An isogeometric collocation method using superconvergent points
An isogeometric collocation method using superconvergent points
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DOI：
10.1016/j.cma.2014.11.038
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发表时间：
2015-02-01
影响因子：
7.2
通讯作者：
Rabczuk, Timon
中科院分区：
文献类型：
--
作者：
Anitescu, Cosmin;Jia, Yue;Rabczuk, Timon
我们提出了一种改进的IGA配置法，通过在标准Greville脓肿以外的点上配置来改进。这种方法与求解微分方程组的正交配置法和超收敛理论有关，因此我们称之为超配置法(IGA-SC)。通过仔细选择配置点，可以看出IGA-SC以类似于Galerkin解的速度以一阶导数(能量)范数收敛。这不同于Greville abscissae(IGA-C)的配置，在该配置中，奇多项式次数的能量范数的收敛通常是次优的。在一维、二维和三维数值算例中对该方法进行了测试，并与IGA-C和Galerkin方法(IGA-G)进行了比较。这种比较包括详细的成本与精度分析，这表明所提出的方法的效率有所提高，特别是对于奇多项式次数。(C)2014爱思唯尔B.V.保留所有权利。
We develop an IGA collocation method modified by collocating at points other than the standard Greville abscissae. The method is related to orthogonal collocation used for solving differential equations and to the superconvergence theory, therefore we refer to this method as "super-collocation" (IGA-SC). By carefully choosing the collocation points, it can be seen that the IGA-SC converges in the first derivative (energy) norms at rates similar to that of the Galerkin solution. This is different from the collocation at Greville abscissae (IGA-C), where the convergence in energy norm for odd polynomial degrees is typically suboptimal. The method is tested on 1D, 2D and 3D numerical examples, in which it is compared to IGA-C and Galerkin's method (IGA-G). The comparison includes a detailed cost vs. accuracy analysis, which shows an improved efficiency of the proposed method in particular for odd polynomial degrees. (C) 2014 Elsevier B.V. All rights reserved.