Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “eigenvalue problems”

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 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Recent Updates in ETOE-2 and MC 2 -3

The MC 2 -3 code is a multigroup cross section generation code for fast reactor applications, developed by Argonne National Laboratory (ANL) under the DOE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. In this work, first, the cross section libraries for ENDF/B-VII.1 and ENDF/B-VIII.0 data were generated using the updated ETOE-2 code. Preliminary verification and validation tests of the ENDF/B-VII.1 MC 2 -3 library were performed with the selected fast reactor benchmark problems. Processing and verifying the libraries suggested that significant efforts would be required for thoroughly verifying the ENDF/B-VII.1 MC 2 -3 library and successfully processing the ENDF/B-VIII.0 MC 2 -3 library. Secondly, the cross section generation capability of MC 2 -3 was updated with the intermediate group lattice calculation and the equivalent Dancoff-factor cell (EDC) method to significantly improve the performance of a twodimensional assembly calculation using the method of characteristics (MOC). This effort was made useful in implementing and verifying the EDC method in the Griffin cross section API. Finally, we analyzed a SFR problem, for which unusually large deviations in core eigenvalues from Monte Carlo solutions were reported, by generating multigroup cross sections with MC 2 -3, performing core calculations with DIF3D-VARIANT, and analyzing cross section and eigenvalue results against Monte Carlo solutions. The analysis confirmed that the MC 2 -3/DIF3D solutions were in good agreement with Monte Carlo solutions, providing the correct process of accurately generating broad-group cross sections with MC 2 -3

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Asymptotic theory of a slender rotating beam with end masses.

The method of matched asymptotic expansions is employed to solve the singular perturbation problem of the vibrations of a rotating beam of small flexural rigidity with concentrated end masses. The problem is complicated by the appearance of the eigenvalue in the boundary conditions. Eigenfunctions and eigenvalues are developed as power series in the perturbation parameter beta to the 1/2 power, and results are given for mode shapes and eigenvalues through terms of the order of beta.

Whitman, A. M.↗
NASA NTRS1979

A new spectral synthesis procedure for multivariable regulators

A method for selecting a multivariable state feedback controller that simultaneously achieves an a priori specification on closed loop eigenvalues and good mode mixing is presented. The problem is solved by projecting a desired modal matrix onto a constraint set containing the null space of the closed-loop state matrix, while assuring that the projection is in the null space. The feedback matrix follows immediately in the formulation. An example involving a helicopter hover controller is presented.

Maynard, R. A.↗
NASA NTRS1986

Implementation of the Lanczos method for structural vibration analysis on a parallel computer

The use of the Lanczos method in a parallel environment is investigated by implementing the algorithm for structural vibration problems on a parallel computer. It is shown that introducing shifts, assigning each processor a different region in the eigenvalue spectrum, and implementing the Lanczos method in parallel is an effective strategy for speeding up calculations. Test problem results include examples of the 'Lanczos phenomenon' where roundoff error in the vector orthogonalization can result in spurious eigenvalues which must be identified and discarded. The calculation strategy described here permits straightforward determination of these spurious eigenvalues. It is demonstrated that significant speedups in calculation time can be realized over traditional sequential methods.

Bostic, S. W.↗
NASA NTRS1990

Fourier analysis of finite element preconditioned collocation schemes

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

Deville, Michel O.↗
DOE OSTI2017

Evaluation of Rapid for a UNF cask benchmark problem

To ensure criticality safety and maintain a high level of security of Used Nuclear Fuel (UNF), it is necessary to perform detailed Particle Transport simulations. The commonly used technique is the 3-D, continuous energy Monte Carlo method that is time-consuming and, for eigenvalue calculations, may have difficulties with the source convergence. Wenner and Haghighat and Dufek demonstrated that in criticality problems with high dominance ratio and/or under-sampling possibilities, the fission matrix (FM) methodology should be used in order to be able to obtain unbiased solution. The RAPID (Real-time Analysis for Particle transport and In-situ Detection) code system is based on the Multi-stage Response-function Transport (MRT) methodology, and uses the FM formulation to determine eigenvalue, subcritical multiplication and fission density distribution of nuclear systems. This paper uses a benchmark problem similar to the GBC-32 Cask to evaluate the accuracy and performance of RAPID against the results of a reference MCNP solution. We performed a detailed sensitivity analysis on a single-assembly model in order to determine the MCNP eigenvalue parameters necessary to obtain a reliable reference solution. These results provided a guide for the selection of an appropriate set of parameters for the eigenvalue calculation for the whole cask. The paper is organized as follows: initially, the RAPID code system is briefly discussed; then, the benchmark problem is introduced. The methodology used to analyze results is proposed and some of the results of different cases are analyzed to identify the best set of eigenvalue parameters for a reference MCNP calculation. The selected case is then compared with the RAPID calculation for both a single assembly and a full cask model. In the end some conclusions and future work perspectives are drawn.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

MPACT Verification With Magnox Reactor Neutronics Progression Problems

MPACT is a state-of-the-art core simulator designed to perform high-fidelity analysis using whole-core, three-dimensional, pin-resolved neutron transport calculations on modern parallel computing hardware. MPACT was originally developed to model light water reactors, and its capabilities are being extended to simulate gas-cooled, graphite-moderated cores such as Magnox reactors. To verify MPACT’s performance in this new application, the code is being formally benchmarked using representative problems. Progression problems are a series of example models that increase in complexity designed to test a code’s performance. The progression problems include both beginning-of-cycle and depletion calculations. Reference solutions for each progression problem have been generated using Serpent 2, a continuous-energy Monte Carlo reactor physics burnup calculation code.Using the neutron multiplication eigenvalue ke as a metric, MPACT’s performance is assessed on each of the progression problems. Initial results showed that MPACT’s multi-group cross section libraries, originally developed for pressurized water reactor problems, were not sufficient to accurately solve Magnox problems. MPACT’s improved performance on the progression problems is demonstrated using this new optimized cross section library.

Luciano, Nicholas↗
DOE OSTI2018

A new relaxed splitting preconditioner for the generalized saddle point problems from the incompressible Navier–Stokes equations

Based on the modified relaxed splitting (MRS) preconditioner proposed by Fan and Zhu (Appl Math Lett 55:18–26, 2016), a new relaxed splitting preconditioner is proposed for the generalized saddle point problems arising from the incompressible Navier–Stokes equations. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are analyzed. Numerical results show that the proposed preconditioner is superior to the MRS preconditioner when they are used as preconditioners to accelerate the convergence rate of the Krylov subspace methods, such as GMRES.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

The parameterized preconditioner for the generalized saddle point problems from the incompressible Navier–Stokes equations

A parameterized preconditioner is proposed for the generalized saddle point problems arising from the incompressible Navier–Stokes equations. The eigenvalues and eigenvectors of the preconditioned matrix are analyzed. Numerical results show that the proposed preconditioner is efficient to accelerate the convergence rate of Krylov subspace methods, such as GMRES method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Convective mixing in vertically-layered porous media: The linear regime and the onset of convection

In this paper, we study the effect of permeability heterogeneity on the stability of gravitationally unstable, transient, diffusive boundary layers in porous media. Permeability is taken to vary periodically in the horizontal plane normal to the direction of gravity. In contrast to the situation for vertical permeability variation, the horizontal perturbation structures are multimodal. We therefore use a two-dimensional quasi-steady eigenvalue analysis as well as a complementary initial value problem to investigate the stability behavior in the linear regime, until the onset of convection. We find that thick permeability layers enhance instability compared with thin layers when heterogeneity is increased. On the contrary, for thin layers the instability is weakened progressively with increasing heterogeneity to the extent that the corresponding homogeneous case is more unstable. For high levels of heterogeneity, we find that a small change in the permeability field results in large variations in the onset time of convection, similar to the instability event in the linear regime. However, this trend does not persist unconditionally because of the reorientation of vorticity pairs due to the interaction of evolving perturbation structures with heterogeneity. Consequently, an earlier onset of instability does not necessarily imply an earlier onset of convection. A resonant amplification of instability is observed within the linear regime when the dominant perturbation mode is equal to half the wavenumber of permeability variation. On the other hand, a substantial damping occurs when the perturbation mode is equal to the harmonic and sub-harmonic components of the permeability wavenumber. Finally, the phenomenon of such harmonic interactions influences both the onset of instability as well as the onset of convection.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Fast calculation of the tokamak vertical instability

There has been recent interest in fast calculations of the tokamak axisymmetric vertical instability for real time feedback control purposes. It is shown that the maximum eigenvalue for the basic rigid version of this stability problem can be obtained by finding the positive root to a simple scalar function. This function can be generalized to include plasma mass and has complexity linear in the number of conductive elements. The formulation is based on standard matrix decompositions of the fixed-geometry part of the eigenproblem. The calculation bottleneck is the summary of mutual inductances from the reconstructed equilibrium current density. The with-mass spectrum can be made fully real-valued by the addition of a critical amount of damping with negligible effect on the vertical growth rate. Furthermore, the calculation has been implemented in the plasma control system at the DIII-D tokamak and used in experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1983

A NASTRAN DMAP procedure for calculation of base excitation modal participation factors

This paper presents a technique for calculating the modal participation factors for base excitation problems using a DMAP alter to the NASTRAN real eigenvalue analysis Rigid Format. The DMAP program automates the generation of the seismic mass to add to the degrees of freedom representing the shaker input directions and calculates the modal participation factors. These are shown in the paper to be a good measure of the maximum acceleration expected at any point on the structure when the subsequent frequency response analysis is run.

Case, W. R.↗
NASA NTRS1994

Nonlinear stability of Halley comethosheath with transverse plasma motion

Weakly nonlinear Magneto Hydrodynamic (MHD) stability of the Halley cometosheath determined by the balance between the outward ion-neutral drag force and the inward Lorentz force is investigated including the transverse plasma motion as observed in the flanks with the help of the method of multiple scales. The eigenvalues and the eigenfunctions are obtained for the linear problem and the time evolution of the amplitude is obtained using the solvability condition for the solution of the second order problem. The diamagnetic cavity boundary and the adjacent layer of about 100 km thickness is found unstable for the travelling waves of certain wave numbers. Halley ionopause has been observed to have strong ripples with a wavelength of several hundred kilometers. It is found that nonlinear effects have stabilizing effect.

Srivastava, Krishna M.↗
DOE OSTI2020

(U) Radiation Transport Sensitivity Capabilities Applicable to INRAD

Intrinsic radiation (INRAD) calculations involve calculating the neutron and gamma-ray source rate densities from given compositions and densities of materials and the subsequent transport of the neutrons and gamma rays to detectors that may be stood off or internal. Related problems deal with measures of subcritical multiplication, such as the k eff eigenvalue. Realistic estimates of the uncertainties in calculated INRAD results are desired. One approach to uncertainty quantification begins with sensitivity analysis. This report describes the present capabilities that XCP-7 can apply to compute sensitivities in INRAD problems and areas where work is needed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Polynomial Preconditioned Arnoldi with Stability Control

Polynomial preconditioning can improve the convergence of the Arnoldi method for computing eigenvalues. Such preconditioning significantly reduces the cost of orthogonalization; for difficult problems, it can also reduce the number of matrix-vector products. Parallel computations can particularly benefit from the reduction of communication-intensive operations. Additoinally, the GMRES algorithm provides a simple and effective way of generating the preconditioning polynomial. For some problems high degree polynomials are especially effective, but they can lead to stability problems that must be mitigated. A two-level “double polynomial preconditioning” strategy provides an effective way to generate high-degree preconditioners.

97 MATHEMATICS AND COMPUTING↗