Search NASA⌕ Search

SEARCH · Search NASA

Results for “numerical algorithm computing”

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 1,315 records · Page 73
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Bayesian Model Selection for Reducing Bloat and Overfitting in Genetic Programming for Symbolic Regression

When performing symbolic regression using genetic programming, overfitting and bloat can negatively impact generalizability and interpretability of the resulting equations as well as increase computation times. A Bayesian fitness metric is introduced and its impact on bloat and overfitting during population evolution is studied and compared to common alternatives in the literature. The proposed approach was found to be more robust to noise and data sparsity in numerical experiments, guiding evolution to a level of complexity appropriate to the dataset. Further evolution of the population resulted not in overfitting or bloat, but rather in slight simplifications in model form. The ability to identify an equation of complexity appropriate to the scale of noise in the training data was also demonstrated. In general, the Bayesian model selection algorithm was shown to be an effective means of regularization which resulted in less bloat and overfitting when any amount of noise was present in the training data.

Uncertainty quantification↗
NASA NTRS2024

Assessing Effects of Climate and Technology Uncertainties in Large Natural Resource Allocation Problems

The productivity of the world's natural resources is critically dependent on a variety of highly uncertain factors, which obscure individual investors and governments that seek to make long-term, sometimes irreversible, investments in their exploration and utilization. These dynamic considerations are poorly represented in disaggregated resource models, as incorporating uncertainty into large-dimensional problems presents a challenging computational task. In this paper, we apply the SCEQ algorithm (Cai and Judd, 2023) to solve a large-scale dynamic stochastic global land resource use problem with stochastic crop yields due to adverse climate impacts and limits on further technological progress. For the same model parameters and bounded shocks, the range of land conversion is considerably smaller for the dynamic stochastic model than for deterministic scenario analysis.

numerical methods↗
NASA NTRS1972

The computation of optimal control programmes using a modified successive sweep method.

A second-order method for numerically solving control optimization problems has been developed. The method, referred to as the modified sweep method (MSM), differs from the successive sweep method (SSM) proposed by McReynolds and Bryson (1965) in that the conditions for local control optimality are used to determine the control as an explicit function of the state variables and time. The control is eliminated from the problem and the solution to the resulting two-point boundary value problem can be obtained by linear perturbation methods. The modified sweep method proposed here uncouples the perturbation equations for the state variables and the Lagrange multipliers by using a generalized matrix-Riccati transformation of variables. The resulting algorithm for the numerical iteration process is concerned with determining the initial values of a set of Lagrange multipliers rather than correcting a numerical control programme over the entire time interval of interest.

Colunga, D.↗
NASA NTRS1985

On numerical integration and computer implementation of viscoplastic models

Due to the stringent design requirement for aerospace or nuclear structural components, considerable research interests have been generated on the development of constitutive models for representing the inelastic behavior of metals at elevated temperatures. In particular, a class of unified theories (or viscoplastic constitutive models) have been proposed to simulate material responses such as cyclic plasticity, rate sensitivity, creep deformations, strain hardening or softening, etc. This approach differs from the conventional creep and plasticity theory in that both the creep and plastic deformations are treated as unified time-dependent quantities. Although most of viscoplastic models give better material behavior representation, the associated constitutive differential equations have stiff regimes which present numerical difficulties in time-dependent analysis. In this connection, appropriate solution algorithm must be developed for viscoplastic analysis via finite element method.

Chang, T. Y.↗
NASA NTRS2009

Auto-Generated Semantic Processing Services

Auto-Generated Semantic Processing (AGSP) Services is a suite of software tools for automated generation of other computer programs, denoted cross-platform semantic adapters, that support interoperability of computer-based communication systems that utilize a variety of both new and legacy communication software running in a variety of operating- system/computer-hardware combinations. AGSP has numerous potential uses in military, space-exploration, and other government applications as well as in commercial telecommunications. The cross-platform semantic adapters take advantage of common features of computer- based communication systems to enforce semantics, messaging protocols, and standards of processing of streams of binary data to ensure integrity of data and consistency of meaning among interoperating systems. The auto-generation aspect of AGSP Services reduces development time and effort by emphasizing specification and minimizing implementation: In effect, the design, building, and debugging of software for effecting conversions among complex communication protocols, custom device mappings, and unique data-manipulation algorithms is replaced with metadata specifications that map to an abstract platform-independent communications model. AGSP Services is modular and has been shown to be easily integrable into new and legacy NASA flight and ground communication systems.

Davis, Rodney↗
NASA NTRS2003

Numerical Modeling of Nanoelectronic Devices

Nanoelectronic Modeling 3-D (NEMO 3-D) is a computer program for numerical modeling of the electronic structure properties of a semiconductor device that is embodied in a crystal containing as many as 16 million atoms in an arbitrary configuration and that has overall dimensions of the order of tens of nanometers. The underlying mathematical model represents the quantummechanical behavior of the device resolved to the atomistic level of granularity. The system of electrons in the device is represented by a sparse Hamiltonian matrix that contains hundreds of millions of terms. NEMO 3-D solves the matrix equation on a Beowulf-class cluster computer, by use of a parallel-processing matrix vector multiplication algorithm coupled to a Lanczos and/or Rayleigh-Ritz algorithm that solves for eigenvalues. In a recent update of NEMO 3-D, a new strain treatment, parameterized for bulk material properties of GaAs and InAs, was developed for two tight-binding submodels. The utility of the NEMO 3-D was demonstrated in an atomistic analysis of the effects of disorder in alloys and, in particular, in bulk In(x)Ga(l-x)As and in In0.6Ga0.4As quantum dots.

Klimeck, Gerhard↗
NASA NTRS1990

Development of comprehensive numerical schemes for predicting evaporating gas-droplets flow processes of a liquid-fueled combustor

An existing Computational Fluid Dynamics code for simulating complex turbulent flows inside a liquid rocket combustion chamber was validated and further developed. The Advanced Rocket Injector/Combustor Code (ARICC) is simplified and validated against benchmark flow situations for laminar and turbulent flows. The numerical method used in ARICC Code is re-examined for incompressible flow calculations. For turbulent flows, both the subgrid and the two equation k-epsilon turbulence models are studied. Cases tested include idealized Burger's equation in complex geometries and boundaries, a laminar pipe flow, a high Reynolds number turbulent flow, and a confined coaxial jet with recirculations. The accuracy of the algorithm is examined by comparing the numerical results with the analytical solutions as well as experimented data with different grid sizes.

Chen, C. P.↗
NASA NTRS1992

Fluid flow and heat convection studies for actively cooled airframes

The work done during the progress report period from May-October 1992 is summarized. The effect of wall thermal boundary conditions on flows over a step or rib when repeated rib roughness is used for heating augmentation is examined. In numerical investigations of various such laminar and turbulent flows, the local heat transfer coefficients on a forward-facing step or on a rib were found to be very sensitive to the wall thermal boundary condition. For the computation of constant property laminar flow, the wall thermal boundary conditions were either a uniform heat flux or a uniform temperature. Results (Nusselt number and isotherms) of the studies are included. The second part of the work consisted of using PHOENICS to solve the conjugate heat transfer problem of flow over a rib in channel. Finally, the algebraic stress model in the TEAM (Turbulent Elliptic Algorithm-Manchester) code was tested for jet impingement flow, but there needs to be an addition of the energy equation to the code.

Mills, A. F.↗
NASA NTRS1997

3-D Deformable Grid Electomagnetic PIC for Parallel Computers

We have developed a three-dimensional non-orthogonal grid electromagnetic PIC code for parallel supercomputers. The numerical formulation is based on hexahedral cells which are logically connected cubic cells but distorted to body-fit complex geometries in physical space. An outstanding area of research is to improve the accuracy of the electromagnetic field solve on distorted meshes.

3D deformable non-orthogonal grid code PIC codes p↗
NASA NTRS1982

Gain optimization with nonlinear controls

An algorithm has been developed for the analysis and design of controls for nonlinear systems. The technical approach is to use statistical linearization to model the nonlinear dynamics of a system. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this report is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general however and numerical computation requires only that the specific nonlinearity be considered in the analysis.

Slater, G. L.↗
NASA NTRS1988

Algorithms and software for solving finite element equations on serial and parallel architectures

The primary objective was to compare the performance of state-of-the-art techniques for solving sparse systems with those that are currently available in the Computational Structural Mechanics (MSC) testbed. One of the first tasks was to become familiar with the structure of the testbed, and to install some or all of the SPARSPAK package in the testbed. A brief overview of the CSM Testbed software and its usage is presented. An overview of the sparse matrix research for the Testbed currently employed in the CSM Testbed is given. An interface which was designed and implemented as a research tool for installing and appraising new matrix processors in the CSM Testbed is described. The results of numerical experiments performed in solving a set of testbed demonstration problems using the processor SPK and other experimental processors are contained.

Chu, Eleanor↗
NASA NTRS1995

Newton-Krylov-Schwarz: An implicit solver for CFD

Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton's method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on aerodynamics applications emphasizing comparisons with a standard defect-correction approach, subdomain preconditioner consistency, subdomain preconditioner quality, and the effect of a coarse grid.

Cai, Xiao-Chuan↗
NASA NTRS2006

Ion Thruster Discharge Performance Per Magnetic Field Topography

DC-ION is a detailed computational model for predicting the plasma characteristics of rain-cusp ion thrusters. The advanced magnetic field meshing algorithm used by DC-ION allows precise treatment of the secondary electron flow. This capability allows self-consistent estimates of plasma potential that improves the overall consistency of the results of the discharge model described in Reference [refJPC05mod1]. Plasma potential estimates allow the model to predict the onset of plasma instabilities, and important shortcoming of the previous model for optimizing the design of discharge chambers. A magnetic field mesh simplifies the plasma flow calculations, for both the ions and the secondary electrons, and significantly reduces numerical diffusion that can occur with meshes not aligned with the magnetic field. Comparing the results of this model to experimental data shows that the behavior of the primary electrons, and the precise manner of their confinement, dictates the fundamental efficiency of ring-cusp. This correlation is evident in simulations of the conventionally sized NSTAR thruster (30 cm diameter) and the miniature MiXI thruster (3 cm diameter).

plasma processes↗
NASA NTRS1992

Numerical analysis of a thermal deicer

An algorithm has been developed to numerically model the concurrent phenomena of two-dimensional transient heat transfer, ice accretion and ice shedding which arise from the use of an electrothermal pad. The Alternating Direction Implicit method is used to simultaneously solve the heat transfer and accretion equations occurring in a multilayered body covered with ice. In order to model the phase change between ice and water, a technique was used which assumes a phase for each node. This allows the equations to be linearized such that a direct solution is possible. This technique requires an iterative procedure to find the correct phase at each node. The computer program developed to find this solution has been integrated with the NASA/Lewis flow/trajectory code LEWICE.

Wright, W. B.↗
NASA NTRS1994

An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations

A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a different formulation of the viscous terms are shown to be necessary. A hybrid Cartesian/body-fitted grid generation approach is demonstrated. In addition, a grid-generation procedure based on body-aligned cell cutting coupled with a viscous stensil-construction procedure based on quadratic programming is presented.

Coirier, William John↗
NASA NTRS1997

An Adaptive Flow Solver for Air-Borne Vehicles Undergoing Time-Dependent Motions/Deformations

This report describes a concurrent Euler flow solver for flows around complex 3-D bodies. The solver is based on a cell-centered finite volume methodology on 3-D unstructured tetrahedral grids. In this algorithm, spatial discretization for the inviscid convective term is accomplished using an upwind scheme. A localized reconstruction is done for flow variables which is second order accurate. Evolution in time is accomplished using an explicit three-stage Runge-Kutta method which has second order temporal accuracy. This is adapted for concurrent execution using another proven methodology based on concurrent graph abstraction. This solver operates on heterogeneous network architectures. These architectures may include a broad variety of UNIX workstations and PCs running Windows NT, symmetric multiprocessors and distributed-memory multi-computers. The unstructured grid is generated using commercial grid generation tools. The grid is automatically partitioned using a concurrent algorithm based on heat diffusion. This results in memory requirements that are inversely proportional to the number of processors. The solver uses automatic granularity control and resource management techniques both to balance load and communication requirements, and deal with differing memory constraints. These ideas are again based on heat diffusion. Results are subsequently combined for visualization and analysis using commercial CFD tools. Flow simulation results are demonstrated for a constant section wing at subsonic, transonic, and a supersonic case. These results are compared with experimental data and numerical results of other researchers. Performance results are under way for a variety of network topologies.

Singh, Jatinder↗
NASA NTRS1998

Polar Hydra Data Analysis

The science activities are: 1) Hydra is still operating successfully on orbit. 2) A large amount of analysis and discovery has occurred with the Hydra ground data processing this past year. 3) Full interdetector calibration has been implemented and documented. This intercalibration was necessitated by the incorrect installation of bias resistors in the pre-acceleration stage to the electron channeltrons. This had the effect of making the counting efficiency for electrons energy dependent as well as channeltron specific. The nature of the error had no impact on the ion detection efficiency since they have a different bias arrangement. This intercalibration is so effective, that the electron and ion moment densities are routinely produced with a level of agreement better than 20%. 4) The data processing routinely removes glint in the sensors and produces public energy time spectrograms on the web overnight. 6) Routine, but more intensive computer processing codes are operational that determine for electrons and ions, the density, the flow vector, the pressure tensor and the heat flux by numerical integration. These codes use the magnetic field to sustain the quality of their output. To gain access to this high quality magnetic field within our data stream we have monitored Russell's web page for zero levels and timing files (since his data acquisition is not telemetry synchronous) and have a local reconstruction of B for our use. We have also detected a routine anomaly in the magnetometer data stream that we have documented to Chris Russell and developed an editing algorithm to intercept these "hits" and remove them from the geophysical analysis.

Scudder, J. D.↗
NASA NTRS2003

Implicit Approaches for Moving Boundaries in a 3-D Cartesian Method

This work considers numerical simulation of three-dimensional flows with time-evolving boundaries. Such problems pose a variety of challenges for numerical schemes, and have received a substantial amount of attention in the recent literature. Since such simulations are unsteady, time-accurate solution of the governing equations is required. In special cases, the body motion can be treated by a uniform rigid motion of the computational domain. For the more general situation of relative-body motion, however, this simplification is unavailable and the simulations require a mechanism for ensuring that the mesh evolves with the moving boundaries. This involves a "remeshing" of the computational domain (either localized or global) at each physical timestep, and places a premium on both the speed and robustness of the remeshing algorithms. This work presents a method which includes unsteady flow simulation, rigid domain motion, and relative body motion using a time-evolving Cartesian grid system in three dimensions.

Murman, Scott M.↗