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At least 829 records · Page 46

An upwind algorithm for the parabolized Navier-Stokes equations

A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method does not require the addition of user specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming scheme in terms of accuracy, stability, computer time and storage, and programming effort. The new algorithm has been validated by applying it to three laminar test cases including flat plate boundary-layer flow, hypersonic flow past a 15 deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with the results obtained using the conventional Beam-Warming algorithm.

Lawrence, S. L.↗

A Real-Time High Performance Data Compression Technique For Space Applications

A high performance lossy data compression technique is currently being developed for space science applications under the requirement of high-speed push-broom scanning. The technique is also error-resilient in that error propagation is contained within a few scan lines. The algorithm is based on block-transform combined with bit-plane encoding; this combination results in an embedded bit string with exactly the desirable compression rate. The lossy coder is described. The compression scheme performs well on a suite of test images typical of images from spacecraft instruments. Hardware implementations are in development; a functional chip set is expected by the end of 2001.

Yeh, Pen-Shu↗

A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

A stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented herein. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and the high order method is scaled element-wise using a limiter and added to the low order scheme. The limiter is solution dependent and computed via an iterative linearity preserving nodal variation limiting strategy. The stabilization also involves an optional consistent background high order dissipation that reduces phase errors. The resulting stabilized scheme is a semi-discrete method that can be applied to inviscid shock MHD problems and may be even extended to resistive and viscous MHD problems. To satisfy the divergence free constraint of the MHD equations, we add parabolic divergence cleaning to the system. Various time integration methods can be used to discretize the scheme in time. We demonstrate the robustness of the scheme by solving several shock MHD problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum Reinforcement Learning for Volt-VAR Control in Power Distribution Systems

Volt-VAR control (VVC) is crucial in active distribution networks for optimizing voltage profiles and minimizing network losses. While traditional deep reinforcement learning (DRL) algorithms exhibit promise for VVC, they often require extensive computational resources to handle such a high-dimensional problem. As a potential solution, quantum reinforcement learning (QRL) algorithms integrate the computational capabilities of quantum computing into the DRL framework. However, existing QRL algorithms struggle with complex VVC problems due to the limitations of current quantum hardware. To bridge this gap, this paper proposes an innovative QRL algorithm featuring an end-to-end architecture that integrates a classical autoencoder, variational quantum circuits (VQCs), and classical post-processing layers. This design efficiently compresses high-dimensional grid states, enabling VQCs to leverage quantum advantages while producing multiple control device outputs tailored for VVC tasks. Numerical studies on three representative distribution systems verify the effectiveness and scalability of the proposed QRL algorithm, and demonstrate its enhanced performance over classical approaches with only approximately 1% of the parameters. Additionally, the robustness of our developed algorithm is validated through noisy quantum environments.

97 MATHEMATICS AND COMPUTING↗

Upwind algorithm for the parabolized Navier-Stokes equations

A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes equations. This method does not require the addition of user-specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming (1978) scheme in terms of accuracy, stability, computer time and storage requirements, and programming effort. The new algorithm has been validated by applying it to three laminar test cases, including flat-plate boundary-layer flow, hypersonic flow past a 15-deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with results obtained using the conventional Beam-Warming algorithm.

Lawrence, Scott L.↗

Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions

The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide statistically-equivalent analytical representations based on relatively few evaluations of the original model. Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropriate univariate polynomials. The classical PCE approach nevertheless faces the “curse of dimensionality”, namely the exponential increase of the basis size with increasing input dimension. To address this limitation, the sparse PCE technique has been proposed, in which the expansion is carried out on only a few relevant basis terms that are automatically selected by a suitable algorithm. An alternative for developing meta-models with polynomial functions in high-dimensional problems is offered by the newly emerged low-rank approximations (LRA) approach. By exploiting the tensor–product structure of the multivariate basis, LRA can provide polynomial representations in highly compressed formats. Through extensive numerical investigations, we herein first shed light on issues relating to the construction of canonical LRA with a particular greedy algorithm involving a sequential updating of the polynomial coefficients along separate dimensions. Specifically, we examine the selection of optimal rank, stopping criteria in the updating of the polynomial coefficients and error estimation. In the sequel, we confront canonical LRA to sparse PCE in structural-mechanics and heat-conduction applications based on finite-element solutions. Canonical LRA exhibit smaller errors than sparse PCE in cases when the number of available model evaluations is small with respect to the input dimension, a situation that is often encountered in real-life problems. By introducing the conditional generalization error, we further demonstrate that canonical LRA tend to outperform sparse PCE in the prediction of extreme model responses, which is critical in reliability analysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A numerical method for prediction of compressible turbulent flows with closure models

A new computer code to solve the time averaged Navier-Stokes equations is developed. Many of the state-of-the-art numerical techniques and algorithms have been tested and implemented in the program in order to achieve a better numerical accuracy and code efficiency. Various turbulence models are tested for a wide range of flows. The initial focus has been on two-equation eddy-viscosity models, which are the most advanced available in current compressible flow codes. The long term goal will be to test Reynolds-Stress models and to explore their performance in the high Mach number range. Although testing and improvement of turbulence models for supersonic and hypersonic flows is the primary objective of this research, part of the effort has been devoted to analyzing the vortex breakdown phenomena using new computer programs. Some preliminary results on the breakdown of a vortex flow in a tube are reported. Present calculations are restricted to two dimensional flow geometry.

Huang, P. G.↗

A VLSI Processor Design of Real-Time Data Compression for High-Resolution Imaging Radar

For the high-resolution imaging radar systems, real-time data compression of raw imaging data is required to accomplish the science requirements and satisfy the given communication and storage constraints. The Block Adaptive Quantizer (BAQ) algorithm and its associated VLSI processor design have been developed to provide a real-time data compressor for high-resolution imaging radar systems.

data compression VLSI processor design imaging rad↗

Single-Scale Retinex Using Digital Signal Processors

The Retinex is an image enhancement algorithm that improves the brightness, contrast and sharpness of an image. It performs a non-linear spatial/spectral transform that provides simultaneous dynamic range compression and color constancy. It has been used for a wide variety of applications ranging from aviation safety to general purpose photography. Many potential applications require the use of Retinex processing at video frame rates. This is difficult to achieve with general purpose processors because the algorithm contains a large number of complex computations and data transfers. In addition, many of these applications also constrain the potential architectures to embedded processors to save power, weight and cost. Thus we have focused on digital signal processors (DSPs) and field programmable gate arrays (FPGAs) as potential solutions for real-time Retinex processing. In previous efforts we attained a 21 (full) frame per second (fps) processing rate for the single-scale monochromatic Retinex with a TMS320C6711 DSP operating at 150 MHz. This was achieved after several significant code improvements and optimizations. Since then we have migrated our design to the slightly more powerful TMS320C6713 DSP and the fixed point TMS320DM642 DSP. In this paper we briefly discuss the Retinex algorithm, the performance of the algorithm executing on the TMS320C6713 and the TMS320DM642, and compare the results with the TMS320C6711.

Hines, Glenn↗

Airborne Demonstration of FPGA Implementation of Fast Lossless Hyperspectral Data Compression System

Efficient on-board lossless hyperspectral data compression reduces data volume in order to meet NASA and DoD limited downlink capabilities. The technique also improves signature extraction, object recognition and feature classification capabilities by providing exact reconstructed data on constrained downlink resources. At JPL a novel, adaptive and predictive technique for lossless compression of hyperspectral data was recently developed. This technique uses an adaptive filtering method and achieves a combination of low complexity and compression effectiveness that far exceeds state-of-the-art techniques currently in use. The JPL-developed 'Fast Lossless' algorithm requires no training data or other specific information about the nature of the spectral bands for a fixed instrument dynamic range. It is of low computational complexity and thus well-suited for implementation in hardware.

data compression↗

Evaluation of Graph Analytics Frameworks Using the GAP Benchmark Suite

The analysis of connected data is an increasingly important application in high-performance computing. Such analyses can reveal fraudulent patterns in financial transactions, optimize telecommunications networks, predict information flow in social networks, etc. However, the landscape of graph analytics is highly diverse. Graph algorithms stress processor architectures differently, and no one graph can represent all topologies. Consequently, no single approach or framework is expected to be optimal for all graph analytics problems. To help make sense of this diverse landscape, we evaluated four approaches to graph analytics: GraphBLAS, Galois, BGL17, GraphIt; and compare them against hand-tuned implementations that take advantage of hardware features on our test platform. Graph- BLAS formulates graph analytics as sparse linear algebra. Galois provides syntactic constructs for data parallelism over irregular data structures. BGL17 is a generic C++ template library for implementing graph algorithms. GraphIt provides a domain- specific language to describe and optimize graph algorithms. We use the GAP Benchmark Suite to establish baseline performance and guide the side-by-side evaluation of each framework. GAP consists of 30 tests: six graph analytics algorithms (breadth- first search, single-source shortest path, PageRank, betweenness centrality, connected components, and triangle counting) run on five graphs, each with different topological characteristics (e.g., high diameter, skewed degree distribution, high average degree). High-performance reference implementations are included for each benchmark algorithm. Because a graph can be loaded into memory a number of ways (e.g., flat file on disk, compressed sparse format, data frames, retrieved from SQL or NoSQL databases), our evaluation focused on computational performance rather than I/O. Our results show the relative strengths of each framework.

Graph algorithms, Benchmarking, shared-memory prog↗

Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm

Construction of the exact exchange matrix, K, is typically the rate-determining step in hybrid density functional theory, and therefore, new approaches with increased efficiency are highly desirable. We present a framework with potential for greatly improved efficiency by computing a compressed exchange matrix that yields the exact exchange energy, gradient, and direct inversion of the iterative subspace (DIIS) error vector. The compressed exchange matrix is constructed with one index in the compact molecular orbital basis and the other index in the full atomic orbital basis. To illustrate the advantages, we present a practical algorithm that uses this framework in conjunction with the resolution of the identity (RI) approximation. We demonstrate that convergence using this method, referred to hereafter as occupied orbital RI-K (occ-RI-K), in combination with the DIIS algorithm is well-behaved, that the accuracy of computed energetics is excellent (identical to conventional RI-K), and that significant speedups can be obtained over existing integral-direct and RI-K methods. For a 4400 basis function C{sub 68}H{sub 22} hydrogen-terminated graphene fragment, our algorithm yields a 14 × speedup over the conventional algorithm and a speedup of 3.3 × over RI-K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An implicit particle code with exact energy and charge conservation for electromagnetic studies of dense plasmas

A collisional particle code based on implicit energy- and charge-conserving methods is presented. A modified version of the particle-suppressed Jacobian-Free Newton-Krylov method that can enhance the solver efficiency is introduced. Mathematically, it is shown that this new approach can be viewed as a fixed-point iteration method for the particle positions. The model can exactly conserve global energy and local charge and can efficiently use time steps larger than the plasma period. In conclusion, the algorithm's ability to simulate dense plasmas accurately and efficiently is quantified by simulating the dynamic compression of a plasma slab via a magnetic piston in 1D planar geometry.

97 MATHEMATICS AND COMPUTING↗

Optical characteristics of p-type GaAs-based semiconductors towards applications in photoemission infrared detectors

Free-carrier effects in a p-type semiconductor including the intra-valence-band and inter-valence-band optical transitions are primarily responsible for its optical characteristics in infrared. Attention has been paid to the inter-valence-band transitions for the development of internal photoemission (IPE) mid-wave infrared (MWIR) photodetectors. The hole transition from the heavy-hole (HH) band to the spin-orbit split-off (SO) band has demonstrated potential applications for 3–5 μm detection without the need of cooling. However, the forbidden SO-HH transition at the Γ point (corresponding to a transition energy Δ{sub 0}, which is the split-off gap between the HH and SO bands) creates a sharp drop around 3.6 μm in the spectral response of p-type GaAs/AlGaAs detectors. Here, we report a study on the optical characteristics of p-type GaAs-based semiconductors, including compressively strained InGaAs and GaAsSb, and a dilute magnetic semiconductor, GaMnAs. A model-independent fitting algorithm was used to derive the dielectric function from experimental reflection and transmission spectra. Results show that distinct absorption dip at Δ{sub 0} is observable in p-type InGaAs and GaAsSb, while GaMnAs displays enhanced absorption without degradation around Δ{sub 0}. This implies the promise of using GaMnAs to develop MWIR IPE detectors. Discussions on the optical characteristics correlating with the valence-band structure and free-hole effects are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Constraining the Multiscale Structure of Geophysical Fields in Machine Learning: The Case of Precipitation

The use of deep-learning algorithms for estimating the value of geophysical variables from remotely sensed information is rapidly expanding. The typical objective function minimized in such algorithms is the mean square error (MSE), which is known to lead to smooth estimates with compressed dynamical range as compared to the true distribution of the variable of interest. Here, we introduce and evaluate alternative objective functions, focusing on the retrieval of precipitation rates from satellite passive microwave radiometric measurements using a deep convolutional neural network. For this testbed application, the results show that explicitly imposing the preservation of the statistical distribution and spatial wavelet power spectrum of the target variable allows to accurately reproduce extreme values and sharp gradients across multiple scales in this study.

58 GEOSCIENCES↗

A Preconditioned Low-Rank Projection Method with a Rank-Reduction Scheme for Stochastic Partial Differential Equations

Herein, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the Kronecker product structure of the linear systems. The proposed algorithm efficiently approximates the solutions in low-rank tensor format. Using standard Krylov subspace methods for the data in tensor format is computationally prohibitive due to the rapid growth of tensor ranks during the iterations. To keep tensor ranks low over the entire iteration process, we devise a rank-reduction scheme that can be combined with the iterative algorithm. The proposed rank-reduction scheme identifies an important subspace in the stochastic domain and compresses tensors of high rank on-the-fly during the iterations. The proposed reduction scheme is a coarse-grid method in that the important subspace can be identified inexpensively in a coarse spatial grid setting. The efficiency of the present method is displayed by numerical experiments on benchmark problems.

97 MATHEMATICS AND COMPUTING↗

buhito

buhito is a Python library for graph analysis and machine learning. Graphs can represent networks with objects as nodes and their relationships as edges. buhito focuses on graphlet methods that study graphs through enumerating their component subgraphs to enable interpretable and fast models of complex systems. The package provides tools for different algorithmic designs for computing, analyzing, and applying graphlets to research problems such as machine learning, data compression, and anomaly detection in graph-structured data. A central feature is performing decomposition data analysis on graphs for machine learning models. Implemented in Python and built upon open-source scientific libraries such as NetworkX, NumPy, and SciPy, buhito provides high-performance methods for researchers exploring the mathematical and computational foundations of graphlet analysis applicable to systems of different sizes.

Pimonova, Yulia↗

Feasibility study of a microprocessor based oculometer system

The elimination of redundancy in data to maximize processing speed and minimize storage requirements were objectives in a feasibility study of a microprocessor based oculometer system that would be portable in size and flexible in use. The appropriate architectural design of the signal processor, improved optics, and the reduction of size, weight, and power to the system were investigated. A flow chart is presented showing the strategy of the design. The simulation for developing microroutines for the high speed algorithmic processor subsystem is discussed as well as the Karhunen-Loeve transform technique for data compression.

Varanasi, M. R.↗