Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linearization”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,477 records · Page 82
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Synthesis and Tests of a 1-m{sup 3} Scintillator Based on Linear Alkylbenzene

The stability of a liquid organic scintillator based on linear alkylbenzene in a volume of 1 m{sup 3} was measured. The measurements were performed using an iDREAM reactor antineutrino detector at the National Research Center Kurchatov Institute. No systemic degradation of the scintillator light yield within an observation time of 225 days was observed. These long-term stability measurements of a large-volume liquid organic scintillator based on linear alkylbenzene are the first in Russia.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2017

Goal-Oriented Optimal Approximations of Bayesian Linear Inverse Problems

We propose optimal dimensionality reduction techniques for the solution of goal-oriented linear-Gaussian inverse problems, where the quantity of interest (QoI) is a function of the inversion parameters. These approximations are suitable for large-scale applications. In particular, we study the approximation of the posterior covariance of the QoI as a low-rank negative update of its prior covariance and prove optimality of this update with respect to the natural geodesic distance on the manifold of symmetric positive definite matrices. Assuming exact knowledge of the posterior mean of the QoI, the optimality results extend to optimality in distribution with respect to the Kullback--Leibler divergence and the Hellinger distance between the associated distributions. We also propose the approximation of the posterior mean of the QoI as a low-rank linear function of the data and prove optimality of this approximation with respect to a weighted Bayes risk. Both of these optimal approximations avoid the explicit computation of the full posterior distribution of the parameters and instead focus on directions that are well informed by the data and relevant to the QoI. These directions stem from a balance among all the components of the goal-oriented inverse problem: prior information, forward model, measurement noise, and ultimate goals. We illustrate the theory using a high-dimensional inverse problem in heat transfer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems

We consider the numerical solution of parameterized linear systems where the system matrix, the solution, and the right-hand side are parameterized by a set of uncertain input parameters. We explore spectral methods in which the solutions are approximated in a chosen finite-dimensional subspace. It has been shown that the stochastic Galerkin projection technique fails to minimize any measure of the solution error [A. Mugler and H.-J. Starkloff, ESAIM Math. Model. Numer. Anal., 47 (2013), pp. 1237--1263]. As a remedy for this, we propose a novel stochatic least-squares Petrov--Galerkin (LSPG) method. The proposed method is optimal in the sense that it produces the solution that minimizes a weighted $\ell^2$-norm of the residual over all solutions in a given finite-dimensional subspace. Moreover, the method can be adapted to minimize the solution error in different weighted $\ell^2$-norms by simply applying a weighting function within the least-squares formulation. In addition, a goal-oriented seminorm induced by an output quantity of interest can be minimized by defining a weighting function as a linear functional of the solution. We establish optimality and error bounds for the proposed method, and extensive numerical experiments show that the weighted LSPG method outperforms other spectral methods in minimizing corresponding target weighted norms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting

Fully implicit Runge--Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic preconditioning framework for solving the systems of equations that arise from IRK methods applied to linear numerical PDEs (without algebraic constraints). Additionally, this framework also naturally applies to discontinuous Galerkin discretizations in time. Under quite general assumptions on the spatial discretization that yield stable time integration, the preconditioned operator is proven to have condition number bounded by a small, order-one constant, independent of the spatial mesh and time-step size, and with only weak dependence on number of stages/polynomial order; for example, the preconditioned operator for 10th-order Gauss IRK has condition number less than two, independent of the spatial discretization and time step. The new method can be used with arbitrary existing preconditioners for backward Euler-type time-stepping schemes and is amenable to the use of three-term recursion Krylov methods when the underlying spatial discretization is symmetric. The new method is demonstrated to be effective on various high-order finite-difference and finite element discretizations of linear parabolic and hyperbolic problems, demonstrating fast, scalable solution of up to 10th-order accuracy. The new method consistently outperforms existing block preconditioning approaches, and in several cases, the new method can achieve 4th-order accuracy using Gauss integration with roughly half the number of preconditioner applications and wallclock time as required using standard diagonally IRK methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Fast and Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices with Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

In this work, we present an efficient and scalable algorithm for performing matrix-vector multiplications (matvecs) for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint, and (2) efficient fast Fourier transform–based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80% of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Potential linear and angular momentum in the scalar diquark model

We present an analytic two-loop calculation within the scalar diquark model of the potential linear and angular momenta, defined as the difference between the Jaffe-Manohar and Ji notions of linear and angular momenta. As expected by parity and time-reversal symmetries, a direct calculation confirms that the potential transverse momentum coincides with the Jaffe-Manohar (or canonical) definition of average quark transverse momentum, also known as the quark Sivers shift. We examine whether initial/final-state interactions at the origin of the Sivers asymmetry can also generate a potential angular momentum in the scalar diquark model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Luminosity Limitations of Linear Colliders Based on Plasma Acceleration

Particle acceleration in plasma creates a possibility of exceptionally high accelerating gradients and appears as a very attractive option for future linear electron-positron and/or photon-photon colliders. These high accelerating gradients were already demonstrated in a number of experiments. Furthermore, a linear collider requires exceptionally high beam brightness which still needs to be demonstrated. In this article we discuss major phenomena which limit the beam brightness of accelerated beam and, consequently, the collider luminosity.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Replicated Computational Results (RCR) Report for “Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software”

The article by Flegar et al. titled “Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software” presents a novel, practical implementation of an adaptive precision block-Jacobi preconditioner. Performance results using state-of-the-art GPU architectures for the block-Jacobi preconditioner generation and application demonstrate the practical usability of the method, compared to a traditional full-precision block-Jacobi preconditioner. A production-ready implementation is provided in the Ginkgo numerical linear algebra library. In this report, the Ginkgo library is reinstalled and performance results are generated to perform a comparison to the original results when using Ginkgo’s Conjugate Gradient solver with either the full or the adaptive precision block-Jacobi preconditioner for a suite of test problems on an NVIDIA GPU accelerator. After completing this process, the published results are deemed reproducible.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Parametric dependencies of resonant layer responses across linear, two-fluid, drift-MHD regimes

Non-axisymmetric magnetic fields arising in a tokamak either by external or internal perturbations can induce complex non-ideal MHD responses in their resonant surfaces while remaining ideally evolved elsewhere. This layer response can be characterized in a linear regime by a single parameter called the inner-layer Delta, which enables outer-layer matching and the prediction of torque balance to non-linear island regimes. Here, we follow strictly one of the most comprehensive analytic treatments including two-fluid and drift MHD effects and keep the fidelity of the formulation by incorporating the numerical method based on the Riccati transformation when quantifying the inner-layer Delta. The proposed scheme reproduces not only the predicted responses in essentially all asymptotic regimes but also with continuous transitions as well as improved accuracies. In particular, the Delta variations across the inertial regimes with viscous or semi-collisional effects have been further resolved, in comparison with additional analytic solutions. The results imply greater shielding of the electromagnetic torque at the layer than what would be expected by earlier work when the viscous or semi-collisional effects can compete against the inertial effects, and also due to the intermediate regulation by kinetic Alfven wave resonances as rotation slows down. These are important features that can alter the nonaxisymmetric plasma responses including the field penetration by external fields or island seeding process in rotating tokamak plasmas.

MHD instability↗
DOE OSTI2018

Small Non-Linear Solver

SNLS (small non-linear solver) is a C++ library for solving non-linear systems. The emphasis is on small systems on equations for which direct factorization of the Jacobian is appropriate. The systems of equations may be numerically ill-conditioned. Implementation is amenable to GPU usage, with the idea that class instantiate would occur within device functions.

Wayne, BrettM.↗
DOE OSTI2019

HALA: Handy Accelerated Linear Algebra

Accelerated linear algebra libraries often come with C-style of interfaces or even older Fortran77 standards, which makes it difficult to use within generic template programming environment of modern C++. For example, the BLAS and derived standards such as cuBLAS do not accept overloads and a different functions have to be called for each input type, thus it is very challenging to write a single template that handles multiple precision modes and works well with different C++ containers. HALA offers a series of templates that wrap around the BLAS/cuBLAS and other similar methods, automatically infer the relevant types and call the appropriate back-end. The templates work out-of-the-box with all C++ standard vector-like containers and can be easily extended (with template specializations) to handle user-provided containers. The HALA API is also overloaded to handle both GPU and CPU cases with a single "engine" class, thus a single high-level algorithms can utilize both CPU or GPU backends, i.e., the HALA API is unified and handles the variations between cuBLAS and BLAS. In addition to BLAS and cuBLAS, wrapper templates are provided for subset of LAPACK, cuSparse, and Cholmod methods. Work is in progress to complete as many of these standards as possible. HALA also includes a module for low-level extended register vectorization for complex number arithmetic and several simple solvers that build on the basic linear algebra capabilities. A single unified C++ API will benefit fast prototyping and easily writing code that is portable across GPU/CPU platforms as well as precision types and user containers. Note that HALA does not provide any accelerated algorithms, it simply serves as a "handy" front-end to other standards.

Stoyanov, MiroslavK.↗
DOE OSTI2021

Linear Grains

LIGR (Linear Grains) implements a linear (Fourier mode) analysis of a shock propagating through density perturbations. It has two primary capabilities. First, it calculates the shock front distortion and post-shock flow variables (density, velocity, pressure) for single Fourier mode pairs in two dimensions (a pair of x and y modes). Second, it calculates these same quantities for a grains-like pre-shock density perturbation, which consists of a sum of many Fourier modes. This grains-like perturbation is a periodic grid of rectangles at a specifiable density and size (the grains), separated by regions of a different specifiable size and density (interstitial spaces between the grains). The single-mode analysis is based on the work of Velikovich et al., Phys. Plasmas 14 072706 (2007).

Li, GraceJ↗
DOE OSTI2025

Ipopt Interface to Re::Solve Linear Solver

The software provides Ipopt optimization package an interface to the Re::Solve linear solver library. Re::Solve features GPU-resident direct and iterative linear solvers that could be used to accelerate optimization computations.

Alam, Maksudul [Oak Ridge National Laboratory (ORN↗
DOE OSTI2024

LAPIS: Linear Algebra Performance for Intermediate Subprograms

SAND2025-11594O LAPIS (Linear Algebra Performance for Intermediate Subprograms) is a compiler infrastructure for linear algebra that targets both high productivity and performance portability. It is based on the open-source MLIR package from the LLVM project. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Kelley, Brian↗
DOE OSTI2025

Bayesian Linear Regression for Hugoniot Data

This repository provides the code and datasets used in the paper Bayesian Analysis of Linear Shock Compression Data. This paper analyzes publicly available shock compression datasets on copper, argon, and nickel from Marsh (1980) using Bayesian linear regression, and compares the results with those obtained using bootstrapping methods. References: - Marsh, S. P. (1980). LASL shock Hugoniot data (Vol. 5). Univ of California Press.

Bernstein, JasonA [Lawrence Livermore National Lab↗
DOE OSTI2019

Theoretical Understanding of the Linear Relationship between Convective Updrafts and Cloud-Base Height for Shallow Cumulus Clouds. Part I: Maritime Conditions

Zheng and Rosenfeld found linear relationships between the convective updrafts and cloud-base height z b using ground-based observations over both land and ocean. The empirical relationships allow for a novel satellite remote sensing technique of inferring the cloud-base updrafts and cloud condensation nuclei concentration, both of which are important for understanding aerosol–cloud–climate interactions but have been notoriously difficult to retrieve from space. In Part I of a two-part study, a theoretical framework is established for understanding this empirical relationship over the ocean. Part II deals with continental cumulus clouds. Using the bulk concept of mixed-layer (ML) model for shallow cumulus, I found that this relationship arises from the conservation law of energetics that requires the radiative flux divergence of an ML to balance surface buoyancy flux. Given a certain ML radiative cooling rate per unit mass Q, a deeper ML (higher z b ) undergoes more radiative cooling and requires stronger surface buoyancy flux to balance it, leading to stronger updrafts. The rate with which the updrafts vary with z b is modulated by Q. The cooling rate Q manifests strong resilience to external large-scale forcing that spans a wide range of climatology, allowing the slope of the updrafts– z b relationship to remain nearly invariant. This causes the relationship to manifest linearity. The physical mechanism underlying the resilience of Q to large-scale forcing, such as free-tropospheric moisture and sea surface temperature, is investigated through the lens of the radiative transfer theory (two-stream Schwarzschild equations) and an ML model for shallow cumulus.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Theoretical Understanding of the Linear Relationship between Convective Updrafts and Cloud-Base Height for Shallow Cumulus Clouds. Part II: Continental Conditions

This is the Part II of a two-part study that seeks a theoretical understanding of an empirical relationship for shallow cumulus clouds: subcloud updraft velocity covaries linearly with the cloud-base height. This work focuses on continental cumulus clouds that are more strongly forced by surface fluxes and more deviated from equilibrium than those over oceans (Part I). We use a simple analytical model for shallow cumulus that is well tested against a high-resolution (25 m in the horizontal) large-eddy simulation model. Consistent with a conventional idea, we find that surface Bowen ratio is the key variable that regulates the covariability of both parameters: under the same solar insolation, a drier surface allows for stronger buoyancy flux, triggering stronger convection that deepens the subcloud layer. We find that the slope of the Bowen-ratio-regulated relationship between the two parameters (defined as λ) is dependent on both the local time and the stability of the lower free atmosphere. The value of λ decreases with time exponentially from sunrise to early afternoon and linearly from early afternoon to sunset. The value of λ is larger in a more stable atmosphere. In addition, continental λ in the early afternoon more than doubles the oceanic λ. Validation of the theoretical results against ground observations over the Southern Great Plains shows a reasonable agreement. Physical mechanisms underlying the findings are explained from the perspective of different time scales at which updrafts and cloud-base height respond to a surface flux forcing.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

A Computationally Efficient Linear Semi-Lagrangian Scheme for the Advection of Microphysical Variables in Cloud-Resolving Models

An efficient semi-Lagrangian (SL) numerical scheme for the advection of positive-definite microphysical variables in cloud-resolving models is proposed. The scheme is a linear combination of SL schemes of the first and second order. The proposed scheme is compared with two high-order, monotonic, nonlinear Eulerian schemes, in two 2D tests. In the first test, advection of a positive scalar field with large gradients is performed within complicated idealized steering flows. In the second test, a hail storm is simulated using the 2D Hebrew University Cloud Model, describing the interactions between 15 size distributions of different microphysical quantities (each distribution is described by 43 mass bins). The proposed scheme is computationally efficient, has a low numerical diffusion and a high level of mass conservation accuracy, and preserves the sum of multiple advected variables as well as the linear relationships between the advected scalar variables. Although the proposed SL scheme is not exactly positive definite, the negative values and their number, which may appear only in the case of very strong gradients, are negligible. The scheme produces results similar to those of nonlinear Eulerian advection schemes while reducing computation time by approximately a factor of 10.

54 ENVIRONMENTAL SCIENCES↗