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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
NASA NTRS1988

Towards developing robust algorithms for solving partial differential equations on MIMD machines

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Saltz, Joel H.↗
DOE OSTI2013

Hybrid reduced order modeling for assembly calculations

While the accuracy of assembly calculations has considerably improved due to the increase in computer power enabling more refined description of the phase space and use of more sophisticated numerical algorithms, the computational cost continues to increase which limits the full utilization of their effectiveness for routine engineering analysis. Reduced order modeling is a mathematical vehicle that scales down the dimensionality of large-scale numerical problems to enable their repeated executions on small computing environment, often available to end users. This is done by capturing the most dominant underlying relationships between the model's inputs and outputs. Previous works demonstrated the use of the reduced order modeling for a single physics code, such as a radiation transport calculation. This manuscript extends those works to coupled code systems as currently employed in assembly calculations. Numerical tests are conducted using realistic SCALE assembly models with resonance self-shielding, neutron transport, and nuclides transmutation/depletion models representing the components of the coupled code system. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2015

Exploiting data representation for fault tolerance

Incorrect computer hardware behavior may corrupt intermediate computations in numerical algorithms, possibly resulting in incorrect answers. Prior work models misbehaving hardware by randomly flipping bits in memory. We start by accepting this premise, and present an analytic model for the error introduced by a bit flip in an IEEE 754 floating-point number. We then relate this finding to the linear algebra concepts of normalization and matrix equilibration. In particular, we present a case study illustrating that normalizing both vector inputs of a dot product minimizes the probability of a single bit flip causing a large error in the dot product's result. Moreover, the absolute error is either less than one or very large, which allows detection of large errors. Then, we apply this to the GMRES iterative solver. We count all possible errors that can be introduced through faults in arithmetic in the computationally intensive orthogonalization phase of GMRES, and show that when the matrix is equilibrated, the absolute error is bounded above by one.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Hybrid reduced order modeling for assembly calculations

While the accuracy of assembly calculations has greatly improved due to the increase in computer power enabling more refined description of the phase space and use of more sophisticated numerical algorithms, the computational cost continues to increase which limits the full utilization of their effectiveness for routine engineering analysis. Reduced order modeling is a mathematical vehicle that scales down the dimensionality of large-scale numerical problems to enable their repeated executions on small computing environment, often available to end users. This is done by capturing the most dominant underlying relationships between the model's inputs and outputs. Previous works demonstrated the use of the reduced order modeling for a single physics code, such as a radiation transport calculation. This paper extends those works to coupled code systems as currently employed in assembly calculations. Finally, numerical tests are conducted using realistic SCALE assembly models with resonance self-shielding, neutron transport, and nuclides transmutation/depletion models representing the components of the coupled code system.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

New computing systems and their impact on computational mechanics

Recent advances in computer technology that are likely to impact computational mechanics are reviewed. The technical needs for computational mechanics technology are outlined. The major features of new and projected computing systems, including supersystems, parallel processing machines, special-purpose computing hardware, and small systems are described. Advances in programming environments, numerical algorithms, and computational strategies for new computing systems are reviewed, and a novel partitioning strategy is outlined for maximizing the degree of parallelism on multiprocessor computers with a shared memory.

Noor, Ahmed K.↗
DOE OSTI2018

Statistical Analysis of the First Passage Path Ensemble of Jump Processes

The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

New computing systems, future computing environment, and their implications on structural analysis and design

Recent advances in computer technology that are likely to impact structural analysis and design of flight vehicles are reviewed. A brief summary is given of the advances in microelectronics, networking technologies, and in the user-interface hardware and software. The major features of new and projected computing systems, including high performance computers, parallel processing machines, and small systems, are described. Advances in programming environments, numerical algorithms, and computational strategies for new computing systems are reviewed. The impact of the advances in computer technology on structural analysis and the design of flight vehicles is described. A scenario for future computing paradigms is presented, and the near-term needs in the computational structures area are outlined.

Noor, Ahmed K.↗
NASA NTRS1982

Computer program for solving laminar, transitional, or turbulent compressible boundary-layer equations for two-dimensional and axisymmetric flow

A numerical algorithm and computer program are presented for solving the laminar, transitional, or turbulent two dimensional or axisymmetric compressible boundary-layer equations for perfect-gas flows. The governing equations are solved by an iterative three-point implicit finite-difference procedure. The software, program VGBLP, is a modification of the approach presented in NASA TR R-368 and NASA TM X-2458, respectively. The major modifications are: (1) replacement of the fourth-order Runge-Kutta integration technique with a finite-difference procedure for numerically solving the equations required to initiate the parabolic marching procedure; (2) introduction of the Blottner variable-grid scheme; (3) implementation of an iteration scheme allowing the coupled system of equations to be converged to a specified accuracy level; and (4) inclusion of an iteration scheme for variable-entropy calculations. These modifications to the approach presented in NASA TR R-368 and NASA TM X-2458 yield a software package with high computational efficiency and flexibility. Turbulence-closure options include either two-layer eddy-viscosity or mixing-length models. Eddy conductivity is modeled as a function of eddy viscosity through a static turbulent Prandtl number formulation. Several options are provided for specifying the static turbulent Prandtl number. The transitional boundary layer is treated through a streamwise intermittency function which modifies the turbulence-closure model. This model is based on the probability distribution of turbulent spots and ranges from zero to unity for laminar and turbulent flow, respectively. Several test cases are presented as guides for potential users of the software.

Harris, J. E.↗
DOE OSTI2013

Application of the multigrid amplitude function method for time-dependent transport equation using MOC

An efficient numerical method for time-dependent transport equation, the mutigrid amplitude function (MAF) method, is proposed. The method of characteristics (MOC) is being widely used for reactor analysis thanks to the advances of numerical algorithms and computer hardware. However, efficient kinetic calculation method for MOC is still desirable since it requires significant computation time. Various efficient numerical methods for solving the space-dependent kinetic equation, e.g., the improved quasi-static (IQS) and the frequency transform methods, have been developed so far mainly for diffusion calculation. These calculation methods are known as effective numerical methods and they offer a way for faster computation. However, they have not been applied to the kinetic calculation method using MOC as the authors' knowledge. Thus, the MAF method is applied to the kinetic calculation using MOC aiming to reduce computation time. The MAF method is a unified numerical framework of conventional kinetic calculation methods, e.g., the IQS, the frequency transform, and the theta methods. Although the MAF method is originally developed for the space-dependent kinetic calculation based on the diffusion theory, it is extended to transport theory in the present study. The accuracy and computational time are evaluated though the TWIGL benchmark problem. The calculation results show the effectiveness of the MAF method. (authors)

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Stability of mixing layers

The research program for the first year of this project (see the original research proposal) consists of developing an explicit marching scheme for solving the parabolized stability equations (PSE). Performing mathematical analysis of the computational algorithm including numerical stability analysis and the determination of the proper boundary conditions needed at the boundary of the computation domain are implicit in the task. Before one can solve the parabolized stability equations for high-speed mixing layers, the mean flow must first be found. In the past, instability analysis of high-speed mixing layer has mostly been performed on mean flow profiles calculated by the boundary layer equations. In carrying out this project, it is believed that the boundary layer equations might not give an accurate enough nonparallel, nonlinear mean flow needed for parabolized stability analysis. A more accurate mean flow can, however, be found by solving the parabolized Navier-Stokes equations. The advantage of the parabolized Navier-Stokes equations is that its accuracy is consistent with the PSE method. Furthermore, the method of solution is similar. Hence, the major part of the effort of the work of this year has been devoted to the development of an explicit numerical marching scheme for the solution of the Parabolized Navier-Stokes equation as applied to the high-seed mixing layer problem.

Tam, Christopher↗
DOE OSTI2011

A CLASS OF RECONSTRUCTED DISCONTINUOUS GALERKIN METHODS IN COMPUTATIONAL FLUID DYNAMICS

A class of reconstructed discontinuous Galerkin (DG) methods is presented to solve compressible flow problems on arbitrary grids. The idea is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting reconstructed discontinuous Galerkin (RDG) methods is that they provide a unified formulation for both finite volume and DG methods, and contain both classical finite volume and standard DG methods as two special cases of the RDG methods, and thus allow for a direct efficiency comparison. Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via a so-called in-cell reconstruction process. The devised in-cell reconstruction is aimed to augment the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. These three reconstructed discontinuous Galerkin methods are used to compute a variety of compressible flow problems on arbitrary meshes to assess their accuracy. The numerical experiments demonstrate that all three reconstructed discontinuous Galerkin methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstructed DG method provides the best performance in terms of both accuracy, efficiency, and robustness.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1979

First principles numerical model of avalanche-induced arc discharges in electron-irradiated dielectrics

The model consists of four phases: single electron dynamics, single electron avalanche, negative streamer development, and tree formation. Numerical algorithms and computer code implementations are presented for the first three phases. An approach to developing a code description of fourth phase is discussed. Numerical results are presented for a crude material model of Teflon.

Beers, B. L.↗
DOE OSTI2019

On the Convergence of the Inexact Running Krasnosel'skii-Mann Method

This letter leverages a framework based on averaged operators to tackle the problem of tracking fixed points associated with maps that evolve over time. In particular, this letter considers the Krasnosel'skii-Mann (KM) method in a settings where: 1) the underlying map may change at each step of the algorithm, thus leading to a 'running' implementation of the KM method, and 2) an imperfect information of the map may be available. An imperfect knowledge of the maps can capture cases where processors feature a finite precision or quantization errors, or the case where (part of) the map is obtained from measurements. The analytical results are applicable to inexact running algorithms for solving optimization problems, whenever the algorithmic steps can be written in the form of (a composition of) averaged operators; examples are provided for inexact running gradient methods and the forward-backward splitting method. Convergence of the average fixed-point residual is investigated for the non-expansive case; linear convergence to a unique fixed-point trajectory is showen in the case of inexact running algorithms emerging from contractive operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Nonperturbative analysis of field theories quantized on the light cone (Final Scientific Report for ER41087)

The primary focus of the work was the development of methods for the nonperturbative solution of quantum chromodynamics (QCD) in a form that yields wave functions for the eigenstates, from which hadronic properties can be computed. The principal approach was to use a light-front Hamiltonian formulation. In light-front coordinates, t+z/c plays the role of time, with t the ordinary time, z a space direction, and c the speed of light. This leads to a relativistic formulation that retains useful characteristics of nonrelativistic treatments. A bound state of many constituents can be represented by wave functions that define probabilities for each possible arrangement of internal momenta. These functions satisfy integral equations that can be approximated numerically to yield a matrix representation. The matrix problem can be solved by iterative methods. The approximate wave functions can then be used to compute properties of the bound state. Methods have been developed for model theories and gauge theories, including quantum electrodynamics and theories that are supersymmetric. The work has required the development of new numerical algorithms and computer codes for singular integral equations and eigenvalue problems. A key aspect of the work is the construction of practical procedures for nonperturbative regularization and renormalization. Two methods of regularization have been studied. One is the addition of heavy Pauli--Villars (PV) particles to the Lagrangian, with their metrics and couplings tuned to provide the necessary cancellations in the regularization. The other method of regularization is the addition of supersymmetric partners, to extend a theory to a supersymmetric form. The supersymmetric theories were solved by the supersymmetric discrete light-cone quantization (SDLCQ) method. The most significant accomplishments of the project were the SDLCQ calculation of direct evidence for a Maldacena duality conjecture, construction of a practical light-front quantization for QED in an arbitrary covariant gauge, and invention of the light-front coupled-cluster method, designed to eliminate the need for Fock-space truncations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2015

Polarized Bidirectional Reflectance of Optically Thick Sparse Particulate Layers: an Efficient Numerically Exact Radiative-Transfer Solution

We describe a simple yet efficient numerical algorithm for computing polarized bidirectional reflectance of an optically thick (semi-infinite), macroscopically flat layer composed of statistically isotropic and mirror symmetric random particles. The spatial distribution of the particles is assumed to be sparse, random, and statistically uniform. The 44 Stokes reflection matrix is calculated by iterating the Ambartsumian's vector nonlinear integral equation. The result is a numerically exact solution of the vector radiative transfer equation and as such fully satisfies the energy conservation law and the fundamental reciprocity relation. Since this technique bypasses the computation of the internal radiation field, it is very fast and highly accurate. The FORTRAN implementation of the technique is publicly available on the World Wide Web at http://www.giss.nasa.gov/staff/ mmishchenko/brf. It can be combined with several existing computer programs providing the requisite single-scattering properties of spherical or morphologically complex particles and applied to a wide range of optical characterization problems. Benchmark results obtained with this program can be used for testing alternative solvers of the vector radiative transfer equation.

radiative transfer↗
DOE OSTI2016

On the asymptotic distribution of block-modified random matrices

We study random matrices acting on tensor product spaces which have been transformed by a linear block operation. Using operator-valued free probability theory, under some mild assumptions on the linear map acting on the blocks, we compute the asymptotic eigenvalue distribution of the modified matrices in terms of the initial asymptotic distribution. Moreover, using recent results on operator-valued subordination, we present an algorithm that computes, numerically but in full generality, the limiting eigenvalue distribution of the modified matrices. Our analytical results cover many cases of interest in quantum information theory: we unify some known results and we obtain new distributions and various generalizations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Hybrid Quantum-Classical Eigensolver without Variation or Parametric Gates

The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here, we present a process for obtaining the eigenenergy spectrum of electronic quantum systems. This is achieved by projecting the Hamiltonian of a quantum system onto a limited effective Hilbert space specified by a set of computational bases. From this projection, an effective Hamiltonian is obtained. Furthermore, a process for preparing short depth quantum circuits to measure the corresponding diagonal and off-diagonal terms of the effective Hamiltonian is given, whereby quantum entanglement and ancilla qubits are used. The effective Hamiltonian is then diagonalized on a classical computer using numerical algorithms to obtain the eigenvalues. The use case of this approach is demonstrated for ground state and excited states of BeH2 and LiH molecules, and the density of states, which agrees well with exact solutions. Additionally, hardware demonstration is presented using IBM quantum devices for H2 molecule.

Jouzdani, Pejman (ORCID:0000000256470381)↗