Padé approximations

This work deals with the convergence acceleration of iterative nonlinear methods. Two convergence accelerating techniques are evaluated: the Modified Mininal Polynomial Extrapolation Method (MMPE) and the Padé approximants. The algorithms studied in this work are iterative correctors: Newton's modified method, a high-order iterative corrector presented in Damil et al. (Commun Numer Methods Eng 15:701-708, 1999) and an original algorithm for vibration of viscoelastic structures. We first describe the iterative algorithms for the considered nonlinear problems. Secondly, the two accelerating techniques are presented. Finally, through several numerical tests from the thin shell theory, Navier-Stokes equations and vibration of viscoelastic shells, the advantages and drawbacks of each accelerating technique is discussed.

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“…Finally when all the terms U k n are computed, the polynomial approximation (11) is then improved by using Padé approximants [2,[14][15][16].…”

Section: Some Iterative Algorithms For Nonlinear Problemsmentioning

confidence: 99%

“…The initial sequence (3) is then replaced by: (15) where the subscript "new" designates the new vector obtained with either a vector extrapolation method or with VPA. In the first case, e i are scalar coefficients and in the second one, e i are rational functions.…”

Section: Two Convergence Acceleration Techniquesmentioning

confidence: 99%

Convergence acceleration of iterative algorithms. Applications to thin shell analysis and Navier–Stokes equations

et al. 2008

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“…To our knowledge, the best path-following technique involves Padé approximants, that are rational fractions, deduced from the series by various algorithms [36,37]. The polynomial approximation…”

Section: Remarkmentioning

confidence: 99%

Asymptotic numerical methods for unilateral contact

Aggoune

Zahrouni

Potier‐Ferry

2006

Int. J. Numer. Meth. Engng

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SUMMARYNew algorithms based upon the asymptotic numerical method (ANM) are proposed to solve unilateral contact problems. ANM leads to a representation of a solution path in terms of series or Padé approximants. To get a smooth solution path, a hyperbolic relation between contact forces and clearance is introduced. Three key points are discussed: the influence of the regularization of the contact law, the discretization of the contact force by Lagrange multipliers and prediction-correction algorithms. Simple benchmarks are considered to evaluate the relevance of the proposed algorithms.

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“…The problem consists in computing the equivalent inductance for arbitrary value of the stage of growth . Following Section II-C a recurrent relationship is derived and Padé approximants [17] are used to estimate the series in involving in the scale changing technique. One founds that, for values of taken between 1 and 8, the numerical convergence of the equivalent inductance is reached for active modes in all scale changing networks.…”

Section: An Illustrative Example: the Cantor Iris In A Waveguidementioning

confidence: 99%

“…The computation is performed for the even configuration (the surface impedance for the odd configuration is zero). Padé approximants [17] are used here to compute the elements of the surface impedance matrices and improve the accuracy of the numerical results recently reported by the authors in [10]. Fig.…”

Section: Application To Multiband Scatterersmentioning

confidence: 99%

Scale Changing Technique for the Electromagnetic Modeling of Planar Self-Similar Structures

Voyer

Aubert

David

2006

IEEE Trans. Antennas Propagat.

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A scale changing approach is proposed for analyzing the electromagnetic scattering from discrete self-similar (e.g., logperiodic or pre-fractal) planar structures. Such structures present metallic patterns at multiple scale levels and are viewed here as the superposition of multiple domains enclosed with appropriate boundary conditions. In each domain higher-order modes provide the accurate local description of the electromagnetic fields while lower-order modes are used to model the electromagnetic coupling between the various domains at large scales. The scale changing technique is applied here to the electromagnetic modeling of multifrequency selective surfaces and discrete self-similar (pre-fractal) scatterers. Experimental data are given for validation purpose. It is seen that the proposed technique is much better than the method of moments in time costing.

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Padé approximations

Cited by 34 publications

References 98 publications

Convergence acceleration of iterative algorithms. Applications to thin shell analysis and Navier–Stokes equations

Convergence acceleration of iterative algorithms. Applications to thin shell analysis and Navier–Stokes equations

Asymptotic numerical methods for unilateral contact

Scale Changing Technique for the Electromagnetic Modeling of Planar Self-Similar Structures

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