SIAM Journal on Scientific Computing, Volume 42, Issue 3, Page B581-B607, January 2020.
In this paper we consider a numerical homogenization technique for curl-curl problems that is based on the framework of the localized orthogonal decomposition and which was proposed in [D. Gallistl, P. Henning, and B. Verfürth, SIAM J. Numer. Anal., 56 (2018), pp. 1570--1596] for problems with essential boundary conditions. The findings of the aforementioned work establish quantitative homogenization results for the time-harmonic Maxwell's equations that hold beyond assumptions of periodicity; however, a practical realization of the approach was left open. In this paper, we transfer the findings from essential boundary conditions to natural boundary conditions, and we demonstrate that the approach yields a computable numerical method. We also investigate how boundary values of the source term can affect the computational complexity and accuracy. Our findings will be supported by various numerical experiments, both in 2D and 3D.

中文翻译：

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时谐麦克斯韦方程组的计算均质化

SIAM科学计算杂志，第42卷，第3期，第B581-B607页，2020年1月。
在本文中，我们考虑了一种基于卷曲正交问题的数值均化技术，该技术基于局部正交分解的框架，并在[D. Gallistl，P。Henning和B.Verfürth，SIAM J. Numer。Anal。，56（2018），pp。1570--1596]。上述工作的发现为时谐麦克斯韦方程组建立了定量均质化结果，该均质结果超出了周期性的假设。然而，该方法的实际实现尚待解决。在本文中，我们将发现从基本边界条件转移到自然边界条件，并证明该方法产生了可计算的数值方法。我们还研究了源项的边界值如何影响计算的复杂性和准确性。我们的发现将得到2D和3D各种数值实验的支持。