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线性弹性问题的局部正交分解方法

余涛1, 张镭2   

  1. 1. 井冈山大学数理学院, 吉安 343009;
    2. 上海交通大学数学科学学院, 自然科学研究院和教育部科学与工程计算重点实验室, 上海 200240
  • 收稿日期:2017-03-02 出版日期:2018-03-15 发布日期:2018-03-13
  • 基金资助:

    国家自然科学基金(11471214,11571314);江西省教育厅科技项目(GJJ160758);吉安市软科学计划项目(吉市科计字[2012]32-7);井冈山大学博士科研启动项目(JZB11002).

余涛, 张镭. 线性弹性问题的局部正交分解方法[J]. 数值计算与计算机应用, 2018, 39(1): 10-19.

Yu Tao, Zhang Lei. A LOCALIZED ORTHOGONAL DECOMPOSITION METHOD FOR LINEAR ELASTICITY[J]. Journal of Numerical Methods and Computer Applications, 2018, 39(1): 10-19.

A LOCALIZED ORTHOGONAL DECOMPOSITION METHOD FOR LINEAR ELASTICITY

Yu Tao1, Zhang Lei2   

  1. 1. Department of Mathematics and Physics, Jinggangshan University, Ji'an 343009, China;
    2. Institute of Natural Science and Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China
  • Received:2017-03-02 Online:2018-03-15 Published:2018-03-13
局部正交分解方法是求解多尺度问题的一种有效算法.该算法不要求介质具有周期性或尺度分离的特点.本文构造了求解多尺度线性弹性问题的局部正交分解方法,并且给出了最佳误差估计.一些数值实验也证实了理论误差结果.
Localized orthogonal decomposition (LOD) method is an effective method for solving multiscale problems. The method does not require any assumptions on periodicity and scale separation. This paper employs an LOD method for solving multiscale problems in linear elasticity. We give a priori error estimates for the proposed method. The theoretical results are confirmed by various numerical experiments.

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[1] Abdulle A. Analysis of a heterogeneous multiscale FEM for problems in elasticity[J]. Math. Mod. Meth. App. Sci., 2006, 16(4): 615-635.

[2] Babuška I and Osborn J E. Generalized finite element methods: their performance and their relation to mixed methods[J]. SIAM J. Numer. Anal., 1983, 20(3): 510-536.

[3] Buck M, Lliev O and Andrä H. Multiscale finite element coarse spaces for the application to linear elasticity[J]. Cent. Eur. J. Math., 2013, 11(4): 680-701.

[4] Ciarlet P G. Mathematical elasticity[M]. North-Holland, 1988.

[5] Chung E T, Efendiev Y and Fu S. Generalized multiscale finite element methods for elasticity equations[J]. GEM - International Journal on Geomathematics, 2014, 5(2): 225-254.

[6] E W and Engquist B. The heterogeneous multiscale methods[J]. Commun. Math. Sci., 2003, 1(1): 87-132.

[7] Francfort G A and Murat F. Homogenization and optimal bounds in linear elasticity[J]. Archive for Rational Mechanics and Analysis, 1986, 94(4): 307-334.

[8] Hou T Y and Wu X H. A multiscale finite element method for elliptic problems in composite materials and porous media[J]. J. Comput. Phys.,1997, 134: 169-189.

[9] Hughes T J R, Feijóo G R, Mazzei L and Quincy J B. The variational multiscale method - a paradigm for computational mechanics[J]. Comput. Methods Appl. Mech. Engrg., 1998, 166(1-2): 3-24.

[10] Jikov V V, Kozlov S M and Oleinik O A. Homogenization of differential operators and integral functionals[M]. Springer-Verlag, 1994.

[11] Peterseim D. Variational multiscale stabilization and the exponential decay of fine-scale correctors[J]. Lecture Notes in Computational Science and Engineering, 2016, 114: 343-369.

[12] Malqvist A and Peterseim D. Localization of elliptic multiscale problems[J]. Math. Comput., 2014, 83(290): 2583-2603.

[13] Owhadi H, Zhang L and Berlyand L. Polyharmonic homogenization, rough polyharmonic splines and spare super-localization[J]. ESAIM: Mathe. Model. Numer. Anal., 2012, 48(2): 766-792.

[14] Vinh P C and Tung D X. Homogenized equations of the linear elasticity theory in two-dimensional domains with interfaces highly oscillating between two circles[J]. Acta Mechanica, 2011, 218(3-4): 333-348.
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