Reduced-Basis Approximation and A Posteriori Error Estimation for Many-Parameter Heat Conduction Problems
Reduced-Basis Approximation and A Posteriori Error Estimation for Many-Parameter Heat Conduction Problems
复制标题
多参数热传导问题的降基近似和后验误差估计
DOI：
10.1080/10407790802424204
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
S. Sen
中科院分区：
文献类型：
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作者：
S. Sen
缩减基（RB）方法使得能够在参数估计、设计、优化和控制的背景下重复和快速地评估参数化偏微分方程（PDE）约束的输入-输出关系。这些方法已成功地应用于少参数的问题[O（3）]。在这里，我们介绍有效的采样算法，使许多参数的有效探索。我们将RB方法应用到一个说明性的热传导问题，P = 25个参数，获得准确和认证的结果，在真实的时间与显着的计算节省相对于标准的有限元技术。
Reduced-basis (RB) methods enable repeated and rapid evaluation of parametrized partial differential equation (PDE)-constrained input–output relationships required in the context of parameter estimation, design, optimization, and control. These methods have been successfully applied to problems with few parameters [O(3)]. Here we introduce efficient sampling algorithms that enable the efficient exploration of many parameters. We apply the RB methods to an illustrative heat conduction problem with P = 25 parameters, obtaining accurate and certified results in real time with significant computational savings relative to standard finite-element techniques.