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All sources NASA NTRS DOE OSTI

DOE OSTI2018

Scaling Structured Multigrid to 500K+ Cores Through Coarse-Grid Redistribution

The effcient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for common discretizations makes them a good candidate for an efficient parallel solver. Yet, modern architectures for high-performance computing systems continue to challenge the parallel scalability of multilevel solvers. While algebraic multigrid methods are robust for solving a variety of problems, the increasing importance of data locality and cost of data movement in modern architectures motivates the need to carefully exploit structure in the problem. Robust logically structured variational multigrid methods, such as Black Box Multigrid (BoxMG), maintain structure throughout the multigrid hierarchy. This avoids indirection and increased coarse- grid communication costs typical in parallel algebraic multigrid. Nevertheless, the parallel scalability of structured multigrid is challenged by coarse-grid problems where the overhead in communication dominates computation. In this paper, an algorithm is introduced for redistributing coarse-grid problems through incremental agglomeration. Guided by a predictive performance model, this algorithm provides robust redistribution decisions for structured multilevel solvers. A two-dimensional diffusion problem is used to demonstrate the significant gain in performance of this algorithm over the previous approach that used agglomeration to one processor. In addition, the parallel scalability of this approach

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1984

Feasibility of using the Massively Parallel Processor for large eddy simulations and other Computational Fluid Dynamics applications

The results of an investigation into the feasibility of using the MPP for direct and large eddy simulations of the Navier-Stokes equations is presented. A major part of this study was devoted to the implementation of two of the standard numerical algorithms for CFD. These implementations were not run on the Massively Parallel Processor (MPP) since the machine delivered to NASA Goddard does not have sufficient capacity. Instead, a detailed implementation plan was designed and from these were derived estimates of the time and space requirements of the algorithms on a suitably configured MPP. In addition, other issues related to the practical implementation of these algorithms on an MPP-like architecture were considered; namely, adaptive grid generation, zonal boundary conditions, the table lookup problem, and the software interface. Performance estimates show that the architectural components of the MPP, the Staging Memory and the Array Unit, appear to be well suited to the numerical algorithms of CFD. This combined with the prospect of building a faster and larger MMP-like machine holds the promise of achieving sustained gigaflop rates that are required for the numerical simulations in CFD.

Bruno, John↗

DOE OSTI2014

A Framework for Lattice QCD Calculations on GPUs

Efficient calculation of the greatest common divisor (GCD) for big integers each whose number of bits is greater than or equal to 1024 has drawn a considerable amount of attention because it can be used to detect a weakness of the RSA security infrastructure. This paper presents a parallel binary GCD algorithm and its implementation for big integers on the Intel Xeon Phi coprocessor. This algorithm is capable of computing GCDs efficiently on many pairs of big integers in parallel by utilizing all cores on a Xeon Phi coprocessor as well as taking advantage of all vector processing units of the coprocessor to speed up critical integer operations within the algorithm. Using 240 threads on a Xeon Phi coprocessor to carry out GCD calculations for a large amount of 2048-bit integers, the implementation achieves the speedup of 30 times over a sequential binary GCD algorithm implementation on a single CPU core, and it delivers twice amount of performance in comparison to the same sequential binary GCD implementation running on 240 threads of the Xeon Phi.

Winter, F. T.↗

DOE OSTI2026

Speedup of UEDGE Parameter Scans Using Machine-Learning Optimized OpenMP Parallelization and a Continuation Solver

This article presents the OpenMP parallelization of the preconditioning Jacobian assembly and right‐hand side residual evaluation in UEDGE. A continuation algorithm, utilizing the internal NKSOL implicit Jacobian‐Free Newton‐Krylov solver to efficiently scan physical parameters, is also presented. The implemented parallelization reduces the computational time for a benchmark scan run on 32 threads by compared to the serial version when using trained random forest regression models to identify the optimal decomposition of the system of equations. Random forest regression models applied to the UEDGE time‐dependent and continuation solver algorithms did not yield meaningful improvement in computational performance. A benchmark DIII‐D gas injection rate scan in the 0.35–0.75 kA interval, performed on a test cluster using the parallelized code and continuation solver, produced 1066 steady‐state solutions with a 22 s average wall‐clock computational time per steady‐state solution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

NEXTorch: A Design and Bayesian Optimization Toolkit for Chemical Sciences and Engineering

Automation and optimization of chemical systems require well-informed decisions on what experiments to run to reduce time, materials, and/or computations. Data-driven active learning algorithms have emerged as valuable tools to solve such tasks. Bayesian optimization, a sequential global optimization approach, is a popular active-learning framework. Past studies have demonstrated its efficiency in solving chemistry and engineering problems. Here we introduce NEXTorch, a library in Python/PyTorch, to facilitate laboratory or computational design using Bayesian optimization. NEXTorch offers fast predictive modeling, flexible optimization loops, visualization capabilities, easy interfacing with legacy software, and multiple types of parameters and data type conversions. It provides GPU acceleration, parallelization, and state-of-the-art Bayesian optimization algorithms and supports both automated an d human-in-the-loop optimization. The comprehensive online documentation introduces Bayesian optimization theory and several examples from catalyst synthesis, reaction condition optimization, parameter estimation, and reactor geometry optimization. NEXTorch is open-source and available on GitHub

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

An advanced algorithm for construction of Integral Transport Matrix Method operators using accumulation of single cell coupling factors

The Integral Transport Matrix Method (ITMM) has been shown to be an effective method for solving the neutron transport equation in large domains on massively parallel architectures. In the limit of very large number of processors, the speed of the algorithm, and its suitability for unstructured meshes, i.e. other than an ordered Cartesian grid, is limited by the construction of four matrix operators required for obtaining the solution in each sub-domain. The existing algorithm used for construction of these matrix operators, termed the differential mesh sweep, is computationally expensive and was developed for a structured grid. This work proposes the use of a new algorithm for construction of these operators based on the construction of a single, fundamental matrix representing the transport of a particle along every possible path throughout the sub-domain mesh. Each of the operators is constructed by multiplying an element of this fundamental matrix by two factors dependent only upon the operator being constructed and on properties of the emitting and incident cells. The ITMM matrix operator construction time for the new algorithm is demonstrated to be shorter than the existing algorithm in all tested cases with both isotropic and anisotropic scattering considered. While also being a more efficient algorithm on a structured Cartesian grid, the new algorithm is promising in its geometric robustness and potential for being applied to an unstructured mesh, with the ultimate goal of application to an unstructured tetrahedral mesh on a massively parallel architecture. (authors)

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2002

Progress in the Simulation of Steady and Time-Dependent Flows with 3D Parallel Unstructured Cartesian Methods

The proposed paper will present recent extensions in the development of an efficient Euler solver for adaptively-refined Cartesian meshes with embedded boundaries. The paper will focus on extensions of the basic method to include solution adaptation, time-dependent flow simulation, and arbitrary rigid domain motion. The parallel multilevel method makes use of on-the-fly parallel domain decomposition to achieve extremely good scalability on large numbers of processors, and is coupled with an automatic coarse mesh generation algorithm for efficient processing by a multigrid smoother. Numerical results are presented demonstrating parallel speed-ups of up to 435 on 512 processors. Solution-based adaptation may be keyed off truncation error estimates using tau-extrapolation or a variety of feature detection based refinement parameters. The multigrid method is extended to for time-dependent flows through the use of a dual-time approach. The extension to rigid domain motion uses an Arbitrary Lagrangian-Eulerlarian (ALE) formulation, and results will be presented for a variety of two- and three-dimensional example problems with both simple and complex geometry.

Aftosmis, M. J.↗

NASA NTRS1974

The question of the possibility of using Associative Computer Devices (ACD) for parallel adaptive discretization of multichannel telemetry information

The method of parallel adaptive discretization of data is considered the most promising and allows the effective compression algorithms to be used for high information-capacity radio telemetry systems. An associative computer device (ACD), i.e., parallel computers based on associative memory units (AMU), are recommended for realization of this method. A detailed discussion of the problems of application of AMU is followed by description of a particular ACD and its recommended use.

Kantor, A. V.↗

NASA NTRS1989

Multilevel decomposition of complete vehicle configuration in a parallel computing environment

This research summarizes various approaches to multilevel decomposition to solve large structural problems. A linear decomposition scheme based on the Sobieski algorithm is selected as a vehicle for automated synthesis of a complete vehicle configuration in a parallel processing environment. The research is in a developmental state. Preliminary numerical results are presented for several example problems.

Bhatt, Vinay↗

NASA NTRS1994

Dynamic Load Balancing for Computational Plasticity on Parallel Computers

The simulation of the computational plasticity on a complex structure remains a formidable computational task, especially when a highly nonlinear, complex material model was used. It appears that the computational requirements for a such problem can only be satisfied by massively parallel architectures. In order to effectively harness the tremendous computational power provided by such architectures, it is imperative to investigate and to study the algorithmic and implementation issues pertaining to dynamic load balancing for computational plasticity on a highly parallel, distributed-memory, multiple-instruction, multiple-data computers. This paper will measure the effectiveness of the algorithms developed in handling the dynamic load balancing.

Pramono, Eddy↗

NASA NTRS1995

Multithreaded Model for Dynamic Load Balancing Parallel Adaptive PDE Computations

We present a multithreaded model for the dynamic load-balancing of numerical, adaptive computations required for the solution of Partial Differential Equations (PDE's) on multiprocessors. Multithreading is used as a means of exploring concurrency in the processor level in order to tolerate synchronization costs inherent to traditional (non-threaded) parallel adaptive PDE solvers. Our preliminary analysis for parallel, adaptive PDE solvers indicates that multithreading can be used an a mechanism to mask overheads required for the dynamic balancing of processor workloads with computations required for the actual numerical solution of the PDE's. Also, multithreading can simplify the implementation of dynamic load-balancing algorithms, a task that is very difficult for traditional data parallel adaptive PDE computations. Unfortunately, multithreading does not always simplify program complexity, often makes code re-usability not an easy task, and increases software complexity.

Chrisochoides, Nikos↗

NASA NTRS1992

Optimistic barrier synchronization

Barrier synchronization is fundamental operation in parallel computation. In many contexts, at the point a processor enters a barrier it knows that it has already processed all the work required of it prior to synchronization. The alternative case, when a processor cannot enter a barrier with the assurance that it has already performed all the necessary pre-synchronization computation, is treated. The problem arises when the number of pre-sychronization messages to be received by a processor is unkown, for example, in a parallel discrete simulation or any other computation that is largely driven by an unpredictable exchange of messages. We describe an optimistic O(log sup 2 P) barrier algorithm for such problems, study its performance on a large-scale parallel system, and consider extensions to general associative reductions as well as associative parallel prefix computations.

Nicol, David M.↗

NASA NTRSDate not supplied

Dynamic Mode Decomposition of Unsteady Pressure-Sensitive Paint Measurements for the NASA Unitary Plan Wind Tunnel Tests

This paper describes the Dynamic Mode Decomposition (DMD) of the pressures on the scale model of the Space Launch System (SLS) Block 1 cargo vehicle with the Unsteady Pressure-Sensitive Paint (uPSP) measurements, which were collected in the Ascent Transient Aerodynamics Tests with the Unitary Plan Wind Tunnel 11-by-11-foot Transonic Wind Tunnel in September 2019 at NASA Ames Research Center. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. The conventional DMD algorithm is based on the Singular Value Decomposition (SVD) of the data matrix. For the matrix of the uPSP measurements of the SLS ATAT, the number of rows is equal to the number of nodes in the grid of the scale model, and the number of columns is equal to the number of frames in the videos taken with 4 Phantom high-speed cameras. In this paper, it is verified that, for the time series with zero mean value, the DMD is equivalent to the decomposition with the Discrete Fourier Transform (DFT). Considering the uPSP is mainly used in the assessment of the unsteady, aerodynamic phenomena, the DMD of the uPSP measurements can be implemented in two steps: (1) subtract the mean value from the uPSP measurement on each of the grid nodes; (2) apply the Fast Fourier Transform (FFT) on the resulting zero-mean time series. The DMD of the uPSP measurements with FFT has two advantages: (1) the computational complexity of FFT is O(N*logN), where N is the length of the time series; (2) compared to the SVD-based DMD algorithm, the DMD with FFT can be easily implemented in parallel processing. A sample matrix of uPSP measurements, at the size of 341 grid nodes and 128 frames, is generated. Figures 1 and 2 show the eigenvalues and the ratios of the eigenvectors, respectively, of the sample matrix, without and with the mean value removed on each of the grid nodes, computed with the SVD-based DMD and the FFT. The figures demonstrate the equivalence of the SVD-based DMD and the decomposition with DFT/FFT for the time series with zero mean value. The results of DMD of the uPSP measurements of the SLS ATAT in September 2019 are presented in the paper. The DMD modes at different frequencies are shown, the aerodynamic phenomena (e.g. shockwave and vortex shedding) are demonstrated and the correlation of the DMD modes with the test configuration parameter (e.g., the Mach Number) is discussed. Figure 3 shows a software tool to visualize the DMD modes. The code to implement the algorithm described in this paper was written in C, with libraries of FFTW for FFT and MPI/OpenMP for parallel processing, and executed on the NASA Pleiades supercomputer. Funding for this research was provided by the NASA Aerosciences Evaluation and Test Capabilities Project.

Pressure-Sensitive Paint↗

DOE OSTI2014

SU-D-18A-02: Towards Real-Time On-Board Volumetric Image Reconstruction for Intrafraction Target Verification in Radiation Therapy

Purpose: To expedite on-board volumetric image reconstruction from limited-angle kV—MV projections for intrafraction verification. Methods: A limited-angle intrafraction verification (LIVE) system has recently been developed for real-time volumetric verification of moving targets, using limited-angle kV—MV projections. Currently, it is challenged by the intensive computational load of the prior-knowledge-based reconstruction method. To accelerate LIVE, we restructure the software pipeline to make it adaptable to model and algorithm parameter changes, while enabling efficient utilization of rapidly advancing, modern computer architectures. In particular, an innovative two-level parallelization scheme has been designed: At the macroscopic level, data and operations are adaptively partitioned, taking into account algorithmic parameters and the processing capacity or constraints of underlying hardware. The control and data flows of the pipeline are scheduled in such a way as to maximize operation concurrency and minimize total processing time. At the microscopic level, the partitioned functions act as independent modules, operating on data partitions in parallel. Each module is pre-parallelized and optimized for multi-core processors (CPUs) and graphics processing units (GPUs). Results: We present results from a parallel prototype, where most of the controls and module parallelization are carried out via Matlab and its Parallel Computing Toolbox. The reconstruction is 5 times faster on a data-set of twice the size, compared to recently reported results, without compromising on algorithmic optimization control. Conclusion: The prototype implementation and its results have served to assess the efficacy of our system concept. While a production implementation will yield much higher processing rates by approaching full-capacity utilization of CPUs and GPUs, some mutual constraints between algorithmic flow and architecture specifics remain. Based on a careful analysis of the prototype performance, it will be feasible to resolve such issues through appropriate algorithmic modifications or special-purpose hardware, thus enabling target verification in seconds with the LIVE system. This work was partially supported by a research grant from Varian Medical Systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Enhancing scalability of a matrix-free eigensolver for studying many-body localization

We propose several techniques to enhance the parallel scalability of a matrix-free eigensolver designed for studying many-body localization (MBL) of quantum spin chain models with nearest-neighbor interactions and on-site disorder. This type of problem is computationally challenging because the dimension of the associated Hamiltonian matrix grows exponentially with respect to the number of spins L, and we need to average over different realizations of the random disorder to obtain relevant statistical behavior. For each disorder realization, we need to compute eigenvalues from different regions of the spectrum and their corresponding eigenvectors. In previous work, the interior eigenstates for a single eigenvalue problem are computed via the shift-and-invert Lanczos algorithm. Due to the extremely high memory footprint of the LU factorizations, this technique is not well suited for large L’s. For example, we need thousands of compute nodes on modern high performance computing infrastructures to go beyond L = 24. The matrix-free approach does not suffer from this memory bottleneck, however, its scalability is limited by a computation and communication load imbalance. To reduce this imbalance and to significantly enhance the scalability of the matrix-free eigensolver, we reorder the matrix and leverage the consistent space runtime, CSPACER. We also show its efficiency in managing irregular communication patterns at scale compared to optimized MPI non-blocking two-sided and one-sided RMA implementation variants. This effort enables us to study MBL for spin chains with a larger number of spins. The efficiency and effectiveness of the proposed algorithm is demonstrated by computing eigenstates on a massively parallel many-core high performance computer.

METIS↗

DOE OSTI2018

Concurrent implicit spectral deferred correction scheme for low-Mach number combustion with detailed chemistry

We present a parallel multi-implicit time integration scheme for the advection-diffusion-reaction systems arising from the equations governing low-Mach number combustion with complex chemistry. Here, our strategy employs parallelisation across the method to accelerate the serial Multi-Implicit Spectral Deferred Correction (MISDC) scheme used to couple the advection, diffusion, and reaction processes. In our approach, the diffusion solves and the reaction solves are performed concurrently by different processors. Our analysis shows that the proposed parallel scheme is stable for stiff problems and that the sweeps converge to the fixed-point solution at a faster rate than with serial MISDC. We present numerical examples to demonstrate that the new algorithm is high-order accurate in time, and achieves a parallel speedup compared to serial MISDC.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1999

Automated Development of Accurate Algorithms and Efficient Codes for Computational Aeroacoustics

The simulation of sound generation and propagation in three space dimensions with realistic aircraft components is a very large time dependent computation with fine details. Simulations in open domains with embedded objects require accurate and robust algorithms for propagation, for artificial inflow and outflow boundaries, and for the definition of geometrically complex objects. The development, implementation, and validation of methods for solving these demanding problems is being done to support the NASA pillar goals for reducing aircraft noise levels. Our goal is to provide algorithms which are sufficiently accurate and efficient to produce usable results rapidly enough to allow design engineers to study the effects on sound levels of design changes in propulsion systems, and in the integration of propulsion systems with airframes. There is a lack of design tools for these purposes at this time. Our technical approach to this problem combines the development of new, algorithms with the use of Mathematica and Unix utilities to automate the algorithm development, code implementation, and validation. We use explicit methods to ensure effective implementation by domain decomposition for SPMD parallel computing. There are several orders of magnitude difference in the computational efficiencies of the algorithms which we have considered. We currently have new artificial inflow and outflow boundary conditions that are stable, accurate, and unobtrusive, with implementations that match the accuracy and efficiency of the propagation methods. The artificial numerical boundary treatments have been proven to have solutions which converge to the full open domain problems, so that the error from the boundary treatments can be driven as low as is required. The purpose of this paper is to briefly present a method for developing highly accurate algorithms for computational aeroacoustics, the use of computer automation in this process, and a brief survey of the algorithms that have resulted from this work. A review of computational aeroacoustics has recently been given by Lele.

Goodrich, John W.↗

NASA NTRS1983

Programming substructure computations for elliptic problems on the CHiP system

A number of studies have been conducted with the aim to apply parallel computation to problems associated with solving finite element equations arising in structural mechanics and fluid dynamics. These studies have provided many important results. The present investigation is concerned with a set of experiments designed to test two ideas, including configurability and substructuring. The considered algorithms and tests are intended for implementation on the Configurable, Highly Parallel (CHiP) family of architecture described by Snyder (1982). The ChiP computer is composed of homogeneous processing elements (PEs) placed at regular intervals in a lattice of programmable switches. Two examples of the role of configurability and substructuring for simple iterative algorithms are considered, giving attention to conjugate gradient iterations, and tridiagonal systems of equations.

Gannon, D.↗