simple mean-based calculations and least mean squared curve fitting techniques. The initial segmentations are generated on a multi-threaded central processing unit (CPU) in 10seconds or less, though the computational simplicity of the algorithms results in a loss of accuracy. A more complex graphics processing unit (GPU)-based algorithm fits flow data to Gaussian waveforms, and produces an initial segmentation in 0.5seconds. Level sets are then applied to a magnitude image, where the initial conditions are given by the previous CPU and GPU algorithms. A comparison of results shows that the GPU algorithm appears to produce the most accurate segmentation.

Medical image segmentation with deformable models on graphics processing units

In this work, the parallel implementation of a segmentation algorithm based on the gradient vector flow (GVF) deformable model in a graphics processing unit (GPU) is presented. The proposed implementation focuses on the parallelization of the computation of the GVF field. In order to make a performance comparison of the proposed GPU algorithm, an OpenMP-based implementation is presented too. We also present an analysis of the textures and global memory performance in the computing of the GVF field. To improve the efficiency and the performance of the active contour segmentation, a novel snaxel reallocation method is proposed. The main advantage of the reallocation process is the small linear system needed to perform the segmentation and its low computational load. To assure the convergence of the active contour deformation, we propose a stopping criterion based on the root mean square error for the iterative solution of the evolution equations.

Efficient decomposition of strongly connected components on GPUs

The GPU (Graphics Processing Unit) has recently become one of the most power efficient processors in embedded and many other environments, and has been integrated into more and more SoCs (System on Chip). Thus modern GPUs play a very important role in power aware computing. Strongly Connected Component (SCC) decomposition is a fundamental graph algorithm which has wide applications in model checking, electronic design automation, social network analysis and other fields. GPUs have been shown to have great potential in accelerating many types of computations including graph algorithms. Recent work have demonstrated the plausibility of GPU SCC decomposition, but the implementation is inefficient due to insufficient consideration of the distinguishing GPU programming model, which leads to poor performance on irregular and sparse graphs. This paper presents a new GPU SCC decomposition algorithm that focuses on full utilization of the contemporary embedded and desktop GPU architecture. In particular, a subgraph numbering scheme is proposed to facilitate the safe and efficient management of the subgraph IDs and to serve as the basis of efficient source selection. Furthermore, we adopt a multi-source partition procedure that greatly reduces the recursion depth and use a vertex labeling approach that can highly optimize the GPU memory access. The evaluation results show that the proposed approach achieves up to 41x speedup over Tarjan's algorithm, one of the most efficient sequential SCC decomposition algorithms, and up to 3.8x speedup over the previous GPU algorithms.

Implementation and performance of a general purpose graphics processing unit in hyperspectral image analysis

A graphics processing unit (GPU) can perform massively parallel computations at relatively low cost. Software interfaces like NVIDIA CUDA allow for General Purpose computing on a GPU (GPGPU). Wrappers of the CUDA libraries for higher-level programming languages such as MATLAB and IDL allow its use in image processing. In this paper, we implement GPGPU in IDL with two distance measures frequently used in image classification, Euclidean distance and spectral angle, and apply these to hyperspectral imagery. First we vary the data volume of a synthetic dataset by changing the number of image pixels, spectral bands and classification endmembers to determine speed-up and to find the smallest data volume that would still benefit from using graphics hardware. Then we process real datasets that are too large to fit in the GPU memory, and study the effect of resulting extra data transfers on computing performance. We show that our GPU algorithms outperform the same algorithms for a central processor unit (CPU), that a significant speed-up can already be obtained on relatively small datasets, and that data transfers in large datasets do not significantly influence performance. Given that no specific knowledge on parallel computing is required for this implementation, remote sensing scientists should now be able to implement and use GPGPU for their data analysis.

GPU-Based Local Tone Mapping in the Context of Virtual Night Driving

Virtual prototyping of automotive headlights requires a realistic illumination model, capable of rendering scenes of high contrast in fine detail. Due to the high dynamic range (HDR) nature of headlight beam-pattern data, which is projected onto the virtual road, high dynamic range illumination models are required. These are used as the basis for illumination in simulations for automotive headlight virtual prototyping. Since high dynamic range illumination models operate on brightness ranges commensurate with the real world, a postprocessing operation, known as tone mapping, is required to map each frame into the device-specific range of the display hardware. Algorithms for tone mapping, called tone-mapping operators, can be classified as global or local. Global operators are efficient to compute at the expense of scene quality. Local operators preserve scene detail, but, due to their additional computational complexity, are rarely used with interactive applications. Local tone-mapping methods produce more usable visualization results for engineering tasks. This paper proposes a local tone-mapping method suitable for use with interactive applications. To develop a suitable tone-mapping operator, a state of the art local tone-mapping method was accelerated using modern, work-efficient GPU (graphics processing unit) algorithms. Optimal performance, both in terms of memory and speed, was achieved by means of general-purpose GPU programming with CUDA (compute unified device architecture). A prototypic implementation has shown that the method works well with high dynamic range OpenGL applications. In the near future, the tone mapper will be integrated into the virtual night driving simulator at our institute.

Reaction–diffusion model Monte Carlo simulations on the GPU

We created an efficient algorithm suitable for graphics processing units (GPUs) to perform Monte Carlo simulations on a subset of reaction–diffusion models. The set of reaction–diffusion models that the algorithm is applied to represents a seemingly simplistic set of problems on a one-dimensional lattice, where each site contains either a particle or is empty. However, these systems exhibit non-equilibrium phase transitions, with very large finite-time corrections, which mandates a fast algorithm to simulate them. The algorithm presented here uses techniques that are specific to GPU programming, and combines these with multispin coding to create one of the fastest algorithms for reaction–diffusion models. As an example, the algorithm is applied to the pair contact process with diffusion (PCPD). Compared to a simple algorithm on the CPU, our GPU algorithm is approximately 4000 times faster. The GPU algorithm is roughly 55 times faster than an optimized version for the CPU.