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Scheduling time-critical graphics on multiple processors

This paper describes an algorithm for the scheduling of time-critical rendering and computation tasks on single- and multiple-processor architectures, with minimal pipelining. It was developed to manage scientific visualization scenes consisting of hundreds of objects, each of which can be computed and displayed at thousands of possible resolution levels. The algorithm generates the time-critical schedule using progressive-refinement techniques; it always returns a feasible schedule and, when allowed to run to completion, produces a near-optimal schedule which takes advantage of almost the entire multiple-processor system.

Meyer, Tom W.↗

Body of Knowledge for Graphics Processing Units (GPUs)

Graphics Processing Units (GPU) have emerged as a proven technology that enables high performance computing and parallel processing in a small form factor. GPUs enhance the traditional computer paradigm by permitting acceleration of complex mathematics and providing the capability to perform weighted calculations, such as those in artificial intelligence systems. Despite the performance enhancements provided by this type of microprocessor, there exist tradeoffs in regards to reliability and radiation susceptibility, which may impact mission success. This report provides an insight into GPU architecture and its potential applications in space and other similar markets. It also discusses reliability, qualification, and radiation considerations for testing GPUs.

NASA Electronic Parts and Packaging (NEPP) Program↗

Nuclear Materials Packaging, Transportation, and Systems Analysis Group Software Quality Assurance Plan: ANSYS Mechanical Finite Element Analysis Software Version 2023R1

ANSYS Inc. develops and markets engineering simulation software and services used in the aerospace, automotive, manufacturing, electronics, biomedical, energy, defense, and many other industries. ANSYS is dedicated to engineering simulation and is the world’s leading software provider. ANSYS was founded in 1970 and is headquartered in Canonsburg, Pennsylvania. ANSYS provides an engineering analysis tool combining structural, thermal, computational fluid dynamics, acoustic, and electromagnetic simulation capabilities. ANSYS has two main programs, which use the same solvers: (1) Mechanical APDL (ANSYS Design Parametric Language), a Fortran-based coding platform, and (2) ANSYS Workbench, which uses a graphical user interface to aid in finite element analysis implementation. This plan covers both APDL and Workbench. The ANSYS computer program is a large-scale, multipurpose finite element program that can be used to solve several classes of engineering analyses. The analysis capabilities of ANSYS include the ability to solve static and dynamic structural analyses, steady-state and transient heat transfer problems, mode-frequency and buckling eigenvalue problems, static or time-varying magnetic analyses, and various types of field and coupled-field applications. The program contains many special features that allow nonlinearities or secondary effects such as plasticity, large strain, hyperelasticity, creep, swelling, large deflections, contact, stress stiffening, temperature dependency, material anisotropy, and radiation to be included in the solution. As ANSYS has been developed, other special capabilities such as substructuring, submodeling, random vibration, kinetostatics, kinetodynamics, free convection fluid analysis, acoustics, magnetics, piezoelectrics, coupled-field analysis, and design optimization have been added to the program. These capabilities contribute further to making ANSYS a multipurpose analysis tool for varied engineering disciplines. The ANSYS program has been in commercial use for over 50 years and has been used extensively in the aerospace, automotive, construction, electronic, energy services, manufacturing, nuclear, plastics, oil, and steel industries. Additionally, many consulting firms and hundreds of universities have used ANSYS for analysis, research, and educational purposes. ANSYS is recognized worldwide as one of the most widely used and capable programs of its type. Ansys design analysis software is the first created within a quality system with ISO 9001 certification, the internationally accepted quality standard. Product development, testing, maintenance and support processes also meet the United States Nuclear Regulatory Commission's quality requirements, as they have for nearly four decades. The Quality Assurance Service Agreement is suitable for the customers working in the nuclear industry who need to meet specific federal regulations including 10CRF50 Appendix B and provisions of 10CFR21. ANSYS has retained its original International Organization for Standardization (ISO) 9001 accreditation certificate since1995-05-04, It’s current certificate is valid until 2027-05-29.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

High-Performance Computing Optimization for Aladyn – Adaptive Neural Network Molecular Dynamics Mini-Application

This report provides a description and performance evaluation of the optimization techniques for high performance computing (HPC) implementation of the open source Computational Materials mini-application Aladyn (https://github.com/nasa/aladyn). Aladyn is a basic molecular dynamics code written in FORTRAN 2003, which is designed to demonstrate the use of adaptive neural networks (ANNs) in atomistic simulations. The role of ANNs is to efficiently reproduce the very complex energy landscape resulting from the atomic interactions in materials with the accuracy of the more expensive quantum mechanics-based calculations. The ANN is trained on a large set of atomic structures calculated using the density functional theory (DFT) method. While achieving orders of magnitude faster computational performance than DFT, the ANN-based approach was still very computationally demanding compared to the conventional approach of using empirically fitted energy functions. After its initial development, Aladyn was evaluated and optimized by experts at the NASA Advanced Supercomputing (NAS) division to exploit modern supercomputer architectures. The code has been optimized for execution on multicore central processing units (CPUs), including Intel® Skylake microarchitecture, and on graphic accelerators, such as Nvidia® V100 graphic processing units (GPUs), using Open Multi-Processing (OpenMP) and Open Accelerators (OpenACC) programming interfaces. The optimization achieved a speedup of 4.7 times the baseline version on CPU performance and an additional 2.4 times on CPU+GPU performance. Atomistic computer simulations are a fundamental tool in materials research to model material properties form physics-based first principles. Atomic interaction, governed by Quantum Mechanics (QM) require sophisticated and highly computationally demanding mathematical models to calculate [1]. Classical methods use approximate functional forms, empirically fitted through a set of variable parameters to emulate atomic energies as direct functions of atomic coordinates [2]. While empirical potentials are computationally much simpler, allowing simulations of large-scale systems of up to a trillion (1012) atoms [3], they are substantially less accurate compared to quantum calculations and applicable only to very specific atomic configurations or predefined crystallographic phases. A recently suggested approach is to use heuristic machine learning methods [4], such as those based on Adaptive Neural Networks (ANNs) to predict atomic energies, after being trained on a sufficiently large database of QM-calculated structures [5,6]. This approach reduces significantly the computational complexity, allowing for simulations of orders of magnitude larger systems compared to QM-based methods without compromising accuracy. Still, compared to classical methods using empirical energy functions, ANN methods remain two- to three orders of magnitude more computationally demanding. Hence, the computational cost of simulations, together with the need for extensive training of ANNs, still makes the practical implementation of ANN-based methods quite challenging. The purpose of the Aladyn mini-application software [7], available as open source at https://github.com/nasa/aladyn, is to be a testbed for exploring possible optimization strategies to develop highly scalable parallel algorithms for ANN-based atomistic simulations. Aladyn is aimed at utilizing the architecture of the high-end modern highperformance computing (HPC) hardware based on multicore central processing units (CPUs) equipped with graphic processing unit (GPU) accelerators. Specifically, the goal is to optimize the performance on a single HPC compute node, before implementing scaling to multi-node parallelization using message passing interface (MPI). At the same time, the open source code of Aladyn can serve as a training model for students and professors in academia.

Yamakov, Vesselin I.↗

Data Locality Enhancement of Dynamic Simulations for Exascale Computing (Final Report)

The development of modern processors exhibits two trends that complicate the optimizations of modern software. The first is the increasing sensitivity of processors' throughput to irregularities in computation. With more processors produced through a massive integration of simple cores, future systems will increasingly favor regular data-level parallel computations, but deviate from the needs of applications with complex patterns. Some evidences are already shown on Graphic Processing Units (GPU): Irregular data accesses (e.g., indirect references A[D[i]]) and conditional branches are limiting many GPU applications' performance at a level an order of magnitude lower than the peak of GPU. The second hardware trend is the growing gap between memory bandwidth and the aggregate speed—that is, the sum of all cores' computing power—of a Chip Multiprocessor (CMP). Despite the capped growth of the peak CPU speed, the aggregate speed of a CMP keeps increasing as more cores get into a single chip. It is expected that by 2018, node concurrency in an exascale system will increase by hundreds of times, whereas, memory bandwidth will expand by only 10 to 20 times. Consequently, data movement and storage is expected to consume more than 70% of the total system power. Bridging this gap is difficult; the complexities of modern CMP memory hierarchy make it even harder: Data cache becomes shared among computing units, and the sharing is often non-uniform—whether two computing units share a cache depends on their proximity and the level of the cache. On the recent IBM Power7 architecture, for instance, four hardware contexts (or SMT threads) in a core share the entire memory hierarchy, all cores in one chip share an on-chip L3 cache, and cores across chips share L3 and main memory through off-chip connections. These two trends complicate the translation of computing power into performance, especially for a program with either intensive data accesses or complex patterns in data accesses or control flow paths. Unfortunately, both attributes present and will persist in a class of important applications. For instance, many scientific simulations deal with a large volume of data. And meanwhile, as most real-world processes are non-uniform and evolving (e.g., the evolution of a galaxy or the process of a drug injection), both the computations and data accesses of these programs tend to be irregular and dynamically changing. Currently, the lack of support to these applications on modern CMP severely limits their performance. On GPU, as our recent study shows and other studies echo, performance enhancement of a factor of integers is possible when memory accesses or control flows are streamlined for a set of GPU applications. On multicore CPU, our studies show that traditional locality enhancement, for being oblivious to the new features of multicore memory hierarchy, may even cause large slowdown to data-intensive dynamic applications. The severity of the issues is expected to worsen as the two hardware trends continue. Some recent studies try to match software with the trends, but in a limited scope or manner. For irregularities on GPU, most studies focus on irregularities analyzable through static analysis (e.g., data accesses in regular loops). Dynamic irregularities are harder to address because the needed analysis and transformations typically have to happen at run time. Some other research resorts to hardware extensions, an actual adoption of which is unclear for the entailed space cost and complexity. For data locality, recent years have seen some exploitations of the new memory hierarchy on multicore for performance, but most of them are on process or thread scheduling, rather than program transformations. Our recent study reveals that program-level transformations may magnify the scheduling benefits by a factor of seven, concluding that program-level transformation should play a central role for data locality enhancement on modern CMP. But research in this direction has been sparse, and most have focused on data layout or cache performance modeling, rather than program transformations to match with the new memory hierarchy features. Overall, it is still an open question how to bridge the gap between dynamic computations and the two prominent properties of modern processors. The goal of this project is to develop a set of techniques and software tools to enhance the matching between memory accesses in dynamic simulations and the prominent features of modern and future CMP, alleviating the memory performance issues for petascale and exascale computing. This report summarizes the discoveries and products produced throughout this project. It includes free launch, a new software approach to overcoming the shortcomings of both methods; coherence-free multiview, an approach that allows multiple views of a single data object to co-exist on GPU memory during a GPU kernel execution; algorithmic optimizations to data analytics problems, especially those that involve lots of distance calculations. Supporting dynamic parallelism is important for GPU to benefit a broad range of applications. There are currently two fundamental ways for programs to exploit dynamic parallelism on GPU: a software-based approach with software-managed worklists, and a hardware-based approach through dynamic subkernel launches. Neither is satisfactory. The former is complicated to program and is often subject to some load imbalance; the latter suffers large runtime overhead. In this work, we propose free launch, a new software approach to overcoming the shortcomings of both methods. It allows programmers to use subkernel launches to express dynamic parallelism. It employs a novel compiler-based code transformation named subkernel launch removal to replace the subkernel launches with the reuse of parent threads. Coupled with an adaptive task assignment mechanism, the transformation reassigns the tasks in the subkernels to the parent threads with a good load balance. The technique requires no hardware extensions, immediately deployable on existing GPUs. It keeps the programming convenience of the subkernel launch-based approach while avoiding its large runtime overhead. Meanwhile, its superior load balancing makes it outperform manual worklist-based techniques by 3X on average. The work was published at the 48th Annual IEEE/ACM International Symposium on Microarchitecture (Micro'2015). A Graphic Processing Unit (GPU) system is typically equipped with many types of memory (e.g., global, constant, texture, shared, cache). Data placement determines what data are placed on which type of memory, essential for GPU memory performance. Prior optimizations of data placement always require a single view of a data object on memory, which limits the optimization effectiveness. In this work, we propose coherence-free multiview, an approach that allows multiple views of a single data object to co-exist on GPU memory during a GPU kernel execution. We demonstrate that under certain conditions, the multiple views can remain incoherent while facilitating enhanced data placement. We present a theorem and some compiler support to ensure the soundness of the usage of coherence-free multiview. We further develop reference-discerning data placement, a new way to enhance data placements on GPU. It enables more flexible data placements by using coherence-free multiview to leverage the slack in coherence requirement of some GPU programs. Experiments on three types of GPU systems show that, with less than 200KB space cost, the new data placement technique can provide a 1.6X average (up to 4.27X) speedup. In addition, we have examined algorithmic optimizations to data analytics problems, especially those that involve lots of distance calculations. Computing distances among data points is an essential part of many important algorithms in data analytics, graph analysis, and other domains. In each of these domains, developers have spent significant manual effort optimizing algorithms, often through novel applications of the triangle equality, in order to minimize the number of distance computations in the algorithms. In this work, we observe that many algorithms across these domains can be generalized as an instance of a generic distance-related abstraction. Based on this abstraction, we derive seven principles for correctly applying the triangular inequality to optimize distance-related algorithms. Guided by the findings, we develop Triangular OPtimizer (TOP), the first software framework that is able to automatically produce optimized algorithms that either matches or outperforms manually designed algorithms for solving distance-related problems. TOP achieves up to 237x speedups and 2.5X on average. The work has been published at the 32nd International Conference on Machine Learning (ICML'15) and the 41st International Conference on Very Large Data Bases (VLDB'15).

42 ENGINEERING↗

Laser anemometer measurements and computations for transonic flow conditions in an annular cascade of high turning core turbine vanes

An advanced laser anemometer (LA) was used to measure the axial and tangential velocity components in an annular cascade of turbine stator vanes operating at transonic flow conditions. The vanes tested were based on a previous redesign of the first-stage stator in a two-stage turbine for a high-bypass-ratio engine. The vanes produced 75 deg of flow turning. Tests were conducted on a 0.771-scale model of the engine-sized stator. The advanced LA fringe system employed an extremely small 50-micron diameter probe volume. Window correction optics were used to ensure that the laser beams did not uncross in passing through the curved optical access port. Experimental LA measurements of velocity and turbulence were obtained at the mean radius upstream of, within, and downstream of the stator vane row at an exit critical velocity ratio of 1.050 at the hub. Static pressures were also measured on the vane surface. The measurements are compared, where possible, with calculations from a three-dimensional inviscid flow analysis. Comparisons were also made with the results obtained previously when these same vanes were tested at the design exit critical velocity ratio of 0.896 at the hub. The data are presented in both graphical and tabulated form so that they can be readily compared against other turbomachinery computations.

Goldman, Louis J.↗

FULCRUM user interface for SCALE 6.2

SCALE 6.2 consolidated the multiple special-purpose graphical user interfaces (GUI) of SCALE 6.1 into a completely new and modern interface called FULCRUM. FULCRUM is a cross-platform GUI designed to create, edit, validate, and visualize SCALE input, output, and data. It is intended to be usable by both novice and experienced SCALE users with an unobtrusive design. This paper presents a summary of FULCRUM capabilities. Specifically, interactive input validation, context-aware auto-completion, navigation, interactive geometry visualization with mesh results overlay, job execution, data plotting, and highly configurable workspace layouts will be discussed. (authors)

97 MATHEMATICS AND COMPUTING↗

PLOT3D Export Tool for Tecplot

The PLOT3D export tool for Tecplot solves the problem of modified data being impossible to output for use by another computational science solver. The PLOT3D Exporter add-on enables the use of the most commonly available visualization tools to engineers for output of a standard format. The exportation of PLOT3D data from Tecplot has far reaching effects because it allows for grid and solution manipulation within a graphical user interface (GUI) that is easily customized with macro language-based and user-developed GUIs. The add-on also enables the use of Tecplot as an interpolation tool for solution conversion between different grids of different types. This one add-on enhances the functionality of Tecplot so significantly, it offers the ability to incorporate Tecplot into a general suite of tools for computational science applications as a 3D graphics engine for visualization of all data. Within the PLOT3D Export Add-on are several functions that enhance the operations and effectiveness of the add-on. Unlike Tecplot output functions, the PLOT3D Export Add-on enables the use of the zone selection dialog in Tecplot to choose which zones are to be written by offering three distinct options - output of active, inactive, or all zones (grid blocks). As the user modifies the zones to output with the zone selection dialog, the zones to be written are similarly updated. This enables the use of Tecplot to create multiple configurations of a geometry being analyzed. For example, if an aircraft is loaded with multiple deflections of flaps, by activating and deactivating different zones for a specific flap setting, new specific configurations of that aircraft can be easily generated by only writing out specific zones. Thus, if ten flap settings are loaded into Tecplot, the PLOT3D Export software can output ten different configurations, one for each flap setting.

Alter, Stephen↗

GPU Implementation of the OVERFLOW CFD Code

The high-performance computing (HPC) landscape is quickly changing to systems where most of the performance comes from specialized chips, specifically graphics processing units (GPUs). Such GPU systems are throughput machines, where efficient use of the GPU often requires code refactoring to expose a few orders of magnitude more fine grain parallelism than was previously used on the CPU. Recent modifications to OVERFLOW, an overset, structured grid, computational fluid dynamics flow solver, written in Fortran will be presented. These modifications include both code modernization efforts and algorithmic changes to enable OVERFLOW to efficiently utilize GPUs. Many of these algorithmic changes would likely also be applicable for other structured grid, stencil-based codes wanting to utilize GPUs. The capabilities that have been ported to run on the GPUs are presented, along with the performance gains of the GPU version relative the CPU version of OVERFLOW.

GPU Programming↗

GPU Implementation of the OVERFLOW CFD Code

The high-performance computing (HPC) landscape is quickly changing to systems where most of the performance comes from specialized chips, specifically graphics processing units (GPUs). Such GPU systems are throughput machines, where efficient use of the GPU often requires code refactoring to expose a few orders of magnitude more fine grain parallelism than was previously used on the CPU. Recent modifications to OVERFLOW, an overset, structured grid, computational fluid dynamics flow solver, written in Fortran will be presented. These modifications include both code modernization efforts and algorithmic changes to enable OVERFLOW to efficiently utilize GPUs. Many of these algorithmic changes would likely also be applicable for other structured grid, stencil-based codes wanting to utilize GPUs. The capabilities that have been ported to run on the GPUs are presented, along with the performance gains of the GPU version relative the CPU version of OVERFLOW.

GPU Programming↗

PRISMA: PARALLEL REFINEMENT AND INTEGRATION SYSTEM FOR MULTI-AZIMUTHAL ANALYSIS

The Parallel Refinement and Integration System for Multi-azimuthal Analysis (PRISMA, version 1.1.0) is a Python application for processing X-ray diffraction (XRD) image data. PRISMA wraps GSAS-II to perform azimuthally-binned peak refinement, computes per-frame strain and d-spacing from those fits, and provides three PyQt5 graphical interfaces: (1) a Recipe Builder for selecting GSAS-II control (.imctrl) files, optional mask (.immask) files or threshold-ased masking, reference and experiment image sets, peaks, zimuthal range and bin size, and an optional ceria-based auto-calibration; (2) a Batch Processor that uses Dask on local workstations and pure MPI (mpi4py.futures.MPICommExecutor) on HPC to distribute GSAS-II refinement across cores or compute nodes and write results to a 4-dimensional (peaks x frames x azimuths x measurements) Zarr dataset; and (3) a Data Analyzer that renders heatmaps of fit parameters, strain, frame-to-frame deltas, and percent-change-vs-reference, and exports user-defined subsections to CSV or Excel. The peak-refinement algorithm is deterministic. Benchmark on ALCF Crux: a 20,000-image set, single-peak fit in frame mode with 44 azimuthal bins on 128 nodes x 128 workers, 48 seconds total wall time.

Lorenzo Martin, Maria De La Cinta [Argonne Nationa↗

Force Field X: A computational microscope to study genetic variation and organic crystals using theory and experiment

Force Field X (FFX) is an open-source software package for atomic resolution modeling of genetic variants and organic crystals that leverages advanced potential energy functions and experimental data. FFX currently consists of nine modular packages with novel algorithms that include global optimization via a many-body expansion, acid–base chemistry using polarizable constant-pH molecular dynamics, estimation of free energy differences, generalized Kirkwood implicit solvent models, and many more. Applications of FFX focus on the use and development of a crystal structure prediction pipeline, biomolecular structure refinement against experimental datasets, and estimation of the thermodynamic effects of genetic variants on both proteins and nucleic acids. The use of Parallel Java and OpenMM combines to offer shared memory, message passing, and graphics processing unit parallelization for high performance simulations. Overall, the FFX platform serves as a computational microscope to study systems ranging from organic crystals to solvated biomolecular systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Updated Primers Generated for SCALE 6.2 for KENO V.a and KENO-VI

Primers were developed and published for the use of the KENO V.a and KENO-VI codes in 2005 and 2008, respectively. These primers were both developed for SCALE 5 using the GeeWiz graphical user interface (GUI). Many new capabilities have been added to the transport codes since the release of these primers. The GUI was also changed to Fulcrum with the release of SCALE 6.2. For these reasons, updated versions of both primers were developed for a planned released in September 2020. The KENO V.a and KENO-VI codes are almost always run within the associated CSAS5 and CSAS6 sequences within SCALE, so the primers use the sequences and do not address running the codes in stand-alone mode.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Updated Primers Generated for SCALE 6.2 for KENO V.a and KENO-VI [Slides]

Primers were developed and published for the use of the KENO V.a and KENO-VI codes in 2005 and 2008, respectively. These primers were both developed for SCALE 5 using the GeeWiz graphical user interface (GUI). Many new capabilities have been added to the transport codes since the release of these primers. The GUI was also changed to Fulcrum with the release of SCALE 6.2. For these reasons, updated versions of both primers were developed for a planned released in September 2020. The KENO V.a and KENO-VI codes are almost always run within the associated CSAS5 and CSAS6 sequences within SCALE, so the primers use the sequences and do not address running the codes in stand-alone mode.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Performance modeling of microsecond scale biological molecular dynamics simulations on heterogeneous architectures

Performance improvements in biomolecular simulations based on molecular dynamics (MD) codes are widely desired. Unfortunately, the factors, which allowed past performance improvements, particularly the microprocessor clock frequencies, are no longer increasing. Hence, novel software and hardware solutions are being explored for accelerating performance of widely used MD codes. In this paper, we describe our efforts on porting, optimizing and tuning of Large-scale Atomic/Molecular Massively Parallel Simulator, a popular MD framework, on heterogeneous architectures: multi-core processors with graphical processing unit (GPU) accelerators. Our implementation is based on accelerating the most computationally expensive non-bonded interaction terms on the GPUs and overlapping the computation on the CPU and GPUs. This functionality is built on top of message passing interface that allows multi-level parallelism to be extracted even at the workstation level with the multi-core CPUs and allows extension of the implementation on GPU-enabled clusters. We hypothesize that the optimal benefit of heterogeneous architectures for applications will come by utilizing all possible resources (for example, CPU-cores and GPU devices on GPU-enabled clusters). Benchmarks for a range of biomolecular system sizes are provided, and an analysis is performed on four generations of NVIDIA's GPU devices. On GPU-enabled Linux clusters, by overlapping and pipelining computation and communication, we observe up to 10-folds application acceleration in multi-core and multi-GPU environments illustrating significant performance improvements. Detailed analysis of the implementation is presented that allows identification of bottlenecks in algorithm, indicating that code optimization and improvements on GPUs could allow microsecond scale simulation throughput on workstations and inexpensive GPU clusters, putting widely desired biologically relevant simulation time-scales within reach of a large user community. In order to systematically optimize simulation throughput and to enable performance prediction, we have developed a parameterized performance model that will allow developers and users to explore the performance potential of future heterogeneous systems for biological simulations.

Agarwal, Pratul K.↗

A Comparative Study of Layer Heating and Continuous Heating Methods on Prediction Accuracy of Residual Stresses in Selective Laser Melted Tube Samples

Thermal distortion and residual stresses are two important factors that affect the quality and reliability of steel parts manufactured by laser powder bed fusion (LPBF) processes. A cost-effective model for evaluation of those heat effects is needed to refine the manufacturing process and provides insights into the product design and heat treatment. In this study, the layer heating method and sophisticated track-layer scanning method were applied to simulate the thermo-mechanical response of IN625 tube parts built by LPBF. Based on the similarity of temperature field in each layer deposit, a swept mesh was constructed to perform the thermal analysis for top layer, with the rest of layers referring to the temperature by node number offsetting. A novel explicit finite element analysis code accelerated by graphics processing unit was used for the massive-element numerical analysis. The computational accuracy and efficiency of the layer heating and track-layer scanning methods were compared in detail. It is shown that layer heating method can efficiently capture the pattern of stress distribution with reasonable accuracy in stress magnitude. The grouped track-layer scanning method can predict the residual stress and strain more accurately at a higher cost (5 ~ 10×). The elastic strain distribution was compared with the measurement by X-ray diffraction, confirming the accuracy of residual stress prediction.

36 MATERIALS SCIENCE↗

Internal wave energy flux from density perturbations in nonlinear stratifications

Internal gravity wave energy contributes significantly to the energy budget of the oceans, affecting mixing and the thermohaline circulation. Hence it is important to determine the internal wave energy flux $\boldsymbol{J}=p\,\boldsymbol{v}$ , where $p$ is the pressure perturbation field and $\boldsymbol{v}$ is the velocity perturbation field. However, the pressure perturbation field is not directly accessible in laboratory or field observations. Previously, a Green’s function based method was developed to calculate the instantaneous energy flux field from a measured density perturbation field $\unicode[STIX]{x1D70C}(x,z,t)$ , given a constant buoyancy frequency $N$ . Here we present methods for computing the instantaneous energy flux $\boldsymbol{J}(x,z,t)$ for an internal wave field with vertically varying background $N(z)$ , as in the oceans where $N(z)$ typically decreases by two orders of magnitude from the pycnocline to the deep ocean. Analytic methods are presented for computing $\boldsymbol{J}(x,z,t)$ from a density perturbation field for $N(z)$ varying linearly with $z$ and for $N^{2}(z)$ varying as $\tanh (z)$ . To generalize this approach to arbitrary $N(z)$ , we present a computational method for obtaining $\boldsymbol{J}(x,z,t)$ . The results for $\boldsymbol{J}(x,z,t)$ for the different cases agree well with results from direct numerical simulations of the Navier–Stokes equations. Our computational method can be applied to any density perturbation data using the MATLAB graphical user interface ‘EnergyFlux’.

Mechanics↗

An Efficient Deterministic Parallel Algorithm for Adaptive Multidimensional Numerical Integration on GPUs

Recent development in Graphics Processing Units (GPUs) has enabled a new possibility for highly efficient parallel computing in science and engineering. Their massively parallel architecture makes GPUs very effective for algorithms where processing of large blocks of data can be executed in parallel. Multidimensional integration has important applications in areas like computational physics, plasma physics, computational fluid dynamics, quantum chemistry, molecular dynamics and signal processing. The computationally intensive nature of multidimensional integration requires a high-performance implementation. In this study, we present an efficient deterministic parallel algorithm for adaptive multidimensional numerical integration on GPUs. Various optimization techniques are applied to maximize the utilization of the GPU. GPU-based implementation outperforms the best known sequential methods and achieves a speed-up of up to 100. It also shows good scalability with the increase in dimensionality.

Arumugam, Kamesh↗