Improved successive constraint method based a posteriori error estimate for reduced basis approximation of 2D Maxwell"s problem
Improved successive constraint method based a posteriori error estimate for reduced basis approximation of 2D Maxwell"s problem
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基于后验误差估计的改进连续约束方法用于二维麦克斯韦问题的简化基近似
DOI：
10.1051/m2an/2009037
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Jerónimo Rodríguez
中科院分区：
文献类型：
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作者：
Yanlai Chen;J. Hesthaven;Y. Maday;Jerónimo Rodríguez
在仿射参数偏微分方程约化基近似的后验误差分析中，矫顽力和超稳定常数的下界的构造是必不可少的。见(Huynh et al.，C.R.Acad.)SCI。巴黎爵士。我是数学。345(2007)473-478)，作者提出了一种与离线/在线策略相兼容的有效方法，其中在线计算简化为在几个线性约束下最小化一个线性泛函。这些约束依赖于使用贪婪算法迭代获得的嵌套参数集。我们在这里改进了这个方法，使它变得更有效和更稳健，因为有两个相关的性质：(I)关于套集的大小的下界是通过单调过程得到的；(Ii)需要解决的特征问题更少。这种改进的Inf-Sup常数的评估然后被用于考虑参数相关的电磁腔问题的简化基近似，这既用于贪婪地构造基元，也用于随后验证简化基近似。我们考虑的问题对于某些参数选择具有共鸣特征，这些参数被方法很好地捕获。
In a posteriori error analysis of reduced basis approximations to affinely parametrized partial differential equations, the construction of lower bounds for the coercivity and inf-sup stability constants is essential. In (Huynh et al., C. R. Acad. Sci. Paris Ser. I Math. 345 (2007) 473-478), the authors presented an efficient method, compatible with an off-line/on-line strategy, where the on- line computation is reduced to minimizing a linear functional under a few linear constraints. These constraints depend on nested sets of parameters obtained iteratively using a greedy algorithm. We improve here this method so that it becomes more efficient and robust due to two related properties: (i) the lower bound is obtained by a monotonic process with respect to the size of the nested sets; (ii) less eigen-problems need to be solved. This improved evaluation of the inf-sup constant is then used to consider a reduced basis approximation of a parameter dependent electromagnetic cavity problem both for the greedy construction of the elements of the basis and the subsequent validation of the reduced basis approximation. The problem we consider has resonance features for some choices of the parameters that are well captured by the methodology.