MATLAB package for discrete dipole approximation by graphics processing unit: Fast Fourier Transform and Biconjugate Gradient

It is known that parallel computing systems have some advantages to solve large scale and hard problems. However, traditional multi-processor parallel architectures are not widely used since they are hard to operate and they have high cost in setting-up .It has been an important point to Graphical Processing Units (GPU) were shown to be used in general-purpose applications because they naturally have hundreds of parallel cores. Studies related with the usage of GPUs in general-purpose are increasing day by day. In this study, Fast Fourier Transform (FFT), Inverse Fast Fourier Transform (IFFT) and Radon Transforms widely used in signal and image processing problems have been implemented on Quadro FX 3800 GPU which is one of the recent graphical cards of NVIDIA. From the results, applications on GPU provided gain in terms of time as compared to the applications implemented on traditional Central Processing Unit (CPU).

Wideband channelization is a compute-intensive task with performance requirements that are arguably greater than what current multi-core CPUs can provide. To date, researchers have used dedicated hardware such as field programmable gate arrays (FPGAs) to address the performance-critical aspects of the channelizer. In this work, we assess the viability of the graphics processing unit (GPU) to achieve the necessary performance. In particular, we focus on the fast Fourier Transform (FFT) stage of a wideband channelizer. While there exists previous work for FFT on a NVIDIA GPU, the substantially higher peak floating-point performance of an AMD GPU has been less explored. Thus, we consider three generations of AMD GPUs and provide insight into the optimization of FFT on these platforms. Our architecture-aware approach across three different generations of AMD GPUs outperforms a multithreaded Intel Sandy Bridge CPU with vector extensions by factors of 4.3, 4.9, and 6.6 on the Radeon HD 5870, 6970, and 7970, respectively.

Mineral dust particles are the second highest emitted aerosol type by mass. Due to changes in particle size, composition, and shape that are caused by physical processes and reactive chemistry, optical properties vary during transport, contributing uncertainty in the calculation of radiative forcing. Hematite is the major absorbing species of mineral dust. In this study, we analyzed the extinction cross sections of nigrosin and hematite particles using cavity ring‐down aerosol extinction spectroscopy (CRD‐AES) and have measured particle shape and size distributions using transmission electron microscopy. Nigrosin was also used in this study as a spherical standard for absorbing particles. The size‐selected nigrosin particles have a narrow size distribution, with extinction cross sections that are described by Mie theory. In contrast, the size distribution of size‐selected hematite particles is more polydisperse. The extinction cross sections were modeled using Mie theory and the discrete dipole approximation (DDA). The DDA was used to model more complex shapes that account for the surface roughness and particle geometry. Of the four models used, Mie theory was the simplest to implement, but had significant error with a 26.1% difference from the CRD‐AES results. By increasing the complexity of the models using the DDA, we determined that spheroids had a 14.7% difference, roughened spheres a 12.8% difference, and roughened spheroids a 11.2% difference from the experimental results. Using additional parameters that account for particle shape is necessary to model the optical properties of hematite particles and leads to improved extinction cross sections for modeling aerosol optical properties.

The technologically-relevant task of feature extraction from data performed in deep-learning systems is routinely accomplished as repeated fast Fourier transforms (FFT) electronically in prevalent domain-specific architectures such as in graphics processing units (GPU). However, electronics systems are limited with respect to power dissipation and delay, due to wire-charging challenges related to interconnect capacitance. Here we present a silicon photonics-based architecture for convolutional neural networks that harnesses the phase property of light to perform FFTs efficiently by executing the convolution as a multiplication in the Fourier-domain. The algorithmic executing time is determined by the time-of-flight of the signal through this photonic reconfigurable passive FFT ‘filter’ circuit and is on the order of 10’s of picosecond short. A sensitivity analysis shows that this optical processor must be thermally phase stabilized corresponding to a few degrees. Furthermore, we find that for a small sample number, the obtainable number of convolutions per {time, power, and chip area) outperforms GPUs by about two orders of magnitude. Lastly, we show that, conceptually, the optical FFT and convolution-processing performance is indeed directly linked to optoelectronic device-level, and improvements in plasmonics, metamaterials or nanophotonics are fueling next generation densely interconnected intelligent photonic circuits with relevance for edge-computing 5G networks by processing tensor operations optically.

We present a graphics processing units (GPU) parallelization based three-dimensional time-dependent Schrödinger equation (3D-TDSE) code to simulate the interaction between single-active-electron atom/molecule and arbitrary types of laser pulses with either velocity gauge or length gauge in Cartesian coordinates. Split-operator method combined with fast Fourier transforms (FFT) is used to perform the time evolution. Sample applications in different scenarios, such as stationary state energies, photon ionization spectra, attosecond clocks, and high-order harmonic generation (HHG), are given for the hydrogen atom. Repeatable results can be obtained with the benchmark program PCTDSE, which is a 3D-TDSE Fortran solver parallelized using message passing interface (MPI) library. With the help of GPU acceleration and vectorization strategy, our code running on a single NVIDIA 3090 RTX GPU can achieve about 10 times faster computation speed than PCTDSE running on a 144 Intel Xeon CPU cores server with the same accuracy. In addition, 3D-GTDSE can also be modified slightly to simulate non-adiabatic dynamics involving the coupling of nuclear and electronic wave packets, as well as pure nuclear wave packet dynamics in the presence of strong laser fields within 3 dimensions. Additionally, we have also discussed the limitations and shortcomings of our code in utilizing GPU memory. The 3D-GTDSE code provides an alternative tool for studying the ultrafast nonlinear dynamics under strong laser fields.

For a phase-sensitive optical time-domain reflectometer (ϕ-OTDR) distributed sensor system, space-frequency analysis can reduce the false alarm by analyzing the frequency distribution compared with the traditional difference value method. We propose a graphics processing unit (GPU)-based parallel computing method to perform multichannel fast Fourier transform (FFT) and realize the real-time space-frequency analysis. The experiment results show that the time taken by the multichannel FFT decreased considerably based on this GPU parallel computing. The method can be completed with a sensing fiber up to 16 km long and an entry-level GPU. Meanwhile, the GPU can reduce the computing load of the central processing unit from 70% down to less than 20%. We carried out an experiment on a two-point space-frequency analysis, and the results clearly and simultaneously show the vibration point locations and frequency components. The sensor system outputs the real-time space-frequency spectra continuously with a spatial resolution of 16.3 m and frequency resolution of 2.25 Hz.

This study performed the system identification of a target structure by analyzing the laser speckle pattern taken by a camera. The laser speckle pattern is generated by the diffuse reflection of the laser beam on a rough surface of the target structure. The camera, equipped with a red filter, records the scattered speckle particles of the laser light in real time and the raw speckle image of the pixel data is fed to the graphic processing unit (GPU) in the system. The algorithm for laser speckle contrast analysis (LASCA) computes: the laser speckle contrast images and the laser speckle flow images. The k-mean clustering algorithm is used to classify the pixels in each frame and the clusters’ centroids, which function as virtual sensors, track the displacement between different frames in time domain. The fast Fourier transform (FFT) and the frequency domain decomposition (FDD) compute the modal properties of the structure: natural frequencies and damping ratios. This study takes advantage of the large scale computational capability of GPU. The algorithm is written in Compute Unifies Device Architecture (CUDA C) that allows the processing of speckle images in real time.

Without doubt, the fast Fourier transform (FFT) belongs to the algorithms with large impact on science and engineering. By appropriate approximations, this scheme has been generalized for arbitrary spatial sampling points. This so called nonequispaced FFT is the core of the sequential NFFT3 library and we discuss its computational costs in detail. On the other hand, programmable graphics processing units have evolved into highly parallel, multithreaded, manycore processors with enormous computational capacity and very high memory bandwidth. By means of the so called Compute Unified Device Architecture (CUDA), we parallelized the nonequispaced FFT using the CUDA FFT library and a dedicated parallelization of the approximation scheme. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Orientation-averaged optical properties of natural aerosol aggregates were analyzed by using discrete dipole approximation (DDA) for the effective radius in the range of 0.01 to 2 m with the corresponding size parameter from 0.1 to 23 for the wavelength of 0.55 m. Effects of the composition and morphology on the optical properties were also investigated. The composition show small influence on the extinction-efficiency factor in Mie scattering region, scattering-and backscattering-efficiency factors, and asymmetry factor, but great on the extinction efficiency factor in Rayleigh scattering region and absorption-efficiency factor. The extinction-efficiency factor with the size parameter from 9 to 23 and asymmetry factor with the size parameter below 2.3 are almost independent of the natural aerosol composition. The extinction-, absorption-, scattering-, and backscattering-efficiency factors with the size parameter below 0.7 are irrespective of the aggregate morphologly. The intrinsic symmetry and discontinuity of the normal direction of the particle surface have obvious effects on the scattering properties for the size parameter above 4.6. Furthermore, the scattering phase functions of natural aerosol aggregates are enhanced at the backscattering direction (opposition effect) for large size parameters in the range of Mie scattering.

Fiber alignment plays a critical role in the structure and function of cells and tissues. While fiber alignment quantification is important to experimental analysis and several different methods for quantifying fiber alignment exist, many studies focus on qualitative rather than quantitative analysis perhaps due to the complexity of current fiber alignment methods. Speed and sensitivity were compared in edge detection and fast Fourier transform (FFT) for measuring actin fiber alignment in cells exposed to shear stress. While edge detection using matrix multiplication was consistently more sensitive than FFT, image processing time was significantly longer. However, when MATLAB functions were used to implement edge detection, MATLAB's efficient element-by-element calculations and fast filtering techniques reduced computation cost 100 times compared to the matrix multiplication edge detection method. The new computation time was comparable to the FFT method, and MATLAB edge detection produced well-distributed fiber angle distributions that statistically distinguished aligned and unaligned fibers in half as many sample images. When the FFT sensitivity was improved by dividing images into smaller subsections, processing time grew larger than the time required for MATLAB edge detection. Implementation of edge detection in MATLAB is simpler, faster, and more sensitive than FFT for fiber alignment quantification.

The discrete dipole approximation (DDA) is a general method to simulate light scattering by arbitrary particles. This talk reviews the DDA with focus on its application to very large particle systems, typically consisting of large numbers of particles with sizes comparable to or larger than the wavelength. Overall, the DDA is a viable option for such problems - it is conceptually simple, can naturally handle arbitrary inhomogeneous particles, and benefits from the availability of open-source codes. However, the major limitation is the computational complexity rapidly increasing with the size of the system. A few ideas to alleviate this issue are discussed, including the fast multipole method and the multi-grid DDA. While the DDA is equally applicable to both connected and disconnected particle systems, when applied to the latter it provides some insights into the notion of multiple scattering.

A simulation model for estimation of the optical properties of spherical and spheroid nano plasmonic geometry coupled with organic media has been studied using discrete dipole approximation (DDA) technique. Silver (Ag) and aluminium (Al) metal nano particles (NPs) are used as a plasmonic element surrounded by organic photovoltaic environment [poly (3-hexyl thiophene)] P3HT-(phenyl-C61-buryricacid methyl ester) PCBM blend. The analysis done in the current article depicts considerable influence of shape, aspect ratio and size on the plasmon resonance that facilitates improvement in the performance of nano plasmonic organic system in the useful spectral domain (250–750 nm). Discretisation of dipoles have been done in the DDA and compared with Mie theory to maintain the accuracy of DDA technique. It has been established that the oblate shape Ag and Al NPs with size of 80 nm (both) with aspect ratio 0.35 and 0.20 are the optimized parameter to enhance the optical properties in an organic surrounding. The optical properties are studied in terms of wavelength dependent extinction spectrum and resonant electric field distribution. Broadband electromagnetic field coupling under the plasmonic effect has led to considerable improvement in the photon absorption inside the organic environment that has been supported by the enhanced J–V curve for different nano geometries. Results of the present article can be used as a guiding principle for the plasmonic light trapping devices to improve their optical properties and electrical properties.

In this paper we evaluate the potential for using an NVIDIA graphics processing unit (GPU) to accelerate high precision integer multiplication, addition, and subtraction. The reported peak vector performance for a typical GPU appears to offer good potential for accelerating such a computation. Because of limitations in the on-chip memory, the high cost of kernel launches, and the nature of the architecture's support for parallelism, we used a hybrid algorithmic approach to obtain good performance on multiplication. On the GPU itself we adapt the Strassen FFT algorithm to multiply 32KB chunks, while on the CPU we adapt the Karatsuba divide-and-conquer approach to optimize application of the GPU's partial multiplies, which are viewed as "digits" by our implementation of Karatsuba. Even with this approach, the result is at best a factor of three increase in performance, compared with using the GMP package on a 64-bit CPU at a comparable technology node. Our implementations of addition and subtraction achieve up to a factor of eight improvement. We identify the issues that limit performance and discuss the likely impact of planned advances in GPU architecture.

We implemented the graphics processing unit (GPU) accelerated compressive sensing (CS) non-uniform in k-space spectral domain optical coherence tomography (SD OCT). Kaiser-Bessel (KB) function and Gaussian function are used independently as the convolution kernel in the gridding-based non-uniform fast Fourier transform (NUFFT) algorithm with different oversampling ratios and kernel widths. Our implementation is compared with the GPU-accelerated modified non-uniform discrete Fourier transform (MNUDFT) matrix-based CS SD OCT and the GPU-accelerated fast Fourier transform (FFT)-based CS SD OCT. It was found that our implementation has comparable performance to the GPU-accelerated MNUDFT-based CS SD OCT in terms of image quality while providing more than 5 times speed enhancement. When compared to the GPU-accelerated FFT based-CS SD OCT, it shows smaller background noise and less side lobes while eliminating the need for the cumbersome k-space grid filling and the k-linear calibration procedure. Finally, we demonstrated that by using a conventional desktop computer architecture having three GPUs, real-time B-mode imaging can be obtained in excess of 30 fps for the GPU-accelerated NUFFT based CS SD OCT with frame size 2048(axial) × 1,000(lateral).

Chapter 9 - Discrete dipole approximation