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At least 1,027 records · Page 57

All sources NASA NTRS DOE OSTI

DOE OSTI2017

HFEM3D

Software solves the three-dimensional Poisson equation div(k(grad(u)) = f, by the finite element method for the case when material properties, k, are distributed over hierarchy of edges, facets and tetrahedra in the finite element mesh. Method is described in Weiss, CJ, Finite element analysis for model parameters distributed on a hierarchy of geometric simplices, Geophysics, v82, E155-167, doi:10.1190/GEO2017-0058.1 (2017). A standard finite element method for solving Poisson’s equation is augmented by including in the 3D stiffness matrix additional 2D and 1D stiffness matrices representing the contributions from material properties associated with mesh faces and edges, respectively. The resulting linear system is solved iteratively using the conjugate gradient method with Jacobi preconditioning. To minimize computer storage for program execution, the linear solver computes matrix-vector contractions element-by-element over the mesh, without explicit storage of the global stiffness matrix. Program output vtk compliant for visualization and rendering by 3rd party software. Program uses dynamic memory allocation and as such there are no hard limits on problem size outside of those imposed by the operating system and configuration on which the software is run. Dimension, N, of the finite element solution vector is constrained by the the addressable space in 32-vs-64 bit operating systems. Total storage requirements for the problem. Total working space required for the program is approximately 13*N double precision words.

Weiss, Chester J↗

NASA NTRS2014

High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order

In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.

Mazaheri, Alireza R.↗

NASA NTRS1999

A Textbook for a First Course in Computational Fluid Dynamics

This paper describes and discusses the textbook, Fundamentals of Computational Fluid Dynamics by Lomax, Pulliam, and Zingg, which is intended for a graduate level first course in computational fluid dynamics. This textbook emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. Its underlying philosophy is that the theory of linear algebra and the attendant eigenanalysis of linear systems provides a mathematical framework to describe and unify most numerical methods in common use in the field of fluid dynamics. Two linear model equations, the linear convection and diffusion equations, are used to illustrate concepts throughout. Emphasis is on the semi-discrete approach, in which the governing partial differential equations (PDE's) are reduced to systems of ordinary differential equations (ODE's) through a discretization of the spatial derivatives. The ordinary differential equations are then reduced to ordinary difference equations (O(Delta)E's) using a time-marching method. This methodology, using the progression from PDE through ODE's to O(Delta)E's, together with the use of the eigensystems of tridiagonal matrices and the theory of O(Delta)E's, gives the book its distinctiveness and provides a sound basis for a deep understanding of fundamental concepts in computational fluid dynamics.

Zingg, D. W.↗

DOE OSTI2014

Fully coupled Pauli-Fierz systems at zero and positive temperature

These notes provide an introduction to the spectral analysis of Pauli-Fierz systems at zero and positive temperature. More precisely, we study finite dimensional quantum systems linearly coupled to a single reservoir, a massless scalar quantum field. We emphasize structure results valid at arbitrary system-reservoir coupling strength. The notes contain a mixture of known, refined, and new results and each section ends with a discussion of open problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

SLAC microresonator RF(SMuRF) electronics: A tone-tracking readout system for superconducting microwave resonator arrays

Here, we describe the newest generation of the SLAC Microresonator RF (SMuRF) electronics, a warm digital control and readout system for microwave-frequency resonator-based cryogenic detector and multiplexer systems, such as microwave superconducting quantum interference device multiplexers (μmux) or microwave kinetic inductance detectors. Ultra-sensitive measurements in particle physics and astronomy increasingly rely on large arrays of cryogenic sensors, which in turn necessitate highly multiplexed readout and accompanying room-temperature electronics. Microwave-frequency resonators are a popular tool for cryogenic multiplexing, with the potential to multiplex thousands of detector channels on one readout line. The SMuRF system provides the capability for reading out up to 3328 channels across a 4–8 GHz bandwidth. Notably, the SMuRF system is unique in its implementation of a closed-loop tone-tracking algorithm that minimizes RF power transmitted to the cold amplifier, substantially relaxing system linearity requirements and effective noise from intermodulation products. Here, we present a description of the hardware, firmware, and software systems of the SMuRF electronics, comparing achieved performance with science-driven design requirements. In particular, we focus on the case of large-channel-count, low-bandwidth applications, but the system has been easily reconfigured for high-bandwidth applications. The system described here has been successfully deployed in lab settings and field sites around the world and is baselined for use on upcoming large-scale observatories.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

Resilience and fault tolerance in high-performance computing for numerical weather and climate prediction

Progress in numerical weather and climate prediction accuracy greatly depends on the growth of the available computing power. As the number of cores in top computing facilities pushes into the millions, increased average frequency of hardware and software failures forces users to review their algorithms and systems in order to protect simulations from breakdown. This report surveys hardware, application-level and algorithm-level resilience approaches of particular relevance to time-critical numerical weather and climate prediction systems. A selection of applicable existing strategies is analysed, featuring interpolation-restart and compressed checkpointing for the numerical schemes, in-memory checkpointing, user-level failure mitigation and backup-based methods for the systems. Numerical examples showcase the performance of the techniques in addressing faults, with particular emphasis on iterative solvers for linear systems, a staple of atmospheric fluid flow solvers. The potential impact of these strategies is discussed in relation to current development of numerical weather prediction algorithms and systems towards the exascale. Trade-offs between performance, efficiency and effectiveness of resiliency strategies are analysed and some recommendations outlined for future developments.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2018

Topology optimization beyond linear elasticity

Complex, non-linear path-dependent and transient response of engineering structures can today be numerically modeled with good accuracy. For linear systems, this modeling has successfully been combined with computational design optimization for many years. The combination of non-linear modeling and numerical design optimization is far less established. In the present paper we discuss some recent steps taken to close the gap between the use of linear and non-linear modeling with numerical optimization. Examples with nonlinear elasticity, finite strain plasticity and dynamic modeling combined with topology optimization are discussed.

42 ENGINEERING↗

DOE OSTI2020

Report on local data recovery approaches suitable for weather and climate prediction (Deliverable 1.3) (V.1.0)

Numerical weather and climate prediction rates as one of the scientific applications whose accuracy improvements greatly depend on the growth of the available computing power. As the number of cores in top computing facilities pushes into the millions, increasing average frequency of hardware and software failures forces users to review their algorithms and systems in order to protect simulations from breakdown. This report surveys approaches for fault-tolerance in numerical algorithms and system resilience in parallel simulations from the perspective of numerical weather and climate prediction systems. A selection of existing strategies is analyzed, featuring interpolation-restart and compressed checkpointing for the numerics, in-memory checkpointing, user-level failure mitigation-based and backup-based methods for the systems. Numerical examples showcase the performance of the techniques in addressing faults, with particular emphasis on iterative solvers for linear systems, a staple of atmospheric fluid flow solvers. The potential impact of these strategies is discussed in relation to current development of numerical weather prediction algorithms and systems towards the exascale. Trade-offs between performance, efficiency and effectiveness of resiliency strategies are analyzed and some recommendations outlined for future developments.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1975

On the Navier-Stokes equations with constant total temperature

For various applications in fluid dynamics, it is assumed that the total temperature is constant. Therefore, the energy equation can be replaced by an algebraic relation. The resulting set of equations in the inviscid case is analyzed. It is shown that the system is strictly hyperbolic and well posed for the initial value problems. Boundary conditions are described such that the linearized system is well posed. The Hopscotch method is investigated and numerical results are presented.

Gottlieb, D.↗

NASA NTRS1979

Linearization of the boundary-layer equations of the minimum time-to-climb problem

Ardema (1974) has formally linearized the two-point boundary value problem arising from a general optimal control problem, and has reviewed the known stability properties of such a linear system. In the present paper, Ardema's results are applied to the minimum time-to-climb problem. The linearized zeroth-order boundary layer equations of the problem are derived and solved.

Ardema, M. D.↗

NASA NTRS1985

A methodology for designing robust multivariable nonlinear feedback control systems

This paper presents an outline of a methodology for the design of nonlinear dynamic compensators for nonlinear multivariable systems with guarantees of closed-loop stability, robustness, and performance. The method is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate nonlinear inverse operator for the plant. A major feature of the method is a unification of both the state-space and Input-Output formulations. The major results of the paper are: (1) Properties of the solution of certain optimal control problems; (2) New results on nonlinear estimation, including a new nonlinear observer with certain guaranteed properties; (3) The Loop Operator Recovery (LOR) procedure, and (4) Inclusion of command-following and disturbance rejection with a goal of a closed-loop stable, robust system.

Grunberg, D. B.↗

NASA NTRS1986

A methodology for designing robust multivariable nonlinear control systems

A new methodology is described for the design of nonlinear dynamic controllers for nonlinear multivariable systems providing guarantees of closed-loop stability, performance, and robustness. The methodology is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate inverse operator for the plant. A major feature of the methodology is a unification of both the state-space and input-output formulations. In addition, new results on stability theory, nonlinear state estimation, and optimal nonlinear regulator theory are presented, including the guaranteed global properties of the extended Kalman filter and optimal nonlinear regulators.

Grunberg, D. B.↗

NASA NTRS1992

Complex generalized minimal residual algorithm for iterative solution of quantum-mechanical reactive scattering equations

Complex dense matrices corresponding to the D + H2 and O + HD reactions were solved using a complex generalized minimal residual (GMRes) algorithm described by Saad and Schultz (1986) and Saad (1990). To provide a test case with a different structure, the H + H2 system was also considered. It is shown that the computational effort for solutions with the GMRes algorithm depends on the dimension of the linear system, the total energy of the scattering problem, and the accuracy criterion. In several cases with dimensions in the range 1110-5632, the GMRes algorithm outperformed the LAPACK direct solver, with speedups for the linear equation solution as large as a factor of 23.

Chatfield, David C.↗

DOE OSTI2023

Explicit model predictive control through robust optimization

A strategy that calculates an explicit state feedback policy to regulate constrained uncertain discrete‐time uncertain linear systems is presented. We consider uncertain processes, affected by box‐bounded multiplicative uncertainty as well as bounded additive uncertainty with linear state and inputs constraints. The proposed method includes (i) the calculation of a terminal set constraint and (ii) the robust reformulation of state constraints in the prediction horizon. These features allow the derivation of the desired policy by solving a single multiparametric quadratic programming problem that guarantees feasible operation in the presence of uncertainty. Additionally, we employ variable and constraint elimination approaches to enhance the computational performance of the strategy. We demonstrate the steps and benefits of these developments with a numerical example and a chemical engineering case study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Space-Dependent Wielandt Shifts for Multigroup Diffusion Eigenvalue Problems

We present a new concept—the space-dependent Wielandt shift (SDWS)—for accelerating the convergence of the power iteration (PI) scheme for multigroup diffusion k-eigenvalue problems. The SDWS improves on standard Wielandt shift (WS) techniques, which are empirical in nature and are typically effective only when the current estimate of the solution is reasonably converged. By accounting for the physics of the problem through SDWS, we are able to improve the acceleration for the initial iterates when the current estimate of the solution is not close to convergence. Numerical results from one-dimensional problems suggest that, compared to standard WS techniques, the new SDWS techniques can provide upward of a 46% reduction in the number of PIs required for convergence and a 40% reduction in the computational time required. This improvement is sensitive to several problem-dependent factors, such as the geometry and energy-dependence of the problem, the spatial discretization, and the initial guess. The reduction in computational time is also dependent on the linear solver in the PI scheme, as it is well known that WSs can significantly worsen the conditioning of the diffusion linear system. In this paper, we provide a detailed study of the impact of WSs on the performance of several iterative linear solvers. Results from our implementation of SDWS in the three-dimensional (3D) code MPACT show that SDWS can provide similar speedups for 3D multigroup diffusion eigenvalue problems. These results also show that moderate speedups can be obtained by applying SDWS to the coarse mesh finite difference (CMFD) solver in a CMFD-accelerated transport scheme. However, the benefit of doing this may be limited because all but the first few CMFD solves are relatively easy to converge, regardless of the WS used.

Nuclear Science & Technology↗

DOE OSTI2023

Estimation of Participation Factors Using the Synchrosqueezed Wavelet Transform

This paper proposes a data-driven approach for estimating participation factors for a power system using only simulation results on selected disturbances. The approach is purely response-based and does not need a linearized system model for eigen-analysis, which makes it applicable to systems whose detailed, complete mathematical models are not available. Considering the unavoidable nonlinearity as exhibited in the transient period of a system response, the Synchrosqueezed Wavelet Transform is applied to simulated responses for modal analysis to obtain participation factors. Based on simulations of Kundur's two-area system using both the electromagnetic transient model and phasor model, the participation factors estimated by the proposed approach are compared with two other signal processing tools, the Prony analysis and continuous wavelet transform, and are also benchmarked with conventional model-based participation factors.

participation factor↗

NASA NTRS1973

Vibrational sensitivity of a measuring instrument and methods of increasing the accuracy of its determinations

The properties and peculiarities of two groups of measuring systems reacting to vibrations are discussed. Specifically, results of the action of a three dimensional, cophasal, monoharmonic vibration on the linear system of a measuring instrument was analyzed. Data are also given on the connection between vibration sensitivity and vibration resistance for instruments, methods for estimating vibration resistance, and formulas for expressing test results of vibration resistance. Experimental data are also given for decreasing errors in nonlinear systems during vibrations.

Mironov, Y. S.↗

NASA NTRS1976

On the Navier-Stokes equations with constant total temperature

For various applications in fluid dynamics, one can assume that the total temperature is constant. Therefore, the energy equations can be replaced by an algebraic relation. The resulting set of equations in the inviscid case is analyzed in this paper. It is shown that the system is strictly hyperbolic and well posed for the initial-value problem. Boundary conditions are described such that the linearized system is well posed. The hopscotch method is investigated and numerical results are presented.

Gottlieb, D.↗