Error Estimation for Model-Order Reduction of Finite-Element Parametric Problems
Error Estimation for Model-Order Reduction of Finite-Element Parametric Problems
复制标题
有限元参数问题模型降阶误差估计
DOI：
10.1109/tmag.2016.2539924
复制
发表时间：
2016
影响因子：
2.1
通讯作者：
T. Henneron
中科院分区：
文献类型：
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作者：
S. Clénet;T. Henneron
在计算电磁学中，为了求解参数模型，经常使用有限元（FE）方法。为了减少计算时间和内存需求，FE方法可以与模型降阶技术相结合，如适当的正交分解和（离散）经验插值方法。这三种数值方法分别引入了离散化误差、归约误差和插值误差。如果这三个误差的阶数相同，则参数模型的解将是有效的，因此需要对它们进行评估和比较。在本文中，我们提出了一个后验误差估计的基础上验证的本构关系，估计三个不同的错误。一个例子中的应用程序在静磁学与11个参数的处理，它是如何显示的误差估计可以用来控制和提高精度的解决方案的简化模型。
To solve a parametric model in computational electromagnetics, the finite-element (FE) method is often used. To reduce the computational time and the memory requirement, the FE method can be combined with the model-order reduction technique like the proper orthogonal decomposition and (discrete) empirical interpolation methods. These three numerical methods introduce the errors of discretization, reduction, and interpolation, respectively. The solution of the parametric model will be efficient if the three errors are of the same order and so they need to be evaluated and compared. In this paper, we propose an a posteriori error estimator based on the verification of the constitutive law, which estimates the three different errors. An example of application in magnetostatics with 11 parameters is treated where it is shown how the error estimator can be used to control and to improve the accuracy of the solution of the reduced model.