A fast GPU based bidiagonal solver for computational aeroacoustics

To understand the mechanism of information processing by a biological neural network, computer simulation of a large-scale spiking neural network is an important method. However, because of a high computation cost of the simulation of a large-scale spiking neural network, the simulation requires high performance computing implemented by a supercomputer or a computer cluster. Recently, hardware for parallel computing such as a multi-core CPU and a graphics card with a graphics processing unit (GPU) is built in a gaming computer and a workstation. Thus, parallel computing using this hardware is becoming widespread, allowing us to obtain powerful computing power for simulation of a large-scale spiking neural network. However, it is not clear how much increased performance the parallel computing method using a new GPU yields in the simulation of a large-scale spiking neural network. In this study, we compared computation time between the computing methods with CPUs and GPUs in a simulation of neuronal models. We developed computer programs of neuronal simulations for the computing systems that consist of a gaming graphics card with new architecture (the NVIDIA GTX 1080) and an accelerator board using a GPU (the NVIDIA Tesla K20C). Our results show that the computing systems can perform a simulation of a large number of neurons faster than CPU-based systems. Furthermore, we investigated the accuracy of a simulation using single precision floating point. We show that the simulation results of single precision were accurate enough compared with those of double precision, but chaotic neuronal response calculated by a GPU using single precision is prominently different from that calculated by a CPU using double precision. Furthermore, the difference in chaotic dynamics appeared even if we used double precision of a GPU. In conclusion, the GPU-based computing system exhibits a higher computing performance than the CPU-based system, even if the GPU system includes data transfer from a graphics card to host memory.

This paper deals with the development of a computational code for the numerical simulation of wave propagation through domains with a complex geometry consisting in both solids and moving fluids. The emphasis is on the numerical simulation of ultrasonic flowmeters (UFMs) by modeling the wave propagation in solids with the equations of linear elasticity (ELE) and in fluids with the linearized Euler equations (LEEs). This approach requires high performance computing because of the high number of degrees of freedom and the long propagation distances. Therefore, the numerical method should be chosen with care. In order to minimize the numerical dissipation which may occur in this kind of configuration, the numerical method employed here is the nodal discontinuous Galerkin (DG) method. Also, this method is well suited for parallel computing. To speed up the code, almost all the computational stages have been implemented to run on graphical processing unit (GPU) by using the compute unified device architecture (CUDA) programming model from NVIDIA. This approach has been validated and then used for the two-dimensional simulation of gas UFMs. The large contrast of acoustic impedance characteristic to gas UFMs makes their simulation a real challenge.

Particle-mesh interpolations are fundamental operations for particle-in-cell codes, as implemented in vortex methods, plasma dynamics and electrostatics simulations. In these simulations, the mesh is used to solve the field equations and the gradients of the fields are used in order to advance the particles. The time integration of particle trajectories is performed through an extensive resampling of the flow field at the particle locations. The computational performance of this resampling turns out to be limited by the memory bandwidth of the underlying computer architecture. We investigate how mesh-particle interpolation can be efficiently performed on graphics processing units (GPUs) and multicore central processing units (CPUs), and we present two implementation techniques. The single-precision results for the multicore CPU implementation show an acceleration of 45-70×, depending on system size, and an acceleration of 85-155× for the GPU implementation over an efficient single-threaded C++ implementation. In double precision, we observe a performance improvement of 30-40× for the multicore CPU implementation and 20-45× for the GPU implementation. With respect to the 16-threaded standard C++ implementation, the present CPU technique leads to a performance increase of roughly 2.8-3.7× in single precision and 1.7-2.4× in double precision, whereas the GPU technique leads to an improvement of 9× in single precision and 2.2-2.8× in double precision.

Traditional methods of target velocity search based on pulse compression using GPU (Graphics Processing Unit) with single precision floating point format are difficult to meet the requirements of real-time processing. In this paper, a novel method for accelerating search process with half precision floating point format, which is based on the latest NVIDIA GPU card Tesla P100, is proposed. The scaling factor is defined to avoid the overflow issues with half precision floating point numbers. And the expression of scaling factor for LFM (Linear frequency modulation) signal is also derived. Measurement results show that about 50% promotion of computation speed is attainable with half precision floating point format when compared to single precision floating point format, which indicates the method can accelerate the searching speed efficiently.

GPU Acceleration of CFD Algorithm: HSMAC and SIMPLE

The variable preconditioned (VP) Krylov subspace method with mixed precision is implemented on graphics processing unit (GPU) using compute unified device architecture (CUDA), and the linear system obtained from the edge element is solved by means of the method. The VPGCR method has the sufficient condition for the convergence. This sufficient condition leads us that the residual equation for the preconditioned procedure of VPGCR can be solved in the range of single precision. To stretch the sufficient condition, we propose the hybrid scheme of VP Krylov subspace method that uses single and double precision operations. The results of computations show that VPCG with mixed precision on GPU demonstrated significant achievement than that of CPU. Especially, VPCG-JOR on GPU with mixed precision is 41.853 times faster than that of VPCG-CG on CPU.

Hands-on Performance Tuning of 3D Finite Difference Earthquake Simulation on GPU Fermi Chipset

We propose a novel graphics processing unit (GPU) algorithm that can handle a large‐scale 3D fast Fourier transform (i.e., 3D‐FFT) problem whose data size is larger than the GPU's memory. A 1D FFT‐based 3D‐FFT computational approach is used to solve the limited device memory issue. Moreover, to reduce the communication overhead between the CPU and GPU, we propose a 3D data‐transposition method that converts the target 1D vector into a contiguous memory layout and improves data transfer efficiency. The transposed data are communicated between the host and device memories efficiently through the pinned buffer and multiple streams. We apply our method to various large‐scale benchmarks and compare its performance with the state‐of‐the‐art multicore CPU FFT library (i.e., fastest Fourier transform in the West [FFTW]) and a prior GPU‐based 3D‐FFT algorithm. Our method achieves a higher performance (up to 2.89 times) than FFTW; it yields more performance gaps as the data size increases. The performance of the prior GPU algorithm decreases considerably in massive‐scale problems, whereas our method's performance is stable.

PCB design aids

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

This work deals with the solution of large non-Hermitian linear systems on desktop workstations with multiple graphics processing units (GPUs). While our implementation is motivated by the need to accelerate volume conductor modeling for bioelectrical brain imaging, the problem itself is common in scientific computing. Whenever a complex partial differential equation is numerically solved, a typically non-Hermitian sparse complex linear system needs to be solved. For problem sizes in the millions, this can take a long time even with highly optimized CPU-based solvers. Our GPU-accelerated solver outperforms an optimized OpenMP-based reference running on two quad-core CPUs by a factor of up to 31× in single precision and up to 7× in double precision, at the cost of a very modest hardware upgrade of two dual-GPU GTX 295 graphics cards. A pair of stronger Fermi GPUs (GTX 480) achieves speedups of 30× in single precision and 15× in double precision.

Due to the reduction of fuel consumption and new global emission limits, especially for the pollutant emissions of NOx, improvements to lean combustion technologies in aeroengine combustors are unavoidable. Near to the lean limits, combustion tends to be unstable. A geometry related coupling between unsteady heat release and acoustic perturbations leads to thermoacoustic instabilities, which show an undesirable impact on pressure, velocity and heat release in the combustor. Such instabilities occur when the unsteady heat release fluctuations are in phase with the acoustic pressure fluctuations. The aim of this study is to find an industrially applicable, three-dimensional numerical model for the prediction of combustion noise, which can also provide insight in thermoacoustic instabilities and acoustic effects in a responsive environment in enclosed, technical combustion systems. The turbulent reacting flow in a realistic gas turbine combustor has been computed by means of Large Eddy Simulation coupled to a tabulated chemistry approach based on the Flamelet Generated Manifold ansatz. The reactive LES provides very well suited method to study the impact of unsteady heat release as a major source of acoustic noise in combustion. For the simultaneous treatment of the reacting flow and its acoustic features, a Computational Aero Acoustics (CAA) solver has been coupled with the LES solver following a hybrid approach. In this work the acoustic wave propagation is calculated by the Linearized Euler Equations (LEE). The interface between both codes is optimized for the realisation of an acoustic feedback loop in order to obtain a suitable representation of acoustically self-excited oscillations. To demonstrate the prediction capability of the hybrid LES/CAA approach, geometry-dependent thermoacoustic instabilities in a generic half-dump combustor, for which experimental data are available, are investigated. The numerical results are compared to measured pressure fluctuations under both thermoacoustically stable and unstable conditions.

The field of Deep Learning has benefitted greatly by the availability of accelerators like Graphics Processing Units (GPUs) and of open source deep learning frameworks which can exploit these GPUs. As the GPUs become faster, a key aspect of system design is being able to supply them data at a rate where they can be kept busy. A balanced system design is important. In this paper, we investigate these issues with experiments on a distributed deep learning system called Phalanx. Phalanx is a data parallel distributed deep learning system which exploits Caffe as its basic learning engine in the nodes. These nodes run on GPUs and uses infiniband for communication1

A wide class of numerical methods needs to solve a linear system, where the matrix pattern of non-zero coefficients can be arbitrary. These problems can greatly benefit from highly multithreaded computational power and large memory bandwidth available on graphics processor units (GPUs), especially since dedicated general purpose APIs such as close-to-metal (CTM) (AMD–ATI) and compute unified device architecture (CUDA) (NVIDIA) have appeared. CUDA even provides a BLAS implementation, but only for dense matrices (CuBLAS). Other existing linear solvers for the GPU are also limited by their internal matrix representation. This paper describes how to combine recent GPU programming techniques and new GPU dedicated APIs with high performance computing strategies (namely block compressed row storage (BCRS), register blocking and vectorization), to implement a sparse general-purpose linear solver. Our implementation of the Jacobi-preconditioned conjugate gradient algorithm outperforms by up to a factor of 6.0 × leading-edge CPU counterparts, making it attractive for applications which are content with single precision.

This paper focuses on designing and implementing parallel adaptive inverse distance weighting (AIDW) interpolation algorithms by using the graphics processing unit (GPU). The AIDW is an improved version of the standard IDW, which can adaptively determine the power parameter according to the data points’ spatial distribution pattern and achieve more accurate predictions than those predicted by IDW. In this paper, we first present two versions of the GPU-accelerated AIDW, i.e. the naive version without profiting from the shared memory and the tiled version taking advantage of the shared memory. We also implement the naive version and the tiled version using two data layouts, structure of arrays and array of aligned structures, on both single and double precision. We then evaluate the performance of parallel AIDW by comparing it with its corresponding serial algorithm on three different machines equipped with the GPUs GT730M, M5000 and K40c. The experimental results indicate that: (i) there is no significant difference in the computational efficiency when different data layouts are employed; (ii) the tiled version is always slightly faster than the naive version; and (iii) on single precision the achieved speed-up can be up to 763 (on the GPU M5000), while on double precision the obtained highest speed-up is 197 (on the GPU K40c). To benefit the community, all source code and testing data related to the presented parallel AIDW algorithm are publicly available.