This study proposed the application of a novel immersed boundary method (IBM) for the treatment of irregular geometries using Cartesian computational grids for high speed compressible gas flows modelled using the unsteady Euler equations. Furthermore, the method is accelerated through the use of multiple Graphics Processing Units – specifically using Nvidia’s CUDA together with MPI - due to the computationally intensive nature associated with the numerical solution to multi-dimensional continuity equations. Due to the high degree of locality required for efficient multiple GPU computation, the Split Harten-Lax-van-Leer (SHLL) scheme is employed for vector splitting of fluxes across cell interfaces. NVIDIA visual profiler shows that our proposed method having a computational speed of 98.6 GFLOPS and 61% efficiency based on the Roofline analysis that provides the theoretical computing speed of reaching 160 GLOPS with an average 2.225 operations/byte. To demonstrate the validity of the method, results from several benchmark problems covering both subsonic and supersonic flow regimes are presented. Performance testing using 96 GPU devices demonstrates a speed up of 89 times that of a single GPU (i.e. 92% efficiency) for a benchmark problem employing 48 million cells. Discussions regarding communication overhead and parallel efficiency for varying problem sizes are also presented.

Scanning transmission electron microscopy (STEM) has become the main stay for materials characterization on atomic level, with applications ranging from visualization of localized and extended defects to mapping order parameter fields. In recent years, attention has focused on the potential of STEM to explore beam induced chemical processes and especially manipulating atomic motion, enabling atom-by-atom fabrication. These applications, as well as traditional imaging of beam sensitive materials, necessitate increasing the dynamic range of STEM in imaging and manipulation modes, and increasing the absolute scanning speed which can be achieved by combining sparse sensing methods with nonrectangular scanning trajectories. Here we have developed a general method for real-time reconstruction of sparsely sampled images from high-speed, noninvasive and diverse scanning pathways, including spiral scan and Lissajous scan. This approach is demonstrated on both the synthetic data and experimental STEM data on the beam sensitive material graphene. This work opens the door for comprehensive investigation and optimal design of dose efficient scanning strategies and real-time adaptive inference and control of e-beam induced atomic fabrication.

This paper presents a GPU-accelerated implementation of the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method with an inexact nullspace filtering approach to find eigenvalues in electromagnetics analysis with higher-order FEM. The performance of the proposed approach is verified using the Kepler (Tesla K40c) graphics accelerator, and is compared to the performance of the implementation based on functions from the Intel MKL on the Intel Xeon (E5-2680 v3, 12 threads) central processing unit (CPU) executed in parallel mode. Compared to the CPU reference implementation based on the Intel MKL functions, the proposed GPU-based LOBPCG method with inexact nullspace filtering allowed us to achieve up to 2.9-fold acceleration.

In this study an explicit Finite Difference Method (FDM) based scheme is developed to solve the Maxwell's equations in time domain for a lossless medium. This manuscript focuses on two unique aspects – the three dimensional time-accurate discretization of the hyperbolic system of Maxwell equations in three-point non-staggered grid stencil and it's application to parallel computing through the use of Graphics Processing Units (GPU). The proposed temporal scheme is symplectic, thus permitting conservation of all Hamiltonians in the Maxwell equation. Moreover, to enable accurate predictions over large time frames, a phase velocity preserving scheme is developed for treatment of the spatial derivative terms. As a result, the chosen time increment and grid spacing can be optimally coupled. An additional theoretical investigation into this pairing is also shown. Finally, the application of the proposed scheme to parallel computing using one Nvidia K20 Tesla GPU card is demonstrated. For the benchmarks performed, the parallel speedup when compared to a single core of an Intel i7-4820K CPU is approximately 190x.

A new solver is developed to numerically simulate the melting phase change with natural convection. This solver was implemented on a single Nvidia GPU based on the CUDA technology in order to simulate the melting phase change in a 2D rectangular enclosure. The Rayleigh number is of the order of magnitude of 108 and Prandlt is 50. The hybrid thermal lattice Boltzmann method (HTLBM) is employed to simulate the natural convection in the liquid phase, and the enthalpy formulation is used to simulate the phase change aspect. The model is validated by experimental data and published analytic results. The simulation results manifest a strong convection in the melted phase and a different flow pattern from the reference results with low Rayleigh number. In addition, the computational performance is estimated for single precision arithmetic, and this solver yields 703.31MLUPS and 61.89GB/s device to device data throughput on a Nvidia Tesla C2050 GPU.

This paper presents a fast surface voxelization technique for the mapping of tessellated triangular surface meshes to uniform and structured grids that provide a basis for CFD simulations with the lattice Boltzmann method (LBM). The core algorithm is optimized for massively parallel execution on graphics processing units (GPUs) and is based on a unique dissection of the inner body shell. This unique definition necessitates a topology based neighbor search as a preprocessing step, but also enables parallel implementation. More specifically, normal vectors of adjacent triangular tessellations are used to construct half-angles that clearly separate the per-triangle regions. For each triangle, the grid nodes inside the axis-aligned bounding box (AABB) are tested for their distance to the triangle in question and for certain well-defined relative angles. The performance of the presented grid generation procedure is superior to the performance of the GPU-accelerated flow field computations per time step which allows efficient fluid-structure interaction simulations, without noticeable performance loss due to the dynamic grid update.

This paper presents a new approach to accurately track a moving vehicle with a multiview setup of red–green–blue depth (RGBD) cameras. We first propose a correction method to eliminate a shift, which occurs in depth sensors when they become worn. This issue could not be otherwise corrected with the ordinary calibration procedure. Next, we present a sensor-wise filtering system to correct for an unknown vehicle motion. A data fusion algorithm is then used to optimally merge the sensor-wise estimated trajectories. We implement most parts of our solution in the graphic processor. Hence, the whole system is able to operate at up to 25 frames per second with a configuration of five cameras. Test results show the accuracy we achieved and the robustness of our solution to overcome uncertainties in the measurements and the modelling.

The direct-summation of N gravitational forces is a complex problem for which there is no analytical solution. Dense stellar systems such as galactic nuclei and stellar clusters are the loci of different interesting problems. In this work we present a new GPU, direct-summation N-body integrator written from scratch and based on the Hermite scheme. The first release of the code consists of the Hermite integrator for a system of N bodies with softening. We find an acceleration factor of about ≈ 90 of the GPU version in a single node as compared to the Serial-Single-CPU one. We additionally investigate the impact of using softening in the dynamics of a dense cluster. We study how it affects the two body relaxation, as compared with another code, NBODY6, which uses KS regularization, so as to understand the role of softening in the evolution of the system. This initial release is the first step towards more and more realistic scenarios, starting for a proper treatment for binary evolution, close encounters and the role of a massive black hole.

With financial modelling requiring a better understanding of model risk, it is helpful to be able to vary assumptions about underlying probability distributions in an efficient manner, preferably without the noise induced by resampling distributions managed by Monte Carlo methods. This paper presents differential equations and solution methods for the functions of the form Q(x) = F−1(G(x)), where F and G are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples from one distribution into samples from another. The method may be developed analytically for certain special cases, and illuminate the idea that it is a more precise form of the traditional Cornish–Fisher expansion. In this manner the model risk of distributional risk may be assessed free of the Monte Carlo noise associated with resampling. The method may also be regarded as providing both analytical and numerical bases for doing more precise Cornish–Fisher transformations. Examples are given of equations for converting normal samples to Student t, and converting exponential to normal. In the case of the normal distribution, the change of variables employed allows the sampling to take place to good accuracy based on a single rational approximation over a very wide range of sample space. The avoidance of branching statements is of use in optimal graphics processing unit (GPU) computations as it avoids the effect of branch divergence. We give a branch-free normal quantile that offers performance improvements in a GPU environment while retaining the best precision characteristics of well-known methods. We also offer models with low probability branch divergence. Comparisons of new and existing forms are made on Nvidia GeForce GTX Titan and Tesla C2050 GPUs. We argue that in both single- and double-precisions, the change-of-variables approach offers the most GPU-optimal Gaussian quantile yet, working faster than the Cuda 5.5 built-in function.

PyFAI is an open-source Python library for Fast Azimuthal Integration which provides 1D- and 2D-azimuthal regrouping with a clean programming interface and tools for calibration. The library is suitable for interactive use in Python. In optimising the speed of the algorithms there has been no compromise on the accuracy compared to reference software. Fast integrations are obtained by the combination of an algorithm ensuring that each pixel from the detector provides a direct contribution to the final diffraction pattern and an OpenCL implementation that can use graphics cards for acceleration. This contribution describes how the algorithms were modified to work better in parallel.

A GPU-based acceleration for the direct boundary integral equation method (GPU-DBIE) to extrapolate solar coronal magnetic fields is developed, which is about 1000 times faster than the original DBIE. The 3-d coronal magnetic field is reconstructed for NOAA 11158 on 14-Feb-2011 with the SDO/HMI vector magnetogram as bottom boundary condition. The extrapolated results agree well with the projected SDO/AIA, EUV loops and the STEREO EUV sideviews, which verifies the correctness of our GPU-DBIE method. It is also found that the group of bright EUV loops along magnetic neutral lines agree well with current lines, which may have played an important role in the flare process of the active region.

Most of the norms used in the field of digital image (and volume) correlation to registertwo images (or volumes) lead to ill-posed problems. One of the frequent solutions is toenforce a restricted kinematics requiring a compromise between the richness of thesolution (i.e., the spatial resolution) and the measurement uncertainty. An alternativeroute is to use a displacement norm that permits to alleviate this compromise by the meansof a mechanical regularization used when the gray levels do not give enough information.It is then possible to compute a displacement vector for each pixel orvoxel, inducing lower residuals (in terms of experimental data) whiledecreasing the noise sensitivity. The resolution performance of these different approachesis discussed, and compared for the analysis of a tensile test on a cast iron specimenbased on a pair of tomographic images. As representative reconstructed volumes lead to alarge number of degrees of freedom, a dedicated GPU computational strategy has beendeveloped and implemented.

Structured illumination fluorescence microscopy is a powerful super-resolution method that is capable of achieving a resolution below 100 nm. Each super-resolution image is computationally constructed from a set of differentially illuminated images. However, real-time application of structured illumination microscopy (SIM) has generally been limited due to the computational overhead needed to generate super-resolution images. Here, we have developed a real-time SIM system that incorporates graphic processing unit (GPU) based in-line parallel processing of raw/differentially illuminated images. By using GPU processing, the system has achieved a 90-fold increase in processing speed compared to performing equivalent operations on a multiprocessor computer—the total throughput of the system is limited by data acquisition speed, but not by image processing. Overall, more than 350 raw images (16-bit depth, 512 × 512 pixels) can be processed per second, resulting in a maximum frame rate of 39 super-resolution images per second. This ultrafast processing capability is used to provide immediate feedback of super-resolution images for real-time display. These developments are increasing the potential for sophisticated super-resolution imaging applications.