A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity

Liviu Marin; B. Tomas Johansson

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A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity

机译：线性各向同性弹性柯西问题的交替迭代算法的松弛方法

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We propose two algorithms involving the relaxation of either the given Dirichlet data (boundary displacements) or the prescribed Neumann data (boundary tractions) on the over-specified boundary in the case of the alternating iterative algorithm of Kozlov et al. [16] applied to Cauchy problems in linear elasticity. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed method.

机译：我们提出了两种算法，其中涉及在Kozlov等人的交替迭代算法的情况下，在给定的边界上放宽给定Dirichlet数据（边界位移）或指定的Neumann数据（边界牵引力）。 [16]应用于线性弹性的柯西问题。给出了这些松弛方法的收敛性证明，以及一个停止准则。使用这些程序结合边界元方法（BEM）获得的数值结果表明了该方法的数值稳定性，收敛性，一致性和计算效率。

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2010年第52期|p.3179-3196|共18页
作者
Liviu Marin; B. Tomas Johansson;
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作者单位

Institute of Solid Mechanics, Romanian Academy, 15 Constantin Mille, P.O. Box 1-863, 010141 Bucharest, Romania;

School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
linear elasticity; inverse problem; cauchy problem; alternating iterative algorithm; relaxation procedures; boundary element method (BEM);

机译：线弹性反问题柯西问题;交替迭代算法;放松程序;边界元法（BEM）;

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专利

1. Relaxation procedures for an iterative MFS algorithm for the stable reconstruction of elastic fields from Cauchy data in two-dimensional isotropic linear elasticity [J] . Marin L., Johansson B.T. International Journal of Solids and Structures . 2010,第25a26期

机译：用于迭代MFS算法的放宽程序，以稳定地重建来自二维各向同性线性弹性的Cauchy数据的弹性场重建
2. Reconstruction of Boundary Data in Two-Dimensional Isotropic Linear Elasticity from Cauchy Data Using an Iterative MFS Algorithm [J] . Liviu Marin Computer Modeling in Engineering & Sciences . 2010,第3期

机译：使用迭代MFS算法从柯西数据重构二维各向同性线性弹性中的边界数据
3. A relaxation method of an alternating iterative MFS algorithm for the Cauchy problem associated with the two-dimensional modified Helmholtz equation [J] . Marin L. Numerical Methods for Partial Differential Equations: An International Journal . 2012,第3期

机译：与二维修正亥姆霍兹方程有关的柯西问题的交替迭代MFS算法的松弛方法
4. An Iterative Method for the Cauchy Problem in Linear Elasticity in Domains with Singularities [C] . Liviu MARIN, Lionel ELLIOTT, Derek B. INGHAM, International seminar on geometry continua and microstructures . 2002

机译：具有奇异性域的线性弹性中Cauchy问题的迭代方法
5. Preconditioned Iterative Methods for Linear Equations of Graph Laplacians: Algorithms and Applications [D] . Lin, Junyuan. 2019

机译：图拉普拉斯图线性方程的预处理方法：算法和应用
6. How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity [O] . L. Angela Mihai, Alain Goriely -1

机译：如何表征非线性弹性材料？各向同性有限弹性中的非线性本构参数研究进展
7. Relaxation procedures for an iterative MFS algorithm for the stable reconstruction of elastic fields from Cauchy data in two-dimensional isotropic linear elasticity [O] . Marin Liviu, Johansson B. Tomas 2010

机译：二维M各向同性线性弹性中基于Cauchy数据的弹性场稳定重构的迭代MFS算法的松弛过程

A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity

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