Novel design and analysis of generalized FE methods based on locally optimal spectral approximations
Novel design and analysis of generalized FE methods based on locally optimal spectral approximations
复制标题
基于局部最优谱近似的广义有限元方法的新颖设计和分析
DOI：
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
T. Dodwell
中科院分区：
文献类型：
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作者：
Chupeng Ma;Robert Scheichl;T. Dodwell
In this paper, the generalized finite element method (GFEM) for solving second order elliptic equations with rough coefficients is studied. New optimal local approximation spaces for GFEMs based on local eigenvalue problems involving a partition of unity are presented. These new spaces have advantages over those proposed in [I. Babuska and R. Lipton, Multiscale Model.\;\,Simul., 9 (2011), pp.~373--406]. First, in addition to a nearly exponential decay rate of the local approximation errors with respect to the dimensions of the local spaces, the rate of convergence with respect to the size of the oversampling region is also established. Second, the theoretical results hold for problems with mixed boundary conditions defined on general Lipschitz domains. Finally, an efficient and easy-to-implement technique for generating the discrete $A$-harmonic spaces is proposed which relies on solving an eigenvalue problem associated with the Dirichlet-to-Neumann operator, leading to a substantial reduction in computational cost. Numerical experiments are presented to support the theoretical analysis and to confirm the effectiveness of the new method.
通过自适应边缘基函数实现多尺度线性椭圆偏微分方程的指数收敛
影响因子：
1.6
作者：
Chen, Yifan;Hou, Thomas Y.;Wang, Yixuan
通讯作者：
Wang, Yixuan
DOI：
10.2478/cmam-2012-0027
发表时间：
2012
期刊：
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影响因子：
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作者：
V. Dolean;F. Nataf;Robert Scheichl;N. Spillane
通讯作者：
V. Dolean;F. Nataf;Robert Scheichl;N. Spillane
高性能沙丘模块，用于解决大规模、强各向异性椭圆问题及其在航空航天复合材料中的应用
影响因子：
6.3
作者：
Butler R
通讯作者：
Butler R