Classical solution methods in fast Fourier transform‐based computational micromechanics operate on, either, compatible strain fields or equilibrated stress fields. By contrast, polarization schemes are primal‐dual methods whose iterates are neither compatible nor equilibrated. Recently, it was demonstrated that polarization schemes may outperform the classical methods. Unfortunately, their computational power critically depends on a judicious choice of numerical parameters. In this work, we investigate the extension of polarization methods by Anderson acceleration and demonstrate that this combination leads to robust and fast general‐purpose solvers for computational micromechanics. We discuss the (theoretically) optimum parameter choice for polarization methods, describe how Anderson acceleration fits into the picture, and exhibit the characteristics of the newly designed methods for problems of industrial scale and interest.

中文翻译：

---

基于快速傅立叶变换的计算均质化的Anderson加速极化方案

基于快速傅立叶变换的计算微力学中的经典求解方法在兼容的应变场或平衡的应力场上运行。相比之下，极化方案是原始对偶方法，其迭代既不兼容也不平衡。最近，已证明极化方案可能优于经典方法。不幸的是，它们的计算能力主要取决于对数字参数的明智选择。在这项工作中，我们研究了通过安德森加速度对极化方法的扩展，并证明了这种组合可为计算微力学带来健壮且快速的通用求解器。我们讨论了极化方法的（理论上）最佳参数选择，描述了安德森加速度如何适合图像，