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NASA NTRS1989

Parallel algorithms and archtectures for computational structural mechanics

The determination of the fundamental (lowest) natural vibration frequencies and associated mode shapes is a key step used to uncover and correct potential failures or problem areas in most complex structures. However, the computation time taken by finite element codes to evaluate these natural frequencies is significant, often the most computationally intensive part of structural analysis calculations. There is continuing need to reduce this computation time. This study addresses this need by developing methods for parallel computation.

Patrick, Merrell↗

NASA NTRS1994

Parallel Preconditioning for CFD Problems on the CM-5

Up to today, preconditioning methods on massively parallel systems have faced a major difficulty. The most successful preconditioning methods in terms of accelerating the convergence of the iterative solver such as incomplete LU factorizations are notoriously difficult to implement on parallel machines for two reasons: (1) the actual computation of the preconditioner is not very floating-point intensive, but requires a large amount of unstructured communication, and (2) the application of the preconditioning matrix in the iteration phase (i.e. triangular solves) are difficult to parallelize because of the recursive nature of the computation. Here we present a new approach to preconditioning for very large, sparse, unsymmetric, linear systems, which avoids both difficulties. We explicitly compute an approximate inverse to our original matrix. This new preconditioning matrix can be applied most efficiently for iterative methods on massively parallel machines, since the preconditioning phase involves only a matrix-vector multiplication, with possibly a dense matrix. Furthermore the actual computation of the preconditioning matrix has natural parallelism. For a problem of size n, the preconditioning matrix can be computed by solving n independent small least squares problems. The algorithm and its implementation on the Connection Machine CM-5 are discussed in detail and supported by extensive timings obtained from real problem data.

Simon, Horst D.↗

NASA NTRS1988

Efficient parallel algorithms for string editing and related problems

The string editing problem for input strings x and y consists of transforming x into y by performing a series of weighted edit operations on x of overall minimum cost. An edit operation on x can be the deletion of a symbol from x, the insertion of a symbol in x or the substitution of a symbol x with another symbol. This problem has a well known O((absolute value of x)(absolute value of y)) time sequential solution (25). The efficient Program Requirements Analysis Methods (PRAM) parallel algorithms for the string editing problem are given. If m = ((absolute value of x),(absolute value of y)) and n = max((absolute value of x),(absolute value of y)), then the CREW bound is O (log m log n) time with O (mn/log m) processors. In all algorithms, space is O (mn).

Apostolico, Alberto↗

NASA NTRS1989

The numerical solution of the Navier-Stokes equations for 3-dimensional, unsteady, incompressible flows by compact schemes

The present numerical method for the solution of unsteady, incompressible three-dimensional flow Navier-Stokes equations using velocity-vorticity variables and irregular Cartesian grids proceeds by solving: (1) equations of Cauchy-Riemann type for the velocity; and (2) transport-diffusion equations for the vorticity, whose solenoidal vorticity components are generated by a Poisson equation for an appropriate scalar potential. Iterations are used to solve the finite difference equations, facilitating the use of vector and parallel-computing methods; numerical experiments have verified the method's second-order spatial and temporal accuracy.

Gatski, T. B.↗

DOE OSTI2014

Calculation of the state-to-state S-matrix for tetra-atomic reactions with transition-state wave packets: H{sub 2}/D{sub 2} + OH → H/D + H{sub 2}O/HOD

This work is concerned with the calculation of state-to-state S-matrix elements for four-atom reactions using a recently proposed method based on the quantum transition-state theory. In this approach, the S-matrix elements are computed from the thermal flux cross-correlation functions obtained in both the reactant and product arrangement channels. Since transition-state wave packets are propagated with only single arrangement channels, the bases/grids required are significantly smaller than those needed in state-to-state approaches based on a single set of scattering coordinates. Furthermore, the propagation of multiple transition-state wave packets can be carried out in parallel. This method is demonstrated for the H{sub 2}/D{sub 2} + OH → H/D + H{sub 2}O/HOD reactions (J = 0) and the reaction probabilities are in excellent agreement with benchmark results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

LLNL Mercury Project Trinity Open Science Final Report

The Mercury Monte Carlo particle transport code developed at Lawrence Livermore National Laboratory (LLNL) is used to simulate the transport of radiation through urban environments. These challenging calculations include complicated geometries and require significant computational resources to complete. As a result, a question arises as to the level of convergence of the calculations with Monte Carlo simulation particle count. In the Trinity Open Science calculations, one main focus was to investigate convergence of the relevant simulation quantities with Monte Carlo particle count to assess the current simulation methodology. Both for this application space but also of more general applicability, we also investigated the impact of code algorithms on parallel scaling on the Trinity machine as well as the utilization of the Trinity DataWarp burst buffer technology in Mercury via the LLNL Scalable Checkpoint/Restart (SCR) library.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2016

Interactive Correlation Analysis and Visualization of Climate Data

The relationship between our ability to analyze and extract insights from visualization of climate model output and the capability of the available resources to make those visualizations has reached a crisis point. The large volume of data currently produced by climate models is overwhelming the current, decades-old visualization workflow. The traditional methods for visualizing climate output also have not kept pace with changes in the types of grids used, the number of variables involved, and the number of different simulations performed with a climate model or the feature-richness of high-resolution simulations. This project has developed new and faster methods for visualization in order to get the most knowledge out of the new generation of high-resolution climate models. While traditional climate images will continue to be useful, there is need for new approaches to visualization and analysis of climate data if we are to gain all the insights available in ultra-large data sets produced by high-resolution model output and ensemble integrations of climate models such as those produced for the Coupled Model Intercomparison Project. Towards that end, we have developed new visualization techniques for performing correlation analysis. We have also introduced highly scalable, parallel rendering methods for visualizing large-scale 3D data. This project was done jointly with climate scientists and visualization researchers at Argonne National Laboratory and NCAR.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2017

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolution in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Calibration of parallel bond parameters in bonded particle models via physics-informed adaptive moment optimisation

This study proposes an automated calibration procedure for bond parameters in bonded discrete element modelling. By exploring the underlying physical correlations between microscopic parameters of bonds and macroscopic strength parameters of the continuum to be modelled, the microscopic shear strength and tensile strength are identified as independent variables for calibration purpose. Then a physics-informed iterative scheme is proposed to automatically approximate the bond parameters by viewing the micro-macro relation as an implicitly defined mathematical mapping function. As a result of highly non-convex features of this implicit mapping, the adaptive moment estimation (Adam), which is especially suitable for problems with noisy gradients, is adopted as the basic iterative scheme, in conjunction with other numerical techniques to approximately evaluate the partial derivatives involved. The whole procedure offers a simple and effective framework for bond parameter calibration. Finally, a numerical example of SiC ceramic is provided for validation. By compared with some existing calibration methods, the proposed method shows significant advantages in terms of calibration efficiency and accuracy.

42 ENGINEERING↗

DOE OSTI2018

An analysis of various solution strategies and perturbations on inputs of the reactor shielding problem - 25584

Previous work focused on the use of automated variance reduction parameters for use in a fixed source reactor shielding problem to solve for ex-core particle transport results. The current work assesses that strategy in light of a fully-coupled Monte Carlo problem run as a critical system with parallel processing and the use of moderate variance reduction parameters set manually. The results from the two strategies compare well. Also, results are compared between the MCNP, Virtual Environment for Reactor Applications (VERA) and Shift computer codes. Shift and VERA deliver similar results and compare well to MCNP. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2022

Artificial Neural Network Modeling for Airline Disruption Management

Since the 1970s, most airlines have incorporated computerized support for managing disruptions during flight schedule execution. However, existing platforms for airline disruption management (ADM) employ monolithic system design methods that rely on the creation of specific rules and requirements through explicit optimization routines, before a system that meets the specifications is designed. Thus, current platforms for ADM are unable to readily accommodate additional system complexities resulting from the introduction of new capabilities, such as the introduction of unmanned aerial systems (UAS), operations and infrastructure, to the system. To this end, we use historical data on airline scheduling and operations recovery to develop a system of artificial neural networks (ANNs), which describe a predictive transfer function model (PTFM) for promptly estimating the recovery impact of disruption resolutions at separate phases of flight schedule execution during ADM. Furthermore, we provide a modular approach for assessing and executing the PTFM by employing a parallel ensemble method to develop generative routines that amalgamate the system of ANNs. Our modular approach ensures that current industry standards for tardiness in flight schedule execution during ADM are satisfied, while accurately estimating appropriate time-based performance metrics for the separate phases of flight schedule execution.

Kolawole Ogunsina↗

DOE OSTI2020

Method and device for controlling heat pump

A method for controlling a heat pump is provided. A working mode of the heat pump is determined. Based on a determination that the working mode of the heat pump is a heating mode, an ambient temperature of the heat pump is determined. Based on a determination that the ambient temperature of the heat pump is higher than a first predetermined temperature, a first compressor of the heat pump is operated. Based on a determination that the ambient temperature of the heat pump is lower than the first predetermined temperature, both the first compressor and a second compressor of the heat pump are enabled to operate, in response to a two-stage thermostat. The first compressor and the second compressor are coupled in parallel. The method allows the heat pump to be suitable for a cold climate.

42 ENGINEERING↗

DOE OSTI2014

Stochastic Optimization of Complex Systems

This project focused on methodologies for the solution of stochastic optimization problems based on relaxation and penalty methods, Monte Carlo simulation, parallel processing, and inverse optimization. The main results of the project were the development of a convergent method for the solution of models that include expectation constraints as in equilibrium models, improvement of Monte Carlo convergence through the use of a new method of sample batch optimization, the development of new parallel processing methods for stochastic unit commitment models, and the development of improved methods in combination with parallel processing for incorporating automatic differentiation methods into optimization.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2013

Applications of Automation Methods for Nonlinear Fracture Test Analysis

Using automated and standardized computer tools to calculate the pertinent test result values has several advantages such as: 1. allowing high-fidelity solutions to complex nonlinear phenomena that would be impractical to express in written equation form, 2. eliminating errors associated with the interpretation and programing of analysis procedures from the text of test standards, 3. lessening the need for expertise in the areas of solid mechanics, fracture mechanics, numerical methods, and/or finite element modeling, to achieve sound results, 4. and providing one computer tool and/or one set of solutions for all users for a more "standardized" answer. In summary, this approach allows a non-expert with rudimentary training to get the best practical solution based on the latest understanding with minimum difficulty.Other existing ASTM standards that cover complicated phenomena use standard computer programs: 1. ASTM C1340/C1340M-10- Standard Practice for Estimation of Heat Gain or Loss Through Ceilings Under Attics Containing Radiant Barriers by Use of a Computer Program 2. ASTM F 2815 - Standard Practice for Chemical Permeation through Protective Clothing Materials: Testing Data Analysis by Use of a Computer Program 3. ASTM E2807 - Standard Specification for 3D Imaging Data Exchange, Version 1.0 The verification, validation, and round-robin processes required of a computer tool closely parallel the methods that are used to ensure the solution validity for equations included in test standard. The use of automated analysis tools allows the creation and practical implementation of advanced fracture mechanics test standards that capture the physics of a nonlinear fracture mechanics problem without adding undue burden or expense to the user. The presented approach forms a bridge between the equation-based fracture testing standards of today and the next generation of standards solving complex problems through analysis automation.

Allen, Phillip A.↗

DOE OSTI2014

Non-Galerkin Coarse Grids for Algebraic Multigrid

Algebraic multigrid (AMG) is a popular and effective solver for systems of linear equations that arise from discretized partial differential equations. And while AMG has been effectively implemented on large scale parallel machines, challenges remain, especially when moving to exascale. Particularly, stencil sizes (the number of nonzeros in a row) tend to increase further down in the coarse grid hierarchy, and this growth leads to more communication. Therefore, as problem size increases and the number of levels in the hierarchy grows, the overall efficiency of the parallel AMG method decreases, sometimes dramatically. This growth in stencil size is due to the standard Galerkin coarse grid operator, $P^T A P$, where $P$ is the prolongation (i.e., interpolation) operator. For example, the coarse grid stencil size for a simple three-dimensional (3D) seven-point finite differencing approximation to diffusion can increase into the thousands on present day machines, causing an associated increase in communication costs. We therefore consider algebraically truncating coarse grid stencils to obtain a non-Galerkin coarse grid. First, the sparsity pattern of the non-Galerkin coarse grid is determined by employing a heuristic minimal “safe” pattern together with strength-of-connection ideas. Second, the nonzero entries are determined by collapsing the stencils in the Galerkin operator using traditional AMG techniques. The result is a reduction in coarse grid stencil size, overall operator complexity, and parallel AMG solve phase times.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Enhancing photoionization rate calculations in low-temperature plasmas using spectral methods

Photoionization plays a central role in the development of streamer discharges and other non-equilibrium plasma phenomena. It creates seed electrons, which are essential for positive streamer propagation, allowing the ionization front to move forward. Because of this, accurate modeling of photoionization is very important for predicting streamer behavior and plasma evolution. The photoionization process in air (N 2 – O 2 mixture) is often described by the Zheleznyak model (1982). This model is usually solved through Helmholtz-type equations that approximate the Zheleznyak photoionization model (Zheleznyak et al. 1982) as Partial Differential Equations (PDEs). Conventional numerical methods, such as the Finite Difference Method (FDM) or Finite Volume Method (FVM), are widely used to solve these equations. Although they are prevalent, the computational cost of these methods due to their need for matrix operations and iterative solver is demanding. To address this challenge, this work develops a spectral solver based on the Fast Fourier Transform (FFT) combined with Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) to calculate the photoionization rate efficiently in an axisymmetric cylindrical domain. This method naturally satisfies the boundary conditions used in the model and converts the PDE into algebraic ones in spectral space. Thus, avoids the need for iterative matrix solvers. When compared with FDM results, it is demonstrated that the new solver not only maintains accuracy, but also reduces the computational cost, showing a performance increase of approximately 100 compared to FDM over a wide range of problem sizes. The method is parallelized using Message Passing Interface (MPI) and has been integrated into a fluid plasma model for streamer simulation. Here, this FFT-based approach provides a fast and reliable alternative for calculating photoionization in fluid models, helping large-scale plasma simulations run faster and efficiently, and allows higher-resolution simulation without extra computational cost.

Axisymmetric system↗

DOE OSTI2013

Giant tunneling magnetoresistance in silicene

We have theoretically studied ballistic electron transport in silicene under the manipulation of a pair of ferromagnetic gate. Transport properties like transmission and conductance have been calculated by the standard transfer matrix method for parallel and antiparallel magnetization configurations. It is demonstrated here that, due to the stray field-induced wave-vector filtering effect, remarkable difference in configuration-dependent transport gives rise to a giant tunneling magnetoresistance. In combination with the peculiar buckled structure of silicene and its electric tunable energy gap, the receiving magnetoresistance can be efficiently modulated by the externally-tunable stray field, electrostatic potential, and staggered sublattice potential, providing some flexible strategies to construct silicene-based nanoelectronic device.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1994

A structural design decomposition method utilizing substructuring

A new method of design decomposition for structural analysis and optimization is described. For this method, the structure is divided into substructures where each substructure has its structural response described by a structural-response subproblem, and its structural sizing determined from a structural-sizing subproblem. The structural responses of substructures that have rigid body modes when separated from the remainder of the structure are further decomposed into displacements that have no rigid body components, and a set of rigid body modes. The structural-response subproblems are linked together through forces determined within a structural-sizing coordination subproblem which also determines the magnitude of any rigid body displacements. Structural-sizing subproblems having constraints local to the substructures are linked together through penalty terms that are determined by a structural-sizing coordination subproblem. All the substructure structural-response subproblems are totally decoupled from each other, as are all the substructure structural-sizing subproblems, thus there is significant potential for use of parallel solution methods for these subproblems.

Scotti, Stephen J.↗