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Thursday, August 6, 2020 | History

3 edition of Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems found in the catalog.

Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems

H. Thomas Banks

Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems

by H. Thomas Banks

  • 140 Want to read
  • 26 Currently reading

Published by National Aeronautics and Space Administration, Langley Research Center, National Technical Information Service, distributor in Hampton, Va, [Springfield, Va .
Written in English

    Subjects:
  • Galerkin methods.,
  • Inverse problems (Differential equations)

  • Edition Notes

    StatementH.T. Banks, Simeon Reich, I.G. Rosen.
    SeriesICASE report -- no. 88-38., NASA contractor report -- 181676., NASA contractor report -- NASA CR-181676.
    ContributionsReich, Simeon., Rosen, I. Gary., Langley Research Center.
    The Physical Object
    FormatMicroform
    Pagination1 v.
    ID Numbers
    Open LibraryOL15392314M

    discretization: application to the inverse acoustic wave problem Florian Faucher Otmar Scherzery Abstract In this paper, we perform non-linear minimization using the Hybridizable Discontinu-ous Galerkin method (HDG) for the discretization of the forward problem, and implement the adjoint-state method for the computation of the functional. This paper is concerned with the numerical solution of the nonlinear Schrödinger (NLS) equation with Neumann boundary conditions by quintic B-spline Galerkin finite element method as the shape and weight functions over the finite domain. The Galerkin B-spline method is more efficient and simpler than the general Galerkin finite element method. For the Galerkin B-spline method, the Crank.

    DOI: /JIE Corpus ID: The Discrete Galerkin method for nonlinear integral equations @inproceedings{AtkinsonTheDG, title={The Discrete Galerkin method for nonlinear integral equations}, author={Kendall E. Atkinson and Florian A. Potra}, year={} }. Galerkin Approximations A simple example In this section we introduce the idea of Galerkin approximations by consid-ering a simple 1-d boundary value problem. Let u be the solution of (¡u00 +u = f in (0;1) u(0) = u(1) = 0 () and suppose that we want to find a computable approximation to u (of.

      This book explains how to identify ill-posed linear and nonlinear inverse problems and solve them using computational methods, complete with exercises. Computer code is included on an accompanying website. Ideal as a textbook or reference guide for graduate students and researchers in mathematics, physics and s: 1. Beard, R. and McLain, T. Successive Galerkin Approximation Algorithms for Nonlinear Optimal and Robust Control, International Journal of Control: Special Issue on Breakthroughs in the Control of Nonlinear Systems, vol. 71, no. 5, pp. , November This Peer-Reviewed Article is brought to you for free and open access by BYU.


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Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems by H. Thomas Banks Download PDF EPUB FB2

We develop an abstract framework and convergence theory for Galerkin approximation for inverse problems involving the identification of nonautonomous, in general nonlinear, distributed parameter by: Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems Author: H Thomas Banks ; Simeon Reich ; I Gary Rosen ; Langley Research Center.

for Galerkin approximations for inverse problems involving nonautonomous nonlinear distributed parameter systems. We consider parameter estimation problems formulated as the minimization over a compact admissible parameter set, of a least-squares-like performance index subject to state.

Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems. By Simeon Reich, H. Banks and I. Rosen. Abstract. An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems.

A Author: Simeon Reich, H. Banks and I. Rosen. An abstract approximation framework for the identification of nonlinear, distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated.

Convergence of Galerkin approximations and the corresponding solutions Cited by: In this paper, we study the meshless local Petrov–Galerkin (MLPG) method based on the moving least squares (MLS) approximation for finding a numerical solution to the Stefan free boundary problem.

Approximation of this problem, due to the moving boundary, is difficult. To overcome this difficulty, the problem is converted to a fixed boundary problem in which it consists of an inverse and. Nonlinear optimal control and nonlinear H infinity control are two of the most significant paradigms in nonlinear systems theory.

Unfortunately, these problems require the solution of Hamilton-Jacobi equations, which are extremely difficult to solve in practice. To make matters worse, approximation techniques for these equations are inherently prone to the so-called 'curse of dimensionality'.

AweakGalerkinscheme. In this section, we introduce the weak Galerkin scheme for the eigenvalue problem () and the weak Galerkin scheme based on the shifted-inverse power technique. We first introduce some notations and definitions.

Suppose {V,(,)a} is a Hilbert space and (,)b is another inner-product on V. Let W be the. H.T. Banks and K. Ito, A unified framework for approximation and inverse problems for distributed parameter systems, Control Theory and Advanced Technology 4 (, 2.

H.T. Banks, S. Reich, and I.G. Rosen, An approximation theory for the identification of nonlinear distributed parameter systems, SIAM J. Contr. and Opt., submitted. We introduce the Galerkin method through the classic Poisson problem in d space dimensions, −∇2˜u = f onΩ, u˜ = 0 on∂Ω.

(1) Of particular interest for purposes of introduction will be the case d = 1, − d2u˜ dx2 = f, u˜(±1) = 0. (2) We use ˜u to represent the exact solution. solution of dense linear systems as described in standard texts such as [7], [],or[].

Our approach is to focus on a small number of methods and treat them in depth. Though this book is written in a finite-dimensional setting, we have selected for coverage mostlyalgorithms and methods of analysis which. The Galerkin method for the approximation of u is based on the variational problem ().

Let V = V h be a C 0-conforming finite element space of piecewise polynomials corresponding to a quasiuniform triangulation T h of Ω. The Galerkin approximation is a function u h ϵ V h such that. An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity is called an inverse problem because it starts with the effects and then calculates the.

An abstract approximation framework and convergence theory for Galerkin approximations to inverse problems involving nonlinear Volterra integral equations is developed.

An application of this theory to a class of nonlinear reaction-diffusion problems that arise in population dynamics is presented. Furthermore, conditions on the initial population density for this class of problems that result in finite time extinction or persistence of the population is discussed.

Approximation and regular perturbation of optimal control problems via Hamilton-Jacobi theory. Caterina Sartori Pages OriginalPaper. Quasi-convex sets and size × curvature condition, application to nonlinear inversion.

Guy Chavent Pages OriginalPaper. Smoothing the function of the multiple-shooting equation. We develop an abstract framework and convergence theory for Galerkin approximation for inverse problems involving the identification of nonautonomous, in general nonlinear, distributed parameter.

Head: Dietmar Hömberg Coworkers: Ingo Bremer, Moritz Ebeling-Rump, Martin Eigel, Robert Gruhlke, Holger Heitsch, René Henrion, Robert Lasarzik, Andreas Rathsfeld, David Sommer Secretary: Anke Giese Overview.

The research group is concerned with problems in optimization and optimal control as well as inverse problems regarding up-to-date technical and economical applications.

If the address matches an existing account you will receive an email with instructions to reset your password. the Dirichlet problem for (2) is also used in showing that the nonlinear algebraic equa-tions arising in the Galerkin method can be solved by Newton's method provided a sufficiently good approximation of the answer can be found with which to begin the Newton iteration.

The Approximate Solution. For 1. The PDE is discretized into a system of ordinary differential equations (ODEs) using the Galerkin method with Legendre polynomials as the basis functions. The BC is imposed using the tau method.

The resulting ODEs are time periodic in nature; thus, we resort to Floquet theory to determine the stability of the ODEs.List of Publications of Simeon Reich. D. Sc. Thesis: 0. On the fixed point theorems of Banach and Schauder, Dissertation Abstracts International, Vol No.In this work, Galerkin approximations are developed for a system of first order nonlinear neutral delay differential equations (NDDEs).

The NDDEs are converted into an equivalent system of hyperbolic partial differential equations (PDEs) along with the nonlinear boundary constraints.