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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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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Efficient Implementation for Unitary Coupled Cluster State Preparation for Near-Term Quantum Computers

Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^(8) determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.

Quantum Computing↗
NASA NTRSDate not supplied

Efficient Implementation for Unitary Coupled Cluster State Preparation for Near-Term Quantum Computers

Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^(8) determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.

Quantum Computing↗
NASA NTRS2019

Cloud Scattering Impact on Thermal Radiative Transfer and Global Longwave Radiation

The potential importance of longwave (LW) cloud scattering has been recognized but the actual estimate of this effect on thermal radiation varies greatly among different studies. General circulation models (GCMs) generally neglect or simplify the multiple scattering in the LW. In this study, we use a rigorous radiative transfer algorithm to explicitly consider LW multiple-scattering and apply the GCM to quantify the impact of cloud LW scattering on thermal radiation fluxes. Our study shows that the cloud scattering effect on downward thermal radiation at the surface is concentrated in the infrared atmospheric window spectrum (800–1250 cm9exp −1)). The scattering effect on the outgoing longwave radiation (OLR) is also present in the window region over low clouds but it is mainly in the far-infrared spectrum (300–600 cm(exp −1)) over high clouds. For clouds with small to moderate optical depth (τ < 10), the scattering effect on thermal fluxes shows large variation with the cloud τ and has a maximum at an optical depth of ∼3. For opaque clouds, the scattering effect approaches an asymptote and is smaller and less important. The 2-stream radiative transfer scheme could have an error over 10% with an RMS error around 3.5%–4.0% in the calculated LW flux. This algorithm error of the 2-stream approximation could readily exceed the no-scattering error in the LW, and thus it is worthless to include the time-consuming computation of multiple scattering in a 2-stream radiative transfer scheme. However, the calculation error rapidly decreases as stream number increases and the RMS error in LW flux using the 4-stream scheme is under 0.3%, an accuracy sufficient for most climate studies. We implement the 4-stream discrete-ordinate algorithm in the GISS GCM and run the GCM for 20 years with and without the LW scattering effect, respectively. When cloud LW scattering is included, we find that the global annual mean OLR is reduced by 2.7 W/m(exp 2), and the downward surface flux and the net atmospheric absorption are increased by 1.6 W/m2 and 1.8 W/m(exp 2), respectively. Using one year of ISCCP clouds and running the standalone radiative transfer offline, the global annual mean non-scattering errors in OLR, surface LW downward flux and net atmospheric absorption are 3.6 W/m(exp 2), −1.1 W/m(exp 2), and −2.5 W/m(exp 2), respectively. The global scattering impact of 2.7 W/m(exp 2) on the OLR is small when compared to the typical global OLR value of 240 W/m2, but it is significant when compared to cloud LW radiative forcing (30 W/m2) and net cloud forcing (−14 W/m(exp 2)). Overall, the effect of neglecting scattering on the thermal fluxes is comparable to the reported clear sky radiative effect of doubling CO2.

longwave cloud scattering↗
NASA NTRS2003

Step Bunch Evolution on Vicinal Faces of KDP

For in-situ studies of the formation and evolution of step patterns in solution growth, we have assembled an experimental setup based on Michelson interferometry with the growing crystal surface as one of the reflective surfaces. The device allows data collection over a relatively large area (approximately 4 sq. mm) in situ and in real time during growth. The depth resolution is improved over traditional interferometry using phase-shifted images combining by a suitable algorithm. We achieve a depth resolution of approximately 50 Angstroms. Lateral resolution, dependent on the degree of magnification, is around 0.3 to 5 microns. The crystal chosen as a model in this work is potassium dihydrogen phosphate (KDP), the optically non-linear material widely used in frequency doubling applications. Kinetics of KDP crystallization is well studied so that KDP can serve as a benchmark for our investigations. We present quantitative results on the onset, initial stages and development of instabilities in moving step trains on vicinal crystal surfaces at varying supersaturation, flow rate, and flow direction. The kinetics data suggest that at low supersaturations, step bunching is caused by impurity retardation of the steps, while at higher supersaturations, we link the non-linearity during growth to interdependence of the velocity and density of the steps evidenced in independent experiments. The behavior on the surface is very dynamic, small bunches both merge and split from larger bunches as they travel across the facet. We present evidence that despite these dynamics, under steady conditions there exists a limiting value to step bunch height. This height is reached at distances between 600 and 1000 microns from the step source. In our experiments, we observed the retention of this step bunch height limit up to the path of 1500 microns.

Booth, N. A.↗
NASA NTRS1975

Algorithms

The implementation of the algorithms used in the flight program to approximate elementary functions and mathematical procedures was checked. This was done by verifying that at least one, and in most cases, more than one function computed through the use of the algorithms was calculated properly. The following algorithms were checked: sine-cosine, arctangent, natural logarithm, square root, inverse square root, as well as the vector dot and cross products.

Source record↗
NASA NTRS2005

Solving Nonlinear Euler Equations with Arbitrary Accuracy

A computer program that efficiently solves the time-dependent, nonlinear Euler equations in two dimensions to an arbitrarily high order of accuracy has been developed. The program implements a modified form of a prior arbitrary- accuracy simulation algorithm that is a member of the class of algorithms known in the art as modified expansion solution approximation (MESA) schemes. Whereas millions of lines of code were needed to implement the prior MESA algorithm, it is possible to implement the present MESA algorithm by use of one or a few pages of Fortran code, the exact amount depending on the specific application. The ability to solve the Euler equations to arbitrarily high accuracy is especially beneficial in simulations of aeroacoustic effects in settings in which fully nonlinear behavior is expected - for example, at stagnation points of fan blades, where linearizing assumptions break down. At these locations, it is necessary to solve the full nonlinear Euler equations, and inasmuch as the acoustical energy is of the order of 4 to 5 orders of magnitude below that of the mean flow, it is necessary to achieve an overall fractional error of less than 10-6 in order to faithfully simulate entropy, vortical, and acoustical waves.

Dyson, Rodger W.↗
NASA NTRS1996

Numerical Algorithms Based on Biorthogonal Wavelets

Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.

Ponenti, Pj.↗
NASA NTRS1996

Numerical Algorithms Based on Biorthogonal Wavelets

Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.

Ponenti, Pj.↗
NASA NTRS1990

Skyline based terrain matching

Skyline-based terrain matching, a new method for locating the vantage point of stereo camera or laser range-finding measurements on a global map previously prepared by satellite or aerial mapping is described. The orientation of the vantage is assumed known, but its translational parameters are determined by the algorithm. Skylines, or occluding contours, can be extracted from the sensory measurements taken by an autonomous vehicle. They can also be modeled from the global map, given a vantage estimate from which to start. The two sets of skylines, represented in cylindrical coordinates about either the true or the estimated vantage, are employed as 'features' or reference objects common to both sources of information. The terrain matching problem is formulated in terms of finding a translation between the respective representations of the skylines, by approximating the two sets of skylines as identical features (curves) on the actual terrain. The search for this translation is based on selecting the longest of the minimum-distance vectors between corresponding curves from the two sets of skylines. In successive iterations of the algorithm, the approximation that the two sets of curves are identical becomes more accurate, and the vantage estimate continues to improve. The algorithm was implemented and evaluated on a simulated terrain. Illustrations and examples are included.

Page, Lance A.↗
NASA NTRS1994

Robust inverse kinematics using damped least squares with dynamic weighting

This paper presents a general method for calculating the inverse kinematics with singularity and joint limit robustness for both redundant and non-redundant serial-link manipulators. Damped least squares inverse of the Jacobian is used with dynamic weighting matrices in approximating the solution. This reduces specific joint differential vectors. The algorithm gives an exact solution away from the singularities and joint limits, and an approximate solution at or near the singularities and/or joint limits. The procedure is here implemented for a six d.o.f. teleoperator and a well behaved slave manipulator resulted under teleoperational control.

Schinstock, D. E.↗
NASA NTRS1986

Multigrid acceleration of the flux split Euler equations

Multigrid acceleration is applied to a flux-split algorithm for solving the Euler equations in two and three dimensions. The basic algorithm is an implicit spatially-split approximate factorization method. The stability of the scheme in comparison to other factorization is examined. Results are presented for two-dimensional airfoil flows and three-dimensional wing flows which demonstrate substantially improved convergence with the multigrid algorithm. An asymptotic spectral radius of 0.89 and 0.93 is attained for a 97 x 17 x 17 wing solution at subcritical and supercritical conditions, respectively.

Anderson, W. K.↗
NASA NTRS1993

Flux-difference split parabolized Navier-Stokes algorithm for non-equilibrium chemically reacting flows

A flux-difference split explicit finite-difference algorithm is presented for solving the parabolized form of the equations governing three-dimensional nonequilibrium chemically reacting flows. The algorithm is based on an explicit noniterative, upwind space-marching scheme developed by Korte, but differs in that the unsteady Riemann problem, rather than the steady Riemann problem, is solved. The algorithm allows either a second or an approximately third-order accurate upwind treatment of the convection terms by employing the unsteady approximate Riemann solver of Roe. The source terms of the species transport equations are treated in either an explicit or implicit manner, and the species diffusion terms are modeled with either a Fickian or a multicomponent model. A validation of the algorithm is performed by comparing computational results with the 2-D Mach 14, 15 degree compression-corner data of Holden. The three-dimensional capability of the algorithm is demonstrated by computing Mach 2.7 flow over a swept wedge scramjet fuel injector, and three-dimensional reacting flow capability is demonstrated by a computing a shock-jet interaction concept for mixing and combustion enhancement.

White, J. A.↗
NASA NTRS1975

A new structural analysis/synthesis capability - ACCESS

The creation of an efficient automated capability for minimum weight design of structures is reported. The ACCESS 1 computer program combines finite element analysis techniques and mathematical programming algorithms using an innovative collection of approximation concepts. Design variable linking, constraint deletion techniques and approximate analysis methods are used to generate a sequence of small explicit mathematical programming problems which retain the essential features of the design problem. Organization of the finite element analysis is carefully matched to the design optimization task. The efficiency of the ACCESS 1 program is demonstrated by giving results for several example problems.

Schmit, L. A.↗
NASA NTRS1979

A fast semi-implicit algorithm for problems of mixed type

Certain physical processes are modeled by partial differential equations which are parabolic over part of the domain and elliptic over the remainder. A family of semi-implicit algorithms which are well suited to initial-boundary value problems of this mixed type is discussed. One important feature of these algorithms is the use of an approximate inverse for the solution of the implicit linear system. A strong error analysis results in an estimate of the total error as a function of approximate inverse error e and time step h.

Frederickson, P. O.↗
NASA NTRS1982

Least-squares sequential parameter and state estimation for large space structures

This paper presents the formulation of simultaneous state and parameter estimation problems for flexible structures in terms of least-squares minimization problems. The approach combines an on-line order determination algorithm, with least-squares algorithms for finding estimates of modal approximation functions, modal amplitudes, and modal parameters. The approach combines previous results on separable nonlinear least squares estimation with a regression analysis formulation of the state estimation problem. The technique makes use of sequential Householder transformations. This allows for sequential accumulation of matrices required during the identification process. The technique is used to identify the modal prameters of a flexible beam.

Thau, F. E.↗
NASA NTRS1985

Developments in the simulation of separated flows using finite difference methods

Compressible viscous flow simulation using finite difference Navier-Stokes and viscous-inviscid interaction methods is described. Recent developments are reviewed that significantly improve the computational efficiency of approximately factored implicit Navier-Stokes algorithms. Compared to Navier-Stokes codes, modern viscous-inviscid interaction codes are more computationally efficient, but have restricted application and are more complicated to program. Therefore, less efficient but more general viscous-inviscid interaction methods are investigated that use forcing functions instead of boundary condition matching, and a simple, direct/inverse, three-dimensional, finite-difference, boundary layer code is presented.

Steger, J. L.↗
NASA NTRS1986

Performance tradeoffs in static and dynamic load balancing strategies

The problem of uniformly distributing the load of a parallel program over a multiprocessor system was considered. A program was analyzed whose structure permits the computation of the optimal static solution. Then four strategies for load balancing were described and their performance compared. The strategies are: (1) the optimal static assignment algorithm which is guaranteed to yield the best static solution, (2) the static binary dissection method which is very fast but sub-optimal, (3) the greedy algorithm, a static fully polynomial time approximation scheme, which estimates the optimal solution to arbitrary accuracy, and (4) the predictive dynamic load balancing heuristic which uses information on the precedence relationships within the program and outperforms any of the static methods. It is also shown that the overhead incurred by the dynamic heuristic is reduced considerably if it is started off with a static assignment provided by either of the other three strategies.

Iqbal, M. A.↗