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

Cadou JM; Duigou L; Damil N; Potier-Ferry M

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

机译：迭代算法的收敛加速。在薄壳分析和Navier-Stokes方程中的应用

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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 Pade 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.

机译：这项工作涉及迭代非线性方法的收敛加速。评估了两种收敛加速技术：改进的最小多项式外推法（MMPE）和Pade近似值。在这项工作中研究的算法是迭代校正器：Damil等人提出的牛顿改进方法，一种高阶迭代校正器。（Commun Numer Methods Eng 15：701-708，1999）和用于粘弹性结构振动的原始算法。我们首先描述考虑非线性问题的迭代算法。其次，介绍了两种加速技术。最后，通过薄壳理论，Navier-Stokes方程和粘弹性壳的振动的几次数值试验，讨论了每种加速技术的优缺点。

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《Computational Mechanics: Solids, Fluids, Fracture Transport Phenomena and Variational Methods》 |2009年第2期|共12页
作者
Cadou JM; Duigou L; Damil N; Potier-Ferry M;
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正文语种 eng
中图分类工程基础科学;
关键词
Convergence acceleration; Iterative correctors; Polynomial; extrapolation; Pade approximants; Nonlinear problems;

机译：收敛加速;迭代校正器;多项式;外推;Pade逼近;非线性问题;

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1. Convergence acceleration of iterative algorithms. Applications to thin shell analysis and Navier-Stokes equations [J] . Cadou JM, Duigou L, Damil N, Computational Mechanics: Solids, Fluids, Fracture Transport Phenomena and Variational Methods . 2009,第2期

机译：迭代算法的收敛加速。在薄壳分析和Navier-Stokes方程中的应用
2. GMRES ACCELERATION OF ITERATIVE IMPLICIT FINITE ELEMENT SOLVERS FOR COMPRESSIBLE EULER AND NAVIER-STOKES EQUATIONS [J] . Remi Choquet, Penelope Leyland, Tiana Tefy International Journal for Numerical Methods in Fluids . 1995,第8a9期

机译：GMRES加速可压缩Euler和Navier-Stokes方程的迭代隐式有限元求解
3. Convergence Acceleration for Solving the Compressible Navier-Stokes Equations [J] . Cord-Christian Rossow AIAA Journal . 2006,第2期

机译：求解可压缩Navier-Stokes方程的收敛加速
4. Convergence Analysis of Pressure-Velocity Iteration Methods for Solving Unsteady Navier-Stokes Equations [C] . Gunter Barwolff International Conference on Numerical Analysis and Applied Mathematics . 2008

机译：求解unsteady Navier-Stokes方程的压力 - 速度迭代方法的收敛性分析
5. Superconvergence of iterated solutions for linear and nonlinear integral equations: Wavelet applications [D] . Novaprateep, Boriboon. 2003

机译：线性和非线性整体方程的迭代解的超计度：小波应用
6. On the Uniform Convergence of the Solutions of the Navier-Stokes Equations [O] . T. Y. Thomas 1943

机译：Navier-Stokes方程解的一致收敛性
7. Convergence acceleration of iterative algorithms. Applications to thin shell analysis and Navier–Stokes equations. [O] . Cadou, Jean Marc, Duigou, Laeticia, Damil, N., 2009

机译：迭代算法的收敛加速。在薄壳分析和Navier–Stokes方程中的应用。

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

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