The development of Hansen's coordinates in the lunar problem by the method of iteration
Computer program using Hansen lunar theory for calculating perturbations of lunar satellite
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SEARCH · Engineering Papers
Results for “Iterative methods”
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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Energy-level iterative NMR method for sets of magnetically nonequivalent, chemical-shift equivalent nuclei.
Energy level NMR spectral analysis for spin systems with sets of magnetically nonequivalent chemical-shift equivalent nuclei
Bowers, M. T.↗
Solution of the symmetric eigenproblem AX=lambda BX by delayed division
Delayed division is an iterative method for solving the linear eigenvalue problem AX = lambda BX for a limited number of small eigenvalues and their corresponding eigenvectors. The distinctive feature of the method is the reduction of the problem to an approximate triangular form by systematically dropping quadratic terms in the eigenvalue lambda. The report describes the pivoting strategy in the reduction and the method for preserving symmetry in submatrices at each reduction step. Along with the approximate triangular reduction, the report extends some techniques used in the method of inverse subspace iteration. Examples are included for problems of varying complexity.
Thurston, G. A.↗
Iterative interference methods in the design of thin cascade blades
Explore the source record for details and available documents.
Diesendruck, Leo↗
Inventing and improving ribozyme function: rational design versus iterative selection methods
Two major strategies for generating novel biological catalysts exist. One relies on our knowledge of biopolymer structure and function to aid in the 'rational design' of new enzymes. The other, often called 'irrational design', aims to generate new catalysts, in the absence of detailed physicochemical knowledge, by using selection methods to search a library of molecules for functional variants. Both strategies have been applied, with considerable success, to the remodeling of existing ribozymes and the development of ribozymes with novel catalytic function. The two strategies are by no means mutually exclusive, and are best applied in a complementary fashion to obtain ribozymes with the desired catalytic properties.
Review, Tutorial↗
Prediction of BVI Noise for an Active Twist Rotor Using a Loosely Coupled CFD/CSD Method and Comparison to Experimental Data
Numerical predictions of the acoustic characteristics of an Active Twist Rotor (ATR), using two methods to compute the rotor blade aerodynamics and elastic blade motion are compared to experimental data from a wind tunnel test in the NASA Langley Transonic Dynamics Tunnel (TDT) in 2000. The first method, a loosely coupled iterative method, utilizes the Computational Fluid Dynamics (CFD) code OVERFLOW 2 and the Computational Structural Dynamics (CSD) code CAMRAD II. The second method utilizes the CAMRAD II free-wake model only. The harmonic active-twist control to the main rotor blade system is identified with three parameters - harmonic actuation frequency, actuation amplitude, and control phase angle. The resulting aerodynamics and blade motion data from the two methods are then used in the acoustics code PSU-WOPWOP to predict acoustic pressure on a spherical array of equally spaced observers surrounding the rotor. This spherical distribution of pressure is used to compute the sound power level representing baseline and actuated conditions. Sound power levels for three categories of noise are defined as - blade-vortex interaction sound power level (BVIPWL), low frequency sound power level (LFPWL), and overall sound power level, OAPWL. Comparisons with measured data indicate the CFD/CSD analysis successfully captures the trends in sound power levels and the effects of active-twist control at advance ratios of 0.14 and 0.17. The free-wake model predictions show inconsistent sound power levels relative to the trends in the experimental and CFD data. This paper presents the first ever comparison between CFD/CSD acoustic predictions for an active-twist rotor and experimental measurements.
Fogarty, David E.↗
Non-iterative partitioned methods based on monolithic formulations of the coupled problem.
Abstract not provided.
Bochev, Pavel B.↗
ON THE ACCURACY OF WEAK-LENSING CLUSTER MASS RECONSTRUCTIONS
We study the bias and scatter in mass measurements of galaxy clusters resulting from fitting a spherically symmetric Navarro, Frenk, and White model to the reduced tangential shear profile measured in weak-lensing (WL) observations. The reduced shear profiles are generated for {approx}10{sup 4} cluster-sized halos formed in a {Lambda}CDM cosmological N-body simulation of a 1 h{sup -1} Gpc box. In agreement with previous studies, we find that the scatter in the WL masses derived using this fitting method has irreducible contributions from the triaxial shapes of cluster-sized halos and uncorrelated large-scale matter projections along the line of sight. Additionally, we find that correlated large-scale structure within several virial radii of clusters contributes a smaller, but nevertheless significant, amount to the scatter. The intrinsic scatter due to these physical sources is {approx}20% for massive clusters and can be as high as {approx}30% for group-sized systems. For current, ground-based observations, however, the total scatter should be dominated by shape noise from the background galaxies used to measure the shear. Importantly, we find that WL mass measurements can have a small, {approx}5%-10%, but non-negligible amount of bias. Given that WL measurements of cluster masses are a powerful way to calibrate cluster mass-observable relations for precision cosmological constraints, we strongly emphasize that a robust calibration of the bias requires detailed simulations that include more observational effects than we consider here. Such a calibration exercise needs to be carried out for each specific WL mass estimation method, as the details of the method determine in part the expected scatter and bias. We present an iterative method for estimating mass M{sub 500c} that can eliminate the bias for analyses of ground-based data.
79 ASTRONOMY AND ASTROPHYSICS↗
An Efficient High-Order Solver for Diffusion Equations with Strong Anisotropy on Non-Anisotropy-Aligned Meshes
This paper concerns numerical solution of the diffusion equation with strong anisotropy on meshes not aligned with the anisotropic vector field. In order to resolve the numerical pollution for simulations on a non-anisotropy-aligned mesh and reduce the associated high computational cost we propose an effective preconditioner, extending our previous work. Similar to the anisotropy-aligned mesh case, we apply the auxiliary space preconditioning framework to design a preconditioner where a continuous finite element space is used as the auxiliary space for the discontinuous finite element space. The key component is an effective line smoother that can mitigate the high-frequency errors perpendicular to the magnetic field. We design a graph-based approach to find such a line smoother that is approximately perpendicular to the vector fields when the mesh does not align with the anisotropy. Finally, numerical experiments for several benchmark problems are presented, demonstrating the effectiveness and robustness of the proposed preconditioner when applied to Krylov iterative methods.
97 MATHEMATICS AND COMPUTING↗
TH-E-17A-02: High-Pitch and Sparse-View Helical 4D CT Via Iterative Image Reconstruction Method Based On Tensor Framelet
Purpose: 4D CT is routinely performed during radiation therapy treatment planning of thoracic and abdominal cancers. Compared with the cine mode, the helical mode is advantageous in temporal resolution. However, a low pitch (∼0.1) for 4D CT imaging is often required instead of the standard pitch (∼1) for static imaging, since standard image reconstruction based on analytic method requires the low-pitch scanning in order to satisfy the data sufficient condition when reconstructing each temporal frame individually. In comparison, the flexible iterative method enables the reconstruction of all temporal frames simultaneously, so that the image similarity among frames can be utilized to possibly perform high-pitch and sparse-view helical 4D CT imaging. The purpose of this work is to investigate such an exciting possibility for faster imaging with lower dose. Methods: A key for highpitch and sparse-view helical 4D CT imaging is the simultaneous reconstruction of all temporal frames using the prior that temporal frames are continuous along the temporal direction. In this work, such a prior is regularized through the sparsity transform based on spatiotemporal tensor framelet (TF) as a multilevel and high-order extension of total variation transform. Moreover, GPU-based fast parallel computing of X-ray transform and its adjoint together with split Bregman method is utilized for solving the 4D image reconstruction problem efficiently and accurately. Results: The simulation studies based on 4D NCAT phantoms were performed with various pitches (i.e., 0.1, 0.2, 0.5, and 1) and sparse views (i.e., 400 views per rotation instead of standard >2000 views per rotation), using 3D iterative individual reconstruction method based on 3D TF and 4D iterative simultaneous reconstruction method based on 4D TF respectively. Conclusion: The proposed TF-based simultaneous 4D image reconstruction method enables high-pitch and sparse-view helical 4D CT with lower dose and faster speed.
60 APPLIED LIFE SCIENCES↗
Generalized Jacobi method for linear bounded operators system
In this paper, we construct a generalization of the Jacobi iterative method adapted to a system of linear bounded operators. This new method is used with product integration method to solve a linear Fredholm integral equation of the second kind with a weakly singular kernel. The convergence analysis is proved. The numerical tests developed show its effectiveness.
97 MATHEMATICS AND COMPUTING↗
Two-Level Transport Methods with Independent Discretization
In this proposal, we introduce two-level nonlinear iteration methods for the transport equation in 1D slab geometry approximated by means of the linear discontinuous finite element method (LDFEM). We develop transport schemes based on the quasidiffusion (QD) method in which the low-order QD (LOQD) equations are discretized by the linear continuous finite element method (LCFEM). This requires a mapping of the LCFEM low-order solution to the LDFEM high-order solution to define the scattering term. Several mappings are proposed and analyzed. Another suggested transport discretization scheme is based on the step characteristics for the transport equation and LCFEM for the LOQD equations. We also develop new nonlinear synthetic acceleration (NSA) methods based on the LCFEM discretization of the QD equation. To gain iterative stability, the NSA algorithms are combined with the nonlinear Krylov acceleration method. We present numerical results that demonstrate performance and basic properties of the proposed discretization schemes and iterative solution methods.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Preconditioned Mixed Spectral Element Methods for Elasticity and Stokes Problems
Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techniques for Stokes problems. The main results of this paper show that the convergence rate of the resulting algorithms is independent of the penalty parameter, the number of spectral elements Nu and mildly dependent on the spectral degree eta via the inf-sup constant. The preconditioners proposed for the whole indefinite system are block-diagonal and block-triangular. Numerical experiments presented in the final section show that these algorithms are a practical and efficient strategy for the iterative solution of the indefinite problems arising from mixed spectral element discretizations of elliptic systems.
Pavarino, Luca F.↗
GLOBAL OPTIMIZATION METHODS FOR GRAVITATIONAL LENS SYSTEMS WITH REGULARIZED SOURCES
Several approaches exist to model gravitational lens systems. In this study, we apply global optimization methods to find the optimal set of lens parameters using a genetic algorithm. We treat the full optimization procedure as a two-step process: an analytical description of the source plane intensity distribution is used to find an initial approximation to the optimal lens parameters; the second stage of the optimization uses a pixelated source plane with the semilinear method to determine an optimal source. Regularization is handled by means of an iterative method and the generalized cross validation (GCV) and unbiased predictive risk estimator (UPRE) functions that are commonly used in standard image deconvolution problems. This approach simultaneously estimates the optimal regularization parameter and the number of degrees of freedom in the source. Using the GCV and UPRE functions, we are able to justify an estimation of the number of source degrees of freedom found in previous work. We test our approach by applying our code to a subset of the lens systems included in the SLACS survey.
79 ASTRONOMY AND ASTROPHYSICS↗
Flux stabilization in neutron problems with fixed sources
Although critical core calculations are the most common in design and safety analysis, fixed source calculations are needed for specific applications, e.g. to compute ex-core detector response functions, to develop new methodologies for dilution and reload error accidents and more in general for all situations involving sub-critical shut-down states. It is well known that the source problem becomes difficult to be solved with core configuration close to criticality, i.e. with the multiplication factor approaching unity, for the occurrence of numerical ill-conditioning and very high number of iterations, possibly leading to failure in the flux convergence. In this work, the Wielandt Eigen-shift technique used in iterative methods of critical problems is developed for source problems too, in order to stabilize the solution. The mathematical basis and the proof of the convergence are discussed. Compared to the existing methods, this technique allows also more control to avoid singular behavior at inner iterations. Numerical tests with a 1D analytical benchmark are reported to prove the robustness of the technique. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Approximating solution of split equality and equilibrium problems by viscosity approximation algorithms
In this paper, we employ viscosity approximation methods to solve split equality and generalized mixed equilibrium problems in Hilbert spaces. The iterative method considered herein does not require the prior estimations of spectral radii. Applications of obtained results have also been discussed. Finally, some numerical computations are presented.
97 MATHEMATICS AND COMPUTING↗
Accident analysis of heavy water cooled thorium breeder reactor
Thorium has lately attracted considerable attention because it is accumulating as a by-product of large scale rare earth mining. The objective of research is to analyze transient behavior of a heavy water cooled thorium breeder that is designed by Tokai University and Tokyo Institute of Technology. That is oxide fueled, PWR type reactor with heavy water as primary coolant. An example of the optimized core has relatively small moderator to fuel volume ratio (MFR) of 0.6 and the characteristics of the core are burn-up of 67 GWd/t, breeding ratio of 1.08, burn-up reactivity loss during cycles of < 0.2% dk/k, and negative coolant reactivity coefficient. One of the nuclear reactor accidents types examined here is Unprotected Transient over Power (UTOP) due to withdrawing of the control rod that result in the positive reactivity insertion so that the reactor power will increase rapidly. Another accident type is Unprotected Loss of Flow (ULOF) that caused by failure of coolant pumps. To analyze the reactor accidents, neutron distribution calculation in the nuclear reactor is the most important factor. The best expression for the neutron distribution is the Boltzmann transport equation. However, solving this equation is very difficult so that the space-time diffusion equation is commonly used. Usually, space-time diffusion equation is solved by employing a point kinetics approach. However, this approach is less accurate for a spatially heterogeneous nuclear reactor and the nuclear reactor with quite large reactivity input. Direct method is therefore used to solve space-time diffusion equation which consider spatial factor in detail during nuclear reactor accident simulation. Set of equations that obtained from full implicit finite-difference method is solved by using iterative methods. The indication of UTOP accident is decreasing macroscopic absorption cross-section that results large external reactivity, and ULOF accident is indicated by decreasing coolant flow. The power reactor has a peak value before reactor has new balance condition. The analysis showed that temperatures of fuel and claddings during accident are still below limitations which are in secure condition.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
MPACT Performance Improvements in VERA-CS
The report summarizes the initial profile of MPACT representative of the version that was distributed with VERA 3.4. It then describes several activities recently performed to increase the overall performance of the code. For the various improvements described in this report, several have been well known to the development team and reactor physics methods community for some time; while others proved novel in their combination of other existing ideas. Still, other improvements were the result of unanticipated breakthroughs in numerical methods research. These performance improvement activities focused on the following components of MPACT. Method of Characteristics Transport Kernel Iterative Methods for Coarse Mesh Finite Difference Linear System Macroscopic Cross Section and Effective Fission Spectrum Calculation Resonance self-shielding (Subgroup) calculation A summary of the overall improvement from this work as tested on a few representative problems is provided in the table below. The incremental improvements for various changes are shown in the figure below.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗