论文标题
对计算均质化的几种基于FFT的方案的数值分析
Numerical analysis of several FFT-based schemes for computational homogenization
论文作者
论文摘要
我们研究了几种基于FFT的方案的融合，这些方案被广泛应用于计算均质化中以得出有效系数，而这里的“收敛”一词意味着限制行为是将空间分辨率作为无限限度的空间分辨率。这些方案包括Moulinec-Suquent的方案[Comput Method Appl M，157（1998），第69-94页]，Willot的方案[ComptesRendusMécanique，343（2015），第232-245页，第232-245页]，以及FEM方案[Int J Numer Meth Eng，109（2017）Eng，109（2017），Pp。1461-1-1-1-49]。在某些合理的假设下，我们证明这些方案获得的有效系数都是收敛于理论的。此外，对于FEM方案，我们可以在其他规律性假设下提出几个收敛速率估计。
We study the convergences of several FFT-based schemes that are widely applied in computational homogenization for deriving effective coefficients, and the term "convergence" here means the limiting behaviors as spatial resolutions going to infinity. Those schemes include Moulinec-Suquent's scheme [Comput Method Appl M, 157 (1998), pp. 69-94], Willot's scheme [Comptes Rendus Mécanique, 343 (2015), pp. 232-245], and the FEM scheme [Int J Numer Meth Eng, 109 (2017), pp. 1461-1489]. Under some reasonable assumptions, we prove that the effective coefficients obtained by those schemes are all convergent to the theoretical ones. Moreover, for the FEM scheme, we can present several convergence rate estimates under additional regularity assumptions.
