Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Convergence analysis”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Acceleration of convergence of vector sequences

A general approach to the construction of convergence acceleration methods for vector sequence is proposed. Using this approach, one can generate some known methods, such as the minimal polynomial extrapolation, the reduced rank extrapolation, and the topological epsilon algorithm, and also some new ones. Some of the new methods are easier to implement than the known methods and are observed to have similar numerical properties. The convergence analysis of these new methods is carried out, and it is shown that they are especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iterative. A stability analysis is also given, and numerical examples are provided. The convergence and stability properties of the topological epsilon algorithm are likewise given.

Sidi, A.↗
DOE OSTI2019

Fractional dynamics of an erbium-doped fiber laser model

In this paper we investigate the model of the time-fractional dynamics of an erbium-doped fiber laser model (TFDEFL) with Liouville–Caputo (LC), Caputo–Fabrizio–Caputo (CFC) and Atangana–Baleanu–Caputo (ABC) time-fractional derivatives. We employ the homotopy analysis transform method (HATM) to calculate approximate solutions for the TFDEFL model. This method gives the solution in the form of a rapidly convergent series that can ensure the convergence in solving the resultant series. We study the convergence analysis of HATM by computing the interval of convergence through the h-curves, the residual error function and the average residual error, respectively. We also show the effectiveness and accuracy of this method by comparing the approximate solutions based upon the LC, CFC and ABC time-fractional derivatives.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Application of hat basis functions for solving two-dimensional stochastic fractional integral equations

This article concerns with a computational scheme to solve two-dimensional stochastic fractional integral equations (2DSFIEs), numerically. In these equations, the fractional integral is considered in the Riemann–Liouville sense. The proposed method is essentially based on two-dimensional hat basis functions and its fractional operational matrices. The fractional-order operational matrices of integration are applied to reduce the solution of 2DSFIEs to the solution of a system of linear equations which can be solved using a direct method or iterative method. Some results concerning the convergence analysis associated with the proposed technique are discussed. In addition, we establish the rate of convergence of this approach for solving 2DSFIEs is O(h{sup 2}). Finally, some examples are solved using present method to indicate the pertinent features of the method.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1999

Approximation of the Newton Step by a Defect Correction Process

In this paper, an optimal control problem governed by a partial differential equation is considered. The Newton step for this system can be computed by solving a coupled system of equations. To do this efficiently with an iterative defect correction process, a modifying operator is introduced into the system. This operator is motivated by local mode analysis. The operator can be used also for preconditioning in Generalized Minimum Residual (GMRES). We give a detailed convergence analysis for the defect correction process and show the derivation of the modifying operator. Numerical tests are done on the small disturbance shape optimization problem in two dimensions for the defect correction process and for GMRES.

Arian, E.↗
DOE OSTI2024

The eXtended virtual element method for elliptic problems with weakly singular solutions

This paper introduces a novel eXtended virtual element method, an extension of the conforming virtual element method. The X-VEM is formulated by incorporating appropriate enrichment functions in the local spaces. The method is designed to handle highly generic enrichment functions, including singularities arising from fractured domains. By achieving consistency on the enrichment space, the method is proven to achieve arbitrary approximation orders even in the presence of singular solutions. The paper includes a complete convergence analysis under general assumptions on mesh regularity, and numerical experiments validating the method’s accuracy on various mesh families, demonstrating optimal convergence rates in the L 2 - and H 1 - norms on fractured or L-shaped domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Fast iterative refinement method for mixed systems of integral and fractional integro-differential equations

The authors’ new method of iterative refinement has been successfully applied to the linear fractional Fredholm integro-differential equation. In this work, we adapt our method to obtain approximate analytical solutions for linear Volterra equations of both the first and the second kind of fractional type. A detailed convergence analysis is presented for each kind. The authors also apply their method to the challenging first kind linear Fredholm integral equation. Three different cases are considered to test the efficacy of our method. These include mixed systems of various forms of linear integral and fractional integro-differential equations. We compare our method with six well-established methods: Picard’s successive approximations, an accelerated form of the latter, the Adomian decomposition, the variational iteration, the homotopy perturbation and the homotopy analysis. The results show the versatility of the new method in solving a wide variety of equations, its high convergence speed and accuracy and its capability of directly dealing with equations of the first kind. We also prove that Picard’s method for linear equations is a special case of our method.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

Averaging analysis for discrete time and sampled data adaptive systems

Earlier continuous time averaging theorems are extended to the nonlinear discrete time case. Theorems for the study of the convergence analysis of discrete time adaptive identification and control systems are used. Instability theorems are also derived and used for the study of robust stability and instability of adaptive control schemes applied to sampled data systems. As a by product, the effects of sampling on unmodeled dynamics in continuous time systems are also studied.

Fu, Li-Chen↗
DOE OSTI2018

New fractional derivatives applied to the Korteweg–de Vries and Korteweg–de Vries–Burger’s equations

In this paper, we extend the model of the Korteweg–de Vries (KDV) and Korteweg–de Vries–Burger’s (KDVB) to new model time fractional Korteweg–de Vries (TFKDV) and time fractional Korteweg–de Vries-Burger’s (TFKDVB) with Liouville–Caputo (LC), Caputo–Fabrizio (CF), and Atangana-Baleanu (AB) fractional time derivative equations, respectively. We utilize the q-homotopy analysis transform method (q-HATM) to compute the approximate solutions of TFKDV and TFKDVB using LC, CF and AB in Liouville–Caputo sense. We study the convergence analysis of q-HATM by computing the Residual Error Function (REF) and finding the interval of the convergence through the h-curves. Also, we find the optimal values of h so that, we assure the convergence of the approximate solutions. The results are very effective and accurate in solving the TFKDV and TFKDVB.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

The Thermalization Verification Problem for EMPIRE-PIC and EMPIRE-Fluid

We report on the verification of elastic collisions in EMPIRE-PIC and EMPIRE-Fluid in support of the ATDM L2 V&V Milestone. The thermalization verification problem and the theory behind it is presented along with an analytic solution for the temperature of each species over time. The problem is run with both codes under multiple parameter regimes. The temperature over time is compared between the two codes and the theoretical results. A preliminary convergence analysis is performed on the results from EMPIRE-PIC and EMPIRE-Fluid showing the rate at which the codes converge to the analytic solution in time (EMPIRE-Fluid) and particles (EMPIRE-PIC).

42 ENGINEERING↗
NASA NTRS1989

Integrated structural analysis and design using 3-D finite elements

The optimum design of the shape of a hole in a plate in tension is obtained with a design algorithm based on partially converged analysis. The plate is modeled by three-dimensional finite elements, and an EBE PCG iterative solution algorithm is used for solving the equations of equilibrium. Several parametrizations of the optimum shape are considered, and it is found that a sine series can describe the optimum shape with only three design variables. The optimum shape compares well with an experimental optimum obtained by Durelli.

Barthelemy, B.↗
DOE OSTI2019

Fast neural network training on a cluster of GPUs for action recognition with high accuracy

In this work, we propose algorithms and techniques to accelerate training of deep neural networks for action recognition on a cluster of GPUs. The convergence analysis of our algorithm shows it is possible to reduce communication cost and at the same time minimize the number of iterations needed for convergence. We customize the Adam optimizer for our distributed algorithm to improve efficiency. In addition, we employ transfer-learning to further reduce training time while improving validation accuracy. For the UCF101 and HMDB51 datasets, the validation accuracies achieved are 93.1% and 67.9% respectively. With an additional end-to-end trained temporal stream, the validation accuracies achieved for UCF101 and HMDB51 are 93.47% and 81.24% respectively. As far as we know, these are the highest accuracies achieved with the two-stream approach using ResNet that does not involve computationally expensive 3D convolutions or pretraining on much larger datasets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A study on the local convergence and dynamics of the two-step and derivative-free Kung–Traub’s method

We present a local convergence analysis of a two-step and derivative-free Kung–Traub’s method, which is based on a parameter and has fourth order of convergence. Using basins of attraction of the method, dynamical behavior of the scheme is studied and the best choice of the parameter is found in the sense of reliability and stability. Some illustrative examples show that as the parameter gets close to zero, radius of convergence of the method becomes larger.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A new accelerated algorithm for ill-conditioned ridge regression problems

In this work, we study the primal and dual formulations of the regularized least squares problem, in special norm L{sub 2}, named ridge regression. We state the Gradient method for the corresponding primal-dual problem through a fixed point approach. For this formulation, we present an original convergence analysis involving the spectral radius of a suitable iteration matrix. The main contribution of this work is to accelerate the studied method by means of a memory-like strategy. Some connections with the spectral properties of the associated iteration matrices were established to prove the convergence of the accelerated method. Preliminary experiments showed the good performance of the proposed algorithm when applied to solve ill-conditioned problems, providing better results than the conjugate gradient method for this class of problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

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↗
NASA NTRS1994

On the convergence of local approximations to pseudodifferential operators with applications

We consider the approximation of a class pseudodifferential operators by sequences of operators which can be expressed as compositions of differential operators and their inverses. We show that the error in such approximations can be bounded in terms of L(1) error in approximating a convolution kernel, and use this fact to develop convergence results. Our main result is a finite time convergence analysis of the Engquist-Majda Pade approximants to the square root of the d'Alembertian. We also show that no spatially local approximation to this operator can be convergent uniformly in time. We propose some temporally local but spatially nonlocal operators with better long time behavior. These are based on Laguerre and exponential series.

Hagstrom, Thomas↗
NASA NTRS2017

Aeroelastic Modeling of X-56A Stiff-Wing Configuration Flight Test Data

Aeroelastic stability and control derivatives for the X-56A Multi-Utility Technology Testbed (MUTT), in the stiff-wing configuration, were estimated from flight test data using the output-error method. Practical aspects of the analysis are discussed. The orthogonal phase-optimized multisine inputs provided excellent data information for aeroelastic modeling. Consistent parameter estimates were determined using output error in both the frequency and time domains. The frequency domain analysis converged faster and was less sensitive to starting values for the model parameters, which was useful for determining the aeroelastic model structure and obtaining starting values for the time domain analysis. Including a modal description of the structure from a finite element model reduced the complexity of the estimation problem and improved the modeling results. Effects of reducing the model order on the short period stability and control derivatives were investigated.

Grauer, Jared A.↗
DOE OSTI2013

Monte Carlo mesh tallies based on a Kernel Density Estimator approach using integrated particle tracks

A new Monte Carlo mesh tally based on a Kernel Density Estimator (KDE) approach using integrated particle tracks is presented. We first derive the KDE integral-track estimator and present a brief overview of its implementation as an alternative to the MCNP fmesh tally. To facilitate a valid quantitative comparison between these two tallies for verification purposes, there are two key issues that must be addressed. The first of these issues involves selecting a good data transfer method to convert the nodal-based KDE results into their cell-averaged equivalents (or vice versa with the cell-averaged MCNP results). The second involves choosing an appropriate resolution of the mesh, since if it is too coarse this can introduce significant errors into the reference MCNP solution. After discussing both of these issues in some detail, we present the results of a convergence analysis that shows the KDE integral-track and MCNP fmesh tallies are indeed capable of producing equivalent results for some simple 3D transport problems. In all cases considered, there was clear convergence from the KDE results to the reference MCNP results as the number of particle histories was increased. (authors)

97 MATHEMATICS AND COMPUTING↗