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Wednesday, May 13, 2020 | History

3 edition of Multigrid techniques for nonlinear eigenvalue problems found in the catalog.

Multigrid techniques for nonlinear eigenvalue problems

Multigrid techniques for nonlinear eigenvalue problems

solutions of a nonlinear schrodinger eigenvalue problem in 2D and 3D

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Published by Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, National Technical Information Service, distributor in Hampton, VA, [Springfield, Va .
Written in English

    Subjects:
  • Algorithms.,
  • Continuity (Mathematics),
  • Eigenvalues.,
  • Eigenvectors.,
  • Iterative solution.,
  • Multigrid methods.,
  • Nonlinearity.

  • Edition Notes

    Other titlesSolutions of a nonlinear schrodinger eigenvalue problem in 2D and 3D.
    StatementSorin Costiner, Shlomo Ta"asan.
    SeriesICASE report -- no. 94-91., NASA contractor report -- 194999., NASA contractor report -- NASA CR-194999.
    ContributionsTa"asan, Shlomo., Institute for Computer Applications in Science and Engineering.
    The Physical Object
    FormatMicroform
    Pagination1 v.
    ID Numbers
    Open LibraryOL15408830M

    Multigrid methods have been used in somewhat more limited fashion to solve nonlinear problems as well. The nonlinear Full Approximation Scheme (FAS) is a well-known multigrid framework for solving nonlinear partial differential equations [7]. Nonlinear multigrid methods have also been used to solve eigenvalue problems [24, 9]. A nonlinear eigenvalue problem known that those boundary points ξ where the requirement lim x→ξ u(x) = 0 fails is a set of p-capacity zero. That is to say that the irregular boundary points form a very small set. If p > n, then every boundary point is regular! It is not difficult to see that every eigenvalue λ is positive. Indeed, byFile Size: KB.

    In [1], [2] we present multigrid (MG) eigenvalue algorithms for linear and nonlinear eigenvalue problems, whose robustness and efficiency rely much on the multigrid projection (MGP) and on the backrotations, introduced in [3], [4], [5]. The applications were for Schr6dinger and electromag-netism eigenvalue problems.   [11] --, Simultaneous multigrid techniques for nonlinear eigenvalue problems: solutions of the nonlinear Schrodinger-Poisson eigenvalue problem in two and three dimensions, Phys. Rev. E (3), 52 (), pp.

    For nonlinear eigenvalue problems, the similar results can also be found in,,. For more results about AFEM, please refer to, and the references cited therein. Since many nonlinear eigenvalue problems, especially in quantum physics, have strong singularities, the AFEM is a competitive : Fei Xu, Qiumei Huang. Multigrid (MG) methods in numerical analysis are algorithms for solving differential equations using a hierarchy of are an example of a class of techniques called multiresolution methods, very useful in problems exhibiting multiple scales of behavior. For example, many basic relaxation methods exhibit different rates of convergence for short- and long-wavelength components.


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Multigrid techniques for nonlinear eigenvalue problems Download PDF EPUB FB2

Multigrid techniques for nonlinear eigenvalue problems solutions of a nonlinear schrodinger eigenvalue problem in 2D and 3D (SuDoc NAS ) [Costiner, Sorin] on *FREE* shipping on qualifying offers. Multigrid techniques for nonlinear eigenvalue problems solutions of a nonlinear schrodinger eigenvalue problem in 2D and 3D (SuDoc NAS )Author: Sorin Costiner.

The main idea is to transform the solution of nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces.

Abstract: A multigrid method is proposed for solving nonlinear eigenvalue problems by the finite element method. With this new scheme, solving nonlinear eigenvalue problem is decomposed to a series of solutions of linear boundary value problems on multilevel finite element spaces and a series of small scale nonlinear eigenvalue by: Multigrid techniques for nonlinear eigenvalue problems: solutions of a nonlinear schrodinger eigenvalue problem in 2D and 3D Author: Sorin Costiner ; Shlomo Ta'asan ; Institute for Computer Applications in Science and Engineering.

Multigrid (MG) algorithms for nonlinear problems and for EP obtained from discretizations of partial di erential EP, haveoften shown to be more e cient than single level algorithms.

This paper presents MG techniques for nonlinear EP and emphasizes an MG algorithm for a Multigrid techniques for nonlinear eigenvalue problems book Schrodinger EP.

Algorithms for nonlinear eigenvalue problems (EP's) often require solving self-consistently a large number of EP's. Convergence difficulties may occur if the solution is not sought in an appropriate region, if global constraints have to be satisfied, or if close or equal eigenvalues are present.

Multigrid (MG) algorithms for nonlinear problems and for EP's obtained from discretizations of. Abstract. We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and nonlinear eigenvalue problems on the coarsest finite element by:   An algebraic multigrid method is proposed to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations.

Nonlinear Eigenvalue Problems Polynomial Eigenvalue Problems Rational Eigenvalue Problems Eigenvalues of Rational Matrix Functions Vibration problems, for example those that occur in a structure such as a bridge,are often modelled by the generalizedeigenvalueproblem (K−λM)x=0, where K is the stiffness matrix and M is the mass matrix.

Nonlinear Eigenvalue Problems (NEPs) Let F:!Cm n be analytic on open set C. The nonlinear eigenvalue problem: Find scalars and nonzero x;y 2Cn satisfying F()x = 0 and y F() = 0. is an e’val, x, y are corresponding right and left e’vecs. When m = n, e’vals are solutions of det(F()) = Size: KB.

This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues.

We present and analyze old and new nonlinear multigrid techniques. Related procedures are often used without proof in practical applications.

After a brief motivation of linear multigrid, we principally concentrate on Newton multigrid for smooth problems and on monotone multigrid Cited by: 4. We investigate multi-grid methods for solving linear systems arising from arc-length continuation techniques applied to nonlinear elliptic eigenvalue problems.

We find that the usual multi-grid met Cited by: We investigate multi-grid methods for solving linear systems arising from arc-length continuation techniques applied to nonlinear elliptic eigenvalue problems.

We find that the usual multi-grid methods diverge in the neighborhood of singular points of the solution by: The chapter describes some of the less known features of full approximation scheme multigrid processing, such as the high efficiency in solving nonlinear and eigenvalue problems as well as chains of many similar problems.

We investigate multi-grid methods for solving linear systems arising from arc-length continuation techniques applied to nonlinear elliptic eigenvalue problems.

We find that the usual multi-grid methods diverge in the neighborhood of singular points of the solution branches. As a result, the continuation method is unable to continue past a limit point in the Bratu by:   Abstract: An algebraic multigrid method is proposed to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations.

The algebraic multigrid method setup procedure is applied to construct the hierarchy and the intergrid transfer operators. In the algebraic multigrid scheme, a large scale eigenvalue problem Cited by: 1. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics.

Jul;52(1) Simultaneous multigrid techniques for nonlinear eigenvalue problems: Solutions of the nonlinear Schrödinger-Poisson eigenvalue problem in two and three by: Eigenvalue Problem For a given matrix A ∈ Cn×n find a non-zero vector x ∈ Cn and a scalar λ ∈ C such that Ax = λx.

The vector x is the (right) eigenvector of A associated with the eigenvalue λ of A. Approximation of Eigenvalues There are two classes of numerical methods: Partial methods: computation of extremal eigenvalues.

⇒ The. Adaptive multigrid techniques for large-scale eigenvalue problems: Solutions of the Schrodinger problem in two and three dimensions. Costiner S, Ta'asan S. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics, (4) MED: Cited by:.

Problems solved by multigrid methods include general elliptic partial differential equations, nonlinear and eigenvalue problems, and systems of equations from fluid dynamics. The efficiency is optimal: the computational work is proportional to the number of by: Multigrid (MG) algorithms for nonlinear problems and for EP obtained from discretizations of partial di erential EP, haveoften shown to be more e cient than single level algorithms.

This paper presents MG techniques for nonlinear EP and emphasizes an MG algorithm for a nonlinear Schrodinger : Sorin Costiner.proaches for numerical solution of eigenvalue problems.

The most traditional multigrid approach to an eigenvalue problem is to treat it as a nonlinear equation and, thus, to apply a nonlinear multigrid solver; e.g., an FAS (full ap-proximation scheme) [7], sometimes explicitly tuned for the eigenvalue computations, e.g.,File Size: KB.