In this paper we use memory-distributed level set-based topology optimisation to design three-dimensional periodic piezoelectric materials with enhanced properties. We compare and assess several existing iterative solvers with respect to their weak scalability and find that an approximate Schur complement preconditioned generalized minimal residual method method demonstrates the best performance and scalability for solving the piezoelectric homogenisation equations. We use the developed techniques to computationally design high-resolution piezoelectric metamaterials with enhanced stiffness and piezoelectric properties that yield new insights into material design for sensor, hydrophone, and actuator applications. We suggest two robust structures with no fine-scale features features that exhibit enhanced piezoelectric properties several times larger than those of the base material. We find that level set-based topology optimisation is well suited to problems involving piezoelectricity and has the advantage of avoiding large regions of intermediate density material. Our memory-distributed level-set implementation is open source and provided for practitioners in the community.

翻译：本文采用基于水平集的内存分布式拓扑优化方法，设计具有增强性能的三维周期性压电材料。我们比较并评估了多种现有迭代求解器在弱可扩展性方面的表现，发现近似Schur补预条件广义最小残差法在求解压电均匀化方程时展现出最佳的性能与可扩展性。利用所开发的技术，我们通过计算设计了具有增强刚度和压电特性的高分辨率压电超材料，为传感器、水听器和致动器应用的材料设计提供了新的见解。我们提出了两种无细观特征的稳健结构，其压电性能比基体材料提升数倍。研究发现，基于水平集的拓扑优化方法非常适用于涉及压电特性的问题，并具有避免大范围中间密度材料分布的优势。我们的内存分布式水平集实现已开源，供领域内实践者使用。