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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 NTRS2003

Eigensolver for a Sparse, Large Hermitian Matrix

A parallel-processing computer program finds a few eigenvalues in a sparse Hermitian matrix that contains as many as 100 million diagonal elements. This program finds the eigenvalues faster, using less memory, than do other, comparable eigensolver programs. This program implements a Lanczos algorithm in the American National Standards Institute/ International Organization for Standardization (ANSI/ISO) C computing language, using the Message Passing Interface (MPI) standard to complement an eigensolver in PARPACK. [PARPACK (Parallel Arnoldi Package) is an extension, to parallel-processing computer architectures, of ARPACK (Arnoldi Package), which is a collection of Fortran 77 subroutines that solve large-scale eigenvalue problems.] The eigensolver runs on Beowulf clusters of computers at the Jet Propulsion Laboratory (JPL).

Tisdale, E. Robert↗
NASA NTRSDate not supplied

A Look at the Truths and Misconceptions of the Variational Quantum Eigensolver and the Implications of Overparameterization

In this work, we investigate loss landscapes of the variational quantum eigensolver (VQE) by quantifying the number of local minima through empirical analyses. We focus on minimal models in chemistry and physics so that we can do a complete analysis using more computationally expensive tools. We employ Hessian eigenvalue calculations and the nudged elastic band algorithm to characterize these landscapes. Our results expand upon the existing literature by highlighting the optimization challenges faced by VQE. We find that, as the number of parameters in our ansatz increases, the number of basins increases while the corresponding loss function values converge toward the global minimum value. This observation implies that overparameterization may lead to an ``effective convexity'' in VQE loss landscapes, a phenomenon supported by theoretical and numerical work in classical machine learning.

quantum computing↗
NASA NTRS1990

A vectorized Lanczos eigensolver for high-performance computers

The computational strategies used to implement a Lanczos-based-method eigensolver on the latest generation of supercomputers are described. Several examples of structural vibration and buckling problems are presented that show the effects of using optimization techniques to increase the vectorization of the computational steps. The data storage and access schemes and the tools and strategies that best exploit the computer resources are presented. The method is implemented on the Convex C220, the Cray 2, and the Cray Y-MP computers. Results show that very good computation rates are achieved for the most computationally intensive steps of the Lanczos algorithm and that the Lanczos algorithm is many times faster than other methods extensively used in the past.

Bostic, Susan W.↗
NASA NTRS1994

Stiffness-generated rigid-body mode shapes for Lanczos eigensolution with SUPORT DOF by way of a MSC/NASTRAN DMAP alter

When using all MSC/NASTRAN eigensolution methods except Lanczos, the analyst can replace the coupled system rigid-body modes calculated within DMAP module READ with mass orthogonalized and normalized rigid-body modes generated from the system stiffness. This option is invoked by defining MSC/NASTRAN r-set degrees of freedom via the SUPORT bulk data card. The newly calculated modes are required if the rigid-body modes calculated by the eigensolver are not 'clean' due to numerical roundoffs in the solution. When performing transient structural dynamic load analysis, the numerical roundoffs can result in inaccurate rigid-body accelerations which affect steady-state responses. Unfortunately, when using the Lanczos method and defining r-set degrees of freedom, the rigid-body modes calculated within DMAP module REIGL are retained. To overcome this limitation and to allow MSC/NASTRAN to handle SUPORT degrees of freedom identically for all eigensolvers, a DMAP Alter has been written which replaces Lanczos-calculated rigid-body modes with stiffness-generated rigid-body modes. The newly generated rigid-body modes are normalized with respect to the system mass and orthogonalized using the Gram-Schmidt technique. This algorithm has been implemented as an enhancement to an existing coupled loads methodology.

Abdallah, Ayman A.↗
NASA NTRSDate not supplied

Surrogate Optimization for Quantum Circuits

Variational quantum Eigensolvers are touted as a near-term algorithm capable of impacting many applications. However, the potential has yet to be realized with few claims of quantum advantage and high resource estimates mainly due to the need for optimization in the presence of noise. Finding algorithms and methods to improve the convergence is essential to accelerate the capabilities of near-term hardware for VQE or more broad applications of hybrid methods in which optimization is required. To this goal we look to use modern approaches recently developed in circuit simulations and stochastic classical optimization that can be combined in a surrogate optimization approach to classical circuits. Using an approximate state vector simulator, we efficiently calculate an approximate Hessian, fed as an input for a detailed quantum circuit simulator. We demonstrate the capabilities of such an approach with and without sampling noise. We also show that this method outperforms Powell in the presence of quantum circuit shot noise by a factor of 2-4

quantum computing↗
NASA NTRSDate not supplied

Quantum Hardware-Enabled Molecular Dynamics via Transfer Learning

The ability to perform ab initio molecular dynamics simulations using potential energy surfaces provided by quantum computers would open the door to virtually exact dynamics for a variety of chemical and biochemical systems, with impacts on catalysis and biophysics. Nonetheless, performing molecular dynamics on surfaces produced by quantum hardware has been hampered by the noisy energies typically produced by quantum computers and challenges associated with computing gradients and scaling to large systems interest. A recent set of advances in machine learning, known as transfer learning, provides a new path forward for molecular dynamics simulations on quantum hardware. Transfer learning offers a workaround, where one first trains models on larger, less accurate classical datasets and then refines them on smaller, more accurate quantum datasets. We explore this approach by training machine learning models to predict a molecule's potential energy based on its geometric structure using Behler-Parrinello neural networks. When successfully trained, the model enables energy gradient predictions necessary for dynamic simulations. To reduce the quantum resources needed, the model is initially trained with data derived from classical density functional theory and subsequently refined with a smaller dataset obtained from a variational quantum eigensolver optimization of the unitary coupled cluster ansatz. We show that this approach significantly reduces the size of the needed quantum training dataset while capturing the high accuracies needed within quantum chemistry simulations. The success of this two-step training method opens more opportunities to apply machine learning models on quantum data, a significant stride towards efficient quantum-classical hybrid computational models.

quantum computing↗
NASA NTRS1976

SPAR reference manual

The functions and operating rules of the SPAR system, which is a group of computer programs used primarily to perform stress, buckling, and vibrational analyses of linear finite element systems, were given. The following subject areas were discussed: basic information, structure definition, format system matrix processors, utility programs, static solutions, stresses, sparse matrix eigensolver, dynamic response, graphics, and substructure processors.

Whetstone, W. D.↗
NASA NTRS1980

A method of order reduction for structural dynamics

This paper presents a new method of order reduction based on recent work of a similar nature applicable to system dynamics and control. This method provides a practical computational procedure for producing a condensed model which exactly preserves the slowest n1 modes (where n1 is the number of 'slow' eigenvalues) of the total n modes of the original model for almost any set of n1 degrees of freedom retained in the condensed model. The method can also be used to compute the eigensolutions corresponding to the n1 slowest modes of the original structural dynamics problem. The accuracy of the condensed model and the speed/accuracy performance of the eigensolver are compared with standard methods for a 90 DOF cantilevered plate.

Anderson, L. R.↗
NASA NTRS1988

An O(N squared) method for computing the eigensystem of N by N symmetric tridiagonal matrices by the divide and conquer approach

An efficient method is proposed to solve the eigenproblem of N by N Symmetric Tridiagonal (ST) matrices. Unlike the standard eigensolvers which necessitate O(N cubed) operations to compute the eigenvectors of such ST matrices, the proposed method computes both the eigenvalues and eigenvectors with only O(N squared) operations. The method is based on serial implementation of the recently introduced Divide and Conquer (DC) algorithm. It exploits the fact that by O(N squared) of DC operations, one can compute the eigenvalues of N by N ST matrix and a finite number of pairs of successive rows of its eigenvector matrix. The rest of the eigenvectors--all of them or one at a time--are computed by linear three-term recurrence relations. Numerical examples are presented which demonstrate the superiority of the proposed method by saving an order of magnitude in execution time at the expense of sacrificing a few orders of accuracy.

Gill, Doron↗
NASA NTRS1990

Recent literature on structural modeling, identification, and analysis

The literature on the mathematical modeling of large space structures is first reviewed, with attention given to continuum models, model order reduction, substructuring, and computational techniques. System identification and mode verification are then discussed with reference to the verification of mathematical models of large space structures. In connection with analysis, the paper surveys recent research on eigensolvers and dynamic response solvers for large-order finite-element-based models.

Craig, Roy R., Jr.↗
NASA NTRS1993

Binary tree eigen solver in finite element analysis

This paper presents a transputer-based binary tree eigensolver for the solution of the generalized eigenproblem in linear elastic finite element analysis. The algorithm is based on the method of recursive doubling, which parallel implementation of a number of associative operations on an arbitrary set having N elements is of the order of o(log2N), compared to (N-1) steps if implemented sequentially. The hardware used in the implementation of the binary tree consists of 32 transputers. The algorithm is written in OCCAM which is a high-level language developed with the transputers to address parallel programming constructs and to provide the communications between processors. The algorithm can be replicated to match the size of the binary tree transputer network. Parallel and sequential finite element analysis programs have been developed to solve for the set of the least-order eigenpairs using the modified subspace method. The speed-up obtained for a typical analysis problem indicates close agreement with the theoretical prediction given by the method of recursive doubling.

Akl, F. A.↗
NASA NTRS1993

A Lanczos algorithm for vibration, suckling and termal analysis

This paper reviews an eigensolver algorithm based on the Lanczos Method for vibration, buckling and thermal analysis. The original code was written for inclusion in the Computational Mechanics Testbed (COMET), a general purpose finite element code. A portable version of the Lanczos code that is optimized for high-performance supercomputers has been developed. Special features of the algorithm include the capability to compute rigid body modes, thermal modes and Lanczos vectors that are derived from the applied load vector. The latter is necessary when using the Lanczos vectors as reduced-basis vectors in transient structural response and transient heat conduction calculations. The modularity of the code allows the user the option of including the most up-to-date utilities, such as the equation solver best suited for the application. The algorithm is discussed in detail and results of several applications are presented. Timing results for a vibration application indicate that the Lanczos algorithm is twenty times faster than the subspace iteration method which has been extensively used in the past.

Bostic, Susan W.↗
NASA NTRS2000

Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems

The ability of computers to solve hitherto intractable problems and simulate complex processes using mathematical models makes them an indispensable part of modern science and engineering. Computer simulations of large-scale realistic applications usually require solving a set of non-linear partial differential equations (PDES) over a finite region. For example, one thrust area in the DOE Grand Challenge projects is to design future accelerators such as the SpaHation Neutron Source (SNS). Our colleagues at SLAC need to model complex RFQ cavities with large aspect ratios. Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency. The PDEs for electromagnetics are discretized by the FEM method, which leads to a generalized eigenvalue problem Kx = AMx, where K and M are the stiffness and mass matrices, and are very sparse. In a typical cavity model, the number of degrees of freedom is about one million. For such large eigenproblems, direct solution techniques quickly reach the memory limits. Instead, the most widely-used methods are Krylov subspace methods, such as Lanczos or Jacobi-Davidson. In all the Krylov-based algorithms, sparse matrix-vector multiplication (SPMV) must be performed repeatedly. Therefore, the efficiency of SPMV usually determines the eigensolver speed. SPMV is also one of the most heavily used kernels in large-scale numerical simulations.

Oliker, Leonid↗
NASA NTRS2000

Finite Element Analysis of Reverberation Chambers

The primary motivating factor behind the initiation of this work was to provide a deterministic means of establishing the validity of the statistical methods that are recommended for the determination of fields that interact in -an avionics system. The application of finite element analysis to reverberation chambers is the initial step required to establish a reasonable course of inquiry in this particularly data-intensive study. The use of computational electromagnetics provides a high degree of control of the "experimental" parameters that can be utilized in a simulation of reverberating structures. As the work evolved there were four primary focus areas they are: 1. The eigenvalue problem for the source free problem. 2. The development of a complex efficient eigensolver. 3. The application of a source for the TE and TM fields for statistical characterization. 4. The examination of shielding effectiveness in a reverberating environment. One early purpose of this work was to establish the utility of finite element techniques in the development of an extended low frequency statistical model for reverberation phenomena. By employing finite element techniques, structures of arbitrary complexity can be analyzed due to the use of triangular shape functions in the spatial discretization. The effects of both frequency stirring and mechanical stirring are presented. It is suggested that for the low frequency operation the typical tuner size is inadequate to provide a sufficiently random field and that frequency stirring should be used. The results of the finite element analysis of the reverberation chamber illustrate io-W the potential utility of a 2D representation for enhancing the basic statistical characteristics of the chamber when operating in a low frequency regime. The basic field statistics are verified for frequency stirring over a wide range of frequencies. Mechanical stirring is shown to provide an effective frequency deviation.

Bunting, Charles F.↗
NASA NTRS1996

New Method Developed for Aeroelastic Stability Analysis

The development of advanced-design ultrahigh bypass ratio engines has led to renewed interest in the study of the flutter of bladed disks. Previously, two fundamental approaches were used in flutter calculations: frequency domain analysis and time-domain analysis. With the development of time-marching computational fluid dynamics (CFD) flow solvers, both approaches have been used with equal ease. In the present work at the NASA Lewis Research Center, substantial computational savings have been achieved by applying a numerical eigensolver to a nonlinear, time-marching fluid-structure interaction system solver for flutter prediction.

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NASA NTRS2003

NASA Tech Briefs, November 2003

Topics covered include: Computer Program Recognizes Patterns in Time-Series Data; Program for User-Friendly Management of Input and Output Data Sets; Noncoherent Tracking of a Source of a Data-Modulated Signal; Software for Acquiring Image Data for PIV; Detecting Edges in Images by Use of Fuzzy Reasoning; A Timer for Synchronous Digital Systems; Prototype Parts of a Digital Beam-Forming Wide-Band Receiver; High-Voltage Droplet Dispenser; Network Extender for MIL-STD-1553 Bus; MMIC HEMT Power Amplifier for 140 to 170 GHz; Piezoelectric Diffraction-Based Optical Switches; Numerical Modeling of Nanoelectronic Devices; Organizing Diverse, Distributed Project Information; Eigensolver for a Sparse, Large Hermitian Matrix; Modified Polar-Format Software for Processing SAR Data; e-Stars Template Builder; Software for Acoustic Rendering; Functionally Graded Nanophase Beryllium/Carbon Composites; Thin Thermal-Insulation Blankets for Very High Temperatures; Prolonging Microgravity on Parabolic Airplane Flights; Device for Locking a Control Knob; Cable-Dispensing Cart; Foam Sensor Structures Would be Self-Deployable and Survive Hard Landings; Real-Gas Effects on Binary Mixing Layers; Earth-Space Link Attenuation Estimation via Ground Radar Kdp; Wedge Heat-Flux Indicators for Flash Thermography; Measuring Diffusion of Liquids by Common-Path Interferometry; Zero-Shear, Low-Disturbance Optical Delay Line; Whispering-Gallery Mode-Locked Lasers; Spatial Light Modulators as Optical Crossbar Switches; Update on EMD and Hilbert-Spectra Analysis of Time Series; Quad-Tree Visual-Calculus Analysis of Satellite Coverage; Dyakonov-Perel Effect on Spin Dephasing in n-Type GaAs; Update on Area Production in Mixing of Supercritical Fluids; and Quasi-Sun-Pointing of Spacecraft Using Radiation Pressure.

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