PCB design aids

High-performance direct gravitational N-body simulations on graphics processing units

A frequent configuration in computational fluid mechanics combines an explicit time advancing scheme for accuracy purposes and a computational grid with a very small portion of much smaller elements than in the remaining mesh. Examples of such situations are the traveling of a discontinuity followed by a moving mesh, and the large eddy simulation of high Reynolds number flows around bluff bodies where together very thin boundary layers and vortices of much more important size need to be captured. For such configurations, explicit time advancing schemes with global time stepping are very costly. In order to overcome this problem, the multirate time stepping approach represents an interesting improvement. The objective of such schemes, which allow to use different time steps in the computational domain, is to avoid penalizing the computational cost of the time advancement of unsteady solutions which can become large due to the use of small global time steps imposed by the smallest elements such as those constituting the boundary layers. In the present work, a new multirate scheme based on control volume agglomeration is proposed for the solution of the compressible Navier-Stokes equations possibly equipped with turbulence models. The method relies on a prediction step where large time steps are performed with an evaluation of the fluxes on macro-cells for the smaller elements for stability purpose, and on a correction step in which small time steps are employed only for the smaller elements. The efficiency of the proposed method is evaluated on several benchmarks flows: the problem of a moving contact discontinuity (inviscid flow), the computation with hybrid turbulence model of flows around bluff bodies like a tandem cylinders at Reynolds number $1.66 × 10 5$ , a circular cylinder at Reynolds number $8.4 × 10 6$ , and a flow around a space probe model at Reynolds number $1 × 10 6$ .

In this paper, we explore the implementation of Monte Carlo based statistical static timing analysis (SSTA) on a Graphics Processing Unit (GPU). SSTA via Monte Carlo simulations is a computationally expensive, but important step required to achieve design timing closure. It provides an accurate estimate of delay variations and their impact on design yield. The large number of threads that can be computed in parallel on a GPU suggests a natural fit for the problem of Monte Carlo based SSTA to the GPU platform. Our implementation performs multiple delay simulations at a single gate in parallel. A parallel implementation of the Mersenne Twister pseudo-random number generator on the GPU, followed by Box-Muller transformations (also implemented on the GPU) is used for generating gate delay numbers from a normal distribution. The μ and σ of the pin-to-output delay distributions for all inputs and for every gate, are obtained using a memory lookup, which benefits from the large memory bandwidth of the GPU. Threads which execute in parallel have no data/control dependencies on each other. All threads compute identical instructions, but on different data, as required by the Single Instruction Multiple Data (SIMD) programming semantics of the GPU. Our approach is implemented on a NVIDIA GeForce GTX 8800 GPU card. Our results indicate that our approach can obtain an average speedup of about 260x as compared to a serial CPU implementation. With the recently announced quad 8800 GPU cards, we estimate that our approach would attain a speedup of over 785x. The correctness of the Monte Carlo based SSTA implemented on a GPU has been verified by comparing its results with a CPU based implementation.

SUMMARYThe Eulerian–Lagrangian Localized Adjoint Method (ELLAM) is well adapted for advection‐dominated transport problems. The method can use large time steps because the advection term is accurately approximated without any CFL restriction.A new formulation of ELLAM was developed by Younes et al. (Adv. Water Resour. 2006; 29:1056–1074) for unstructured triangular meshes. This formulation uses only strategic numerical integration points and thus requires a very limited number of integration points (usually 1 per element). To avoid numerical dispersion due to interpolation when several time steps are used, the method continuously tracks characteristics, and only changes due to dispersion are interpolated at each time step.In this work, we study the applicability and efficiency of this formulation for highly heterogeneous domains. The results show that (i) this formulation remains efficient even for highly heterogeneous domains, (ii) special care must be taken for the approximation of the dispersive term when large time steps are used, (iii) interpolation at intermediate times can be used to reduce memory requirement for problems with a large number of elements and small time steps, and (iv) the method can be used successfully for heterogeneous problems including injection and pumping wells, and remains much more efficient than the discontinuous Galerkin finite element method even when small time steps are required. Copyright © 2011 John Wiley & Sons, Ltd.

With the availability of high-frame-rate (HFR) PIV systems, it is possible to capture time series of particle images at rates which can exceed the necessary frequency to temporally resolve essential flow. In this case, some of the recorded frames can be skipped, in order to obtain an adequate time step between two images, leading to favorable values for pixel displacement. In this paper a technique for decreasing pixel locking in complex flows based on an adaptive time step processing procedure is proposed. If PIV data are taken at much higher frequency than needed, the processing can be repeated for multiple time steps, ensuring the optimal pixel displacement for every interrogation spot. A smaller time step is used for large velocities and larger time steps are used in the areas of low velocity. To illustrate this technique, a sample data set was acquired of the flow on the suction side and the region just downstream of a NACA 0015 hydrofoil at a high angle of attack (16 degrees), ensuring a wide range of velocities within the PIV field of view. The experiments were performed in the University of New Hampshire High-Speed Cavitation Tunnel – HiCaT, at a comparatively low speed (2 m/s) in order to increase the range of possible time steps for post processing. HFR PIV data were obtained at 1800 frames per second for a field of view of approximately 100 mm × 100 mm. The data were processed multiple times, each time skipping between 0 and 19 frames, resulting in time steps between 1 to 20 times of the original time step between two images. As expected, there is a significant difference between the results for mean velocities with different time step processing, most notably in the region of the suction side of the foil. The RMS velocity fields also show a similar trend. In order to obtain a more accurate representation of the mean flow, the data for each interrogation spot were combined based on the pixel displacement values. The resulting velocity field was compared to that obtained with single-time-step PIV. A “map” was created showing what time step was selected for each interrogation spot. Suggestions were made on what time steps should be selected for the post processing in order to decrease the post processing computational time. A discussion was provided on the feasibility of using the technique for instantaneous velocity fields. Using ATS PIV may be beneficial in flows where both large and small velocities are of importance, e.g., flows with separation.

Feedback control has become a crucial tool in the research on magnetic confinement of plasmas for achieving controlled nuclear fusion. This thesis presents a novel plasma feedback control system that, for the first time, employs a Graphics Processing Unit (GPU) for microsecond-latency, real-time control computations. This novel application area for GPU computing is opened up by a new system architecture that is optimized for low-latency computations on less than kilobyte sized data samples as they occur in typical plasma control algorithms. In contrast to traditional GPU computing approaches that target complex, high-throughput computations with massive amounts of data, the architecture presented in this thesis uses the GPU as the primary processing unit rather than as an auxiliary of the CPU, and data is transferred from A-D/D-A converters directly into GPU memory using peer-to-peer PCI Express transfers. The described design has been implemented in a new, GPU-based control system for the High-Beta Tokamak – Extended Pulse (HBT-EP) device. The system is built from commodity hardware and uses an NVIDIA GeForce GPU and D-TACQ A-D/D-A converters providing a total of 96 input and 64 output channels. The system is able to run with sampling periods down to 4 μs and latencies down to 8 μs. The GPU provides a total processing power of 1.5 x 1012 floating point operations per second. To illustrate the performance and versatility of both the general architecture and concrete implementation, a new control algorithm has been developed. The algorithm is designed for the control of multiple rotating magnetic perturbations in situations where the plasma equilibrium is not known exactly and features an adaptive system model: instead of requiring the rotation frequencies and growth rates embedded in the system model to be set a priori, the adaptive algorithm derives these parameters from the evolution of the perturbation amplitudes themselves. This results in non-linear control computations with high computational demands, but is handled easily by the GPU based system. Both digital processing latency and an arbitrary multi-pole response of amplifiers and control coils is fully taken into account for the generation of control signals. To separate sensor signals into perturbed and equilibrium components without knowledge of the equilibrium fields, a new separation method based on biorthogonal decomposition is introduced and used to derive a filter that performs the separation in real-time. The control algorithm has been implemented and tested on the new, GPU-based feedback control system of the HBT-EP tokamak. In this instance, the algorithm was set up to control four rotating n = 1 perturbations at different poloidal angles. The perturbations were treated as coupled in frequency but independent in amplitude and phase, so that the system effectively controls a helical n = 1 perturbation with unknown poloidal spectrum. Depending on the plasma's edge safety factor and rotation frequency, the control system is shown to be able to suppress the amplitude of the dominant 8 kHz mode by up to 60% or amplify the saturated amplitude by a factor of up to two. Intermediate feedback phases combine suppression and amplification with a speed up or slow down of the mode rotation frequency. Increasing feedback gain results in the excitation of an additional, slowly rotating 1.4 kHz mode without further effects on the 8 kHz mode. The feedback performance is found to exceed previous results obtained with an FPGA- and Kalman-filter based control system without requiring any tuning of system model parameters. Experimental results are compared with simulations based on a combination of the Boozer surface current model and the Fitzpatrick-Aydemir model. Within the subset of phenomena that can be represented by the model as well as determined experimentally, qualitative agreement is found.

With the development of wire/wireless network applications, numerous network attacks and security threats have brought great attention to all of us. Fast processing network traffic to the exclusion of malicious packets becomes increasingly important. Intrusion Detection/Prevention System (IDPS) is a network security system that monitors networks or system activities for malicious and unwanted behaviors without breaking the network traffic.In this paper, we study a kernel component of most IDPS, multi-pattern matching by exploiting two wellknown algorithms, namely Wu-Manber and Aho-Corasick. For this purpose, we implement both algorithms over Graphic Processing Units (GPU) to speed up the malicious packet detection. Extensive experiments are conducted to compare the performance of our implementations on both CPU and GPU. Our experimental results show that the throughput of GPU implementation is about four times faster than CPU. Therefore, on the basis of considering the lower cost, easy expansion and better performance, rather than specific hardware, such as ASIC, TCAM, Bloom Filter, and so on, IDPS over GPU offers an attractive solution to speed up malicious packets detection among the normal traffic.

Summary form only given. Present day computers equipped with powerful graphics processing units (GPUs) show considerable promise of increased performance for the electromagnetic (EM) modeler. In order to determine the degree of performance gain achievable for electro-energetic physics computations, the MAGIC EM finite difference-time domain (FDTD) particle-in-cell (PIC) plasma code is undergoing testing for parallel speedup on typical large scale plasma wave EM calculations using GPU processing. The results of the tests are expected to be of great interest to the EM community because MAGIC is widely employed and implements the methods common to many large scale applications. The performance data obtained will quantify the benefits of GPUs, and aid in selecting the proper system including GPUs potentially critical to effectiveness with EM/plasma codes where calculation times often run into days due to small zone and time step requirements. GPUs promise a relatively low cost boost leveraging the vast development driven by the computer game industry.

Detailed switching models (DSM) of ac–dc converters are available in many offline and real-time electromagnetic transient (EMT) simulation programs. However, such discrete models typically require small simulation time steps for accurately handling the switching events without interpolation. This paper proposes a new parametric modeling approach for line-commutated and 2-level voltage-source ac–dc converters. The proposed methodology is based on parametric functions that relate ac and dc variables in the instantaneous sense, which allows the reconstruction of the waveforms of voltages and currents (with the same of details as the switching models of converters) without topological changes in the converter circuit. Thus, it can operate at larger time steps without requiring interpolation, thereby enhancing simulation efficiency. The computational advantages of the proposed models over the conventional switching models are demonstrated in offline PSCAD and real-time RTDS NovaCor simulators in terms of maximum possible time step size and accuracy. It is shown that the proposed models can accurately run with much larger time steps (up to ∼200 μs for LCRs, and up to ∼50 μs for VSCs) compared to detailed switching models, which are limited to relatively small time steps of ∼10 μs.

This paper presents a computational acceleration of image inpainting using parallel processing based on Graphics Processing Unit (GPU) Compute Unified Device Architecture (CUDA). We use parabolic partial differential equation (PDE) called heat equation as the model equation. The heat equation is discretized numerically using Finite Difference method. Semi-algebraic equation that formed then solved by using Alternating-Direction Implicit (ADI) scheme. The numerical algorithm is implemented in GPU CUDA parallel computing to speed up the computational time. The computational process of the inpainting can be done using larger time-step. The computational time can be accelerated to 5.86 times faster using an image with 2736×1824 resolution.

Multi-phase SPH modelling of violent hydrodynamics on GPUs

Abstract. A new anelastic large-eddy simulation (LES) model with an Eulerian dynamical core and Lagrangian particle-based microphysics is presented. The dynamical core uses the multidimensional positive-definite advection transport algorithm (MPDATA) advection scheme and the generalized conjugate residual pressure solver, whereas the microphysics scheme is based on the super-droplet method. Algorithms for coupling of Lagrangian microphysics with Eulerian dynamics are presented, including spatial and temporal discretizations and a condensation substepping algorithm. The model is free of numerical diffusion in the droplet size spectrum. Activation of droplets is modeled explicitly, making the model less sensitive to local supersaturation maxima than models in which activation is parameterized. Simulations of a drizzling marine stratocumulus give results in agreement with other LES models. It is shown that in the super-droplet method a relatively low number of computational particles is sufficient to obtain correct averaged properties of a cloud, but condensation and collision–coalescence have to be modeled with a time step of the order of 0.1 s. Such short time steps are achieved by substepping, as the model time step is typically around 1 s. Simulations with and without an explicit subgrid-scale turbulence model are compared. Effects of modeling subgrid-scale motion of super-droplets are investigated. The model achieves high computational performance by using graphics processing unit (GPU) accelerators.

Currently, the mechanical dynamics of soft tissue deformation is achieved by numerical time integrations such as the explicit or implicit integration; however, the explicit integration is stable only under a small time step, whereas the implicit integration is computationally expensive in spite of the accommodation of a large time step. This paper presents a cellular neural network method for stable simulation of soft tissue deformation dynamics. The non-rigid motion equation is formulated as a cellular neural network with local connectivity of cells, and thus the dynamics of soft tissue deformation is transformed into the neural dynamics of the cellular neural network. Results show that the proposed method can achieve good accuracy at a small time step. It still remains stable at a large time step, while maintaining the computational efficiency of the explicit integration. The proposed method can achieve stable soft tissue deformation with efficiency of explicit integration for surgical simulation.

In this paper we re-examine the idea that implicit integrators with large time steps offer the best stability/performance trade-off for stiff systems. We make the surprising observation that performing a single large time step with n constraint solver iterations is less effective than computing n smaller time steps, each with a single constraint solver iteration. Based on this observation, our approach is to split every visual time step into n substeps of length Δt/n and to perform a single iteration of extended position-based dynamics (XPBD) in each such substep. When compared to a traditional implicit integrator with large time steps we find constraint error and damping are significantly reduced. When compared to an explicit integrator we find that our method is more stable and robust for a wider range of stiffness parameters. This result holds even when compared against more sophisticated implicit solvers based on Krylov methods. Our method is straightforward to implement, and is not sensitive to matrix conditioning nor is it to overconstrained problems.

Using modern Graphic Processing Units (GPUs) becomes very useful for computing complex and time consuming processes. GPUs provide high-performance computation capabilities with a good price. This paper deals with a multi-GPU OpenCL implementation of k-Nearest Neighbor (k-NN) algorithm. The proposed OpenCL algorithm achieves acceleration up to 750x in comparison with a single thread CPU version. The common k-NN was modified to be faster when the lower number of k neighbors is set. The performance of algorithm was verified with two GPUs dual-core NVIDIA GeForce GTX 690 and CPU Intel Core i7 3770 with 4.1 GHz frequency. The results of speed up were measured for one GPU, two GPUs, three and four GPUs. We performed several tests with data sets containing up to 4 million elements with various number of attributes.