We show that under suitable hypotheses on the nonporous material law and a geometric regularity condition on the pore space, Moulinec‐Suquet's basic solution scheme converges linearly. We also discuss for which derived solvers a (super)linear convergence behavior may be obtained, and for which such results do not hold, in general. The key technical argument relies on a specific subspace on which the homogenization problem is nondegenerate, and which is preserved by iterations of the basic scheme. Our line of argument is based in the nondiscretized setting, and we draw conclusions on the convergence behavior for discretized solution schemes in FFT‐based computational homogenization. Also, we see how the geometry of the pores' interface enters the convergence estimates. We provide computational experiments underlining our claims.

中文翻译：

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Lippmann-Schwinger求解器，用于带孔材料的计算均质化

我们证明，在关于无孔材料定律的适当假设以及在孔隙空间上的几何规则性条件下，Moulinec-Suquet的基本解方案是线性收敛的。通常，我们还将讨论可以为哪些派生的求解器获得（超）线性收敛行为，以及哪些结果不成立。关键技术论点依赖于特定子空间，在该子空间上均质化问题不会退化，并且通过基本方案的迭代得以保留。我们的论点基于非离散化设置，并且我们得出了基于FFT的计算均质化中离散解方案的收敛性结论。同样，我们看到了孔隙界面的几何形状如何进入收敛估计。我们提供强调我们主张的计算实验。