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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Advanced trust region optimization strategies for glass box / black box models

We present an improved trust region filter (TRF) method for optimization of combined glass box/black box systems. Glass box systems refer to models that are easily expressed in an algebraic modeling language, providing cheap and accurate derivative information. By contrast, black box systems may be computationally expensive and derivatives are unavailable. The TRF method, as first introduced in our previous work (Eason and Biegler, AIChE J . 2016; 62:3124–3136), is able to handle hybrid systems containing both glass and black box components, which can frequently arise in chemical engineering, for example, when a multiphase reactor model is included in a flow sheet optimization problem. We discuss several recent modifications in the algorithm such as the sampling region, which maintains the algorithm's global convergence properties without requiring the trust region to shrink to zero in the limit. To benchmark the development of this optimization method, a test set of problems is generated based on modified problems from the CUTEr and COPS sets. The modified algorithm demonstrates improved performance using the test problem set. Finally, the algorithm is implemented within the Pyomo environment and demonstrated on a rigorous process optimization case study for carbon capture. © 2018 American Institute of Chemical Engineers AIChE J , 64: 3934–3943, 2018

Eason, John P.↗
DOE OSTI2019

An adaptive fast multipole method in Cartesian basis, enabled by algorithmic differentiation

A novel form of the fast multipole method is realized by the combination of adaptive data structures with implementation of the multipole expansions and their translations in Cartesian basis, and enabled by algorithmic differentiation. It may be possible to generalize it to any kernel that allows its formulation as a function of small quantities with respect to which they can be expanded. There is no hard and fast rule recipe that works for all cases. However, it is shown how to do it for the softened Coulomb kernel, which is different from the Coulomb kernel. The characteristics and performance of the method are mapped and shown to provide an attractive option for a generic fast multipole algorithm in a wide region of the parameter space. The algorithm is illustrated with a beam dynamics application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

A preconditioned dual–primal finite element tearing and interconnecting method for solving three-dimensional time-harmonic Maxwell's equations

A new preconditioned dual–primal nonoverlapping domain decomposition method is proposed for the finite element solution of three-dimensional large-scale electromagnetic problems. With the aid of two Lagrange multipliers, the new method converts the original volumetric problem to a surface problem by using a higher-order transmission condition at the subdomain interfaces to significantly improve the convergence of the iterative solution of the global interface equation. Similar to the previous version, a global coarse problem related to the degrees of freedom at the subdomain corner edges is formulated to propagate the residual error to the whole computational domain at each iteration, which further increases the rate of convergence. In addition, a fully algebraic preconditioner based on matrix splitting is constructed to make the proposed domain decomposition method even more robust and scalable. Perfectly matched layers (PMLs) are considered for the boundary truncation when solving open-region problems. The influence of the PML truncation on the convergence performance is investigated by examining the convergence of the transmission condition for an interface inside the PML. Numerical examples including wave propagation and antenna radiation problems truncated with PMLs are presented to demonstrate the validity and the capability of this method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

BCFW tilings and cluster adjacency for the amplituhedron

In 2005, Britto, Cachazo, Feng, and Witten gave a recurrence (now known as the BCFW recurrence) for computing scattering amplitudes in N = 4 super Yang–Mills theory. Arkani-Hamed and Trnka subsequently introduced the amplituhedron to give a geometric interpretation of the BCFW recurrence. Arkani-Hamed and Trnka conjectured that each way of iterating the BCFW recurrence gives a “triangulation” or “tiling” of the m=4 amplituhedron. In this article, we prove the BCFW tiling conjecture of Arkani-Hamed and Trnka. We also prove the cluster adjacency conjecture for BCFW tiles of the amplituhedron, which says that facets of tiles are cut out by collections of compatible cluster variables for the Grassmannian Gr4,n. Moreover we show that each BCFW tile is the subset of the Grassmannian where certain cluster variables have particular signs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

One dimensional staggered bosons, clock models, and their noninvertible symmetries

We study systems of staggered boson Hamiltonians in a one dimensional lattice and in particular how the translation symmetry by one unit in these systems is in reality a noninvertible symmetry closely related to T-duality. We also study the simplest systems of clock models derived from these staggered boson Hamiltonians. We show that the noninvertible symmetries of these lattice models together with the discrete Z N symmetry predict that these are critical points with a U ( 1 ) current algebra at c = 1 and radius 2 N whenever N > 4 . We also present an independent computation of this value that arises directly from the staggered boson variables and does not use these additional symmetries. We also present a theoretical estimate of the values of critical coupling constants away from the self-dual symmetry point in these clock models. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2017

Embedded ensemble propagation for improving performance, portability, and scalability of uncertainty quantification on emerging computational architectures

In this study, quantifying simulation uncertainties is a critical component of rigorous predictive simulation. A key component of this is forward propagation of uncertainties in simulation input data to output quantities of interest. Typical approaches involve repeated sampling of the simulation over the uncertain input data, and can require numerous samples when accurately propagating uncertainties from large numbers of sources. Often simulation processes from sample to sample are similar and much of the data generated from each sample evaluation could be reused. We explore a new method for implementing sampling methods that simultaneously propagates groups of samples together in an embedded fashion, which we call embedded ensemble propagation. We show how this approach takes advantage of properties of modern computer architectures to improve performance by enabling reuse between samples, reducing memory bandwidth requirements, improving memory access patterns, improving opportunities for fine-grained parallelization, and reducing communication costs. We describe a software technique for implementing embedded ensemble propagation based on the use of C++ templates and describe its integration with various scientific computing libraries within Trilinos. We demonstrate improved performance, portability and scalability for the approach applied to the simulation of partial differential equations on a variety of CPU, GPU, and accelerator architectures, including up to 131,072 cores on a Cray XK7 (Titan).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Entanglement entropy across the lattice-continuum correspondence

This paper revisits the standard calculations of free field entanglement entropy in light of the newly developed lattice-continuum correspondence. This correspondence prescribes an explicit method to extract an approximately continuum quantum field theory out of a fully regularized lattice theory. This prescription will here be extended to subregion algebras, and it will be shown how entropies of continuum boson and fermion theories can be computed by working purely with lattice quantities. This gives a clear picture of the origin of divergences in entanglement entropy while also presenting a concise and detailed recipe for calculating this important quantity in continuum theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

CSPlib: A performance portable parallel software toolkit for analyzing complex kinetic mechanisms

Computational singular perturbation (CSP) is a method to analyze dynamical systems. It targets the decoupling of fast and slow dynamics using an alternate linear expansion of the right-hand side of the governing equations based on eigenanalysis of the associated Jacobian matrix. This representation facilitates diagnostic analysis, detection and control of stiffness, and the development of simplified models. For this work, we have implemented CSP in a C++ open-source library CSPlib using the Kokkos parallel programming model to address portability across diverse heterogeneous computing platforms, i.e., multi/many-core CPUs and GPUs. We describe the CSPlib implementation and present its computational performance across different computing platforms using several test problems. Specifically, we test the CSPlib performance for a constant pressure ignition reactor model on different architectures, including IBM Power 9, Intel Xeon Skylake, and NVIDIA V100 GPU. The size of the chemical kinetic mechanism is varied in these tests. As expected, the Jacobian matrix evaluation, the eigensolution of the Jacobian matrix, and matrix inversion are the most expensive computational tasks. When considering the higher throughput characteristic of GPUs, GPUs performs better for small matrices with higher occupancy rate. CPUs gain more advantages from the higher performance of well-tuned and optimized linear algebra libraries such as OpenBLAS.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Demonstration and performance testing of extreme-resolution simulations with static meshes on Summit (CPU & GPU) for a parked-turbine configuration and an actuator-line (mid-fidelity model) wind farm configuration (ECP-Q4 FY2020 Milestone Report)

The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary physics codes in the ExaWind simulation environment are Nalu-Wind, an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, AMR-Wind, a block-structured-grid solver with adaptive mesh refinement capabilities, and OpenFAST, a wind-turbine structural dynamics solver. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and Helmholtz-type equations for transport of momentum and other scalars. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. The choice of overset-mesh methodology to model the moving and non-moving parts of the computational domain introduces constraint equations in the elliptic pressure-Poisson solver. The presence of constraints greatly affects the performance of algebraic multigrid preconditioners.

17 WIND ENERGY↗
DOE OSTI2020

Fast Computational Algorithms for Partial Differential Equations and Uncertainty Quantifications

This project concerned the construction, testing and analysis of computational algorithms for solving parameterized and stochastic partial differential equations. The study and understanding of equations of this type is of fundamental importance in numerous engineering and scientific applications. Examples include simulation of plasma dynamics in models of electric propulsion and nuclear fusion, simulation of multiphase flows, such as the flow of water, gas and oil in reservoirs, and structural analysis of the dependence of structures on materials. Parametrization is used in such settings when properties of the models such as viscosity of fluids or electric resistivity of materials are not precisely understood and instead are treated as random variables. The resulting solutions are themselves random, and having such solutions will enable engineers to use probabilistic methods to assess the likelihood of events, for example, whether a pollutant in a liquid will exceed a limit, and to use such analyses to develop ways to ensure positive outcomes. Construction of accurate (high resolution) computational solutions is expensive, requiring significant computer time and computational resources, and there is need to reduce computational cost to make simulation useful and effective. The aim of the project was to construct algorithms to efficiently compute surrogate solutions to parameterized problems to allow for efficient and accurate simulation. The technical approach used focused on two related strategies, based on rank-reduction methods and reduced-order models. These methods construct surrogate solutions of parameter-dependent models by projection or interpolation into low-dimensional approximation spaces. Cost savings are achieved if the low-dimensional spaces can be identified and constructed efficiently and if the resulting low-dimensional algebraic systems can be solved cheaply. Accomplishments include: Theoretical and empirical demonstration of the effectiveness of fast multigrid solution strategies for computing low-rank representations of parameter-dependent solutions to discrete partial differential equations, including the first proof establishing so-called textbook convergence properties for low-rank methods. Development of efficient solution algorithms for solving nonlinear parameter-dependent partial differential equations used in models of fluid dynamics. Developent of efficient algorithms for low-rank representation of solutions of time-dependent simulations of fluid dynamics using multi-dimensional tensor representations of solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Effects of refractive index mismatch in optical CT imaging of polymer gel dosimeters

Purpose: Proposing an image reconstruction technique, algebraic reconstruction technique-refraction correction (ART-rc). The proposed method takes care of refractive index mismatches present in gel dosimeter scanner at the boundary, and also corrects for the interior ray refraction. Polymer gel dosimeters with high dose regions have higher refractive index and optical density compared to the background medium, these changes in refractive index at high dose results in interior ray bending. Methods: The inclusion of the effects of refraction is an important step in reconstruction of optical density in gel dosimeters. The proposed ray tracing algorithm models the interior multiple refraction at the inhomogeneities. Jacob’s ray tracing algorithm has been modified to calculate the pathlengths of the ray that traverses through the higher dose regions. The algorithm computes the length of the ray in each pixel along its path and is used as the weight matrix. Algebraic reconstruction technique and pixel based reconstruction algorithms are used for solving the reconstruction problem. The proposed method is tested with numerical phantoms for various noise levels. The experimental dosimetric results are also presented. Results: The results show that the proposed scheme ART-rc is able to reconstruct optical density inside the dosimeter better than the results obtained using filtered backprojection and conventional algebraic reconstruction approaches. The quantitative improvement using ART-rc is evaluated using gamma-index. The refraction errors due to regions of different refractive indices are discussed. The effects of modeling of interior refraction in the dose region are presented. Conclusions: The errors propagated due to multiple refraction effects have been modeled and the improvements in reconstruction using proposed model is presented. The refractive index of the dosimeter has a mismatch with the surrounding medium (for dry air or water scanning). The algorithm reconstructs the dose profiles by estimating refractive indices of multiple inhomogeneities having different refractive indices and optical densities embedded in the dosimeter. This is achieved by tracking the path of the ray that traverses through the dosimeter. Extensive simulation studies have been carried out and results are found to be matching that of experimental results.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

PBW Degeneration: Algebra, Geometry, and Combinatorics

We review the recent progress in the theory of Poincaré–Birkhoff–Witt degenerations of irreducible representations of simple Lie algebras. We describe algebraic, geometric, and combinatorial aspects of the theory.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Muon Tracing and Image Reconstruction Algorithms for Cosmic Ray Muon Computed Tomography

Cosmic ray muon-computed tomography (μCT) is a new imaging modality with unique characteristics that could be particularly important for diverse applications including nuclear nonproliferation, spent nuclear fuel monitoring, cargo scanning, and volcano imaging. The strong scattering dependence of muons on atomic number Z in combination with high penetration range could offer a significant advantage over existing techniques when dense, shielded containers must be imaged. However, μCT reconstruction using conventional filtered back-projection is limited due to the overly simple assumptions that do not consider the curved path caused by multiple Coulomb scattering prompting the need for more sophisticated approaches to be developed. Here, we argue that the use of improved muon tracing and scattering angle projection algorithms as well as an algebraic reconstruction technique should produce muon tomographic images with improved quality–or require fewer muons to produce the same image quality–compared to the case where conventional methods are used. We report on the development and assessment of three novel muon tracing methods and two scattering angle projection methods for μCT. Simulated dry storage casks with single and partial missing fuel assemblies were used as numerical examples to assess and compare the proposed methods. The reconstructed images showed an expected improvement in image quality when compared with conventional techniques, even without muon momentum information, which should lead to improved detection capability, even for partial defects.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Computation of magnetic fields from field components on a plane grid

An algorithm is presented to calculate the field components of the magnetic field [B x (x, y, z), B y (x, y, z), B z (x, y, z)] at a point (x, y, z) in space, from the knowledge of the components [B x (x, y) = 0, z), B y (x, y = 0, z), B z (x, y = 0,z)] on a “reference plane”, which is normal to the y-axis at . The algorithm, which is a general one and is not restricted to fields with mid-plane symmetry is based on the Maclaurin series expansion of the magnetic field components at any point in space in terms of the distance (y) of the point from the reference plane. The coefficients of the Maclaurin series expansion are expressed in terms of the on-plane field components and their partial derivatives with respect to spatial coordinates (). The field components are usually generated from magnetic field measurements on a rectangular grid on the plane. This algorithm was employed in 1986 in the RAYTRACE computer code to help calculate the optical properties of magnets and of the Alternating Gradient Synchrotron (AGS) at the Brookhaven National Laboratory (BNL). Here, a general mathematical formulation of this algorithm based on the differential algebraic method was presented by Makino in 2011. This paper presents the step by step derivation of the algorithm and provides the necessary formulas to be introduced by the reader in any computer code which requires the field components generated by magnetic devices. In addition provides an example of the use of the algorithm and its limitations as applied to a Halbach type magnet with or without median plane symmetry.

43 PARTICLE ACCELERATORS↗