论文标题
平行的3D形状优化针对大型分布式内存簇上的细胞复合材料的优化
Parallel 3d shape optimization for cellular composites on large distributed-memory clusters
论文作者
论文摘要
皮肤建模是一个正在进行的研究领域，可从现代平行算法中受益匪浅。本文旨在将形状优化应用于计算细胞大小和排列，以最大程度地减少人类皮肤上层的细胞复合材料模型。在德国HLRS，HLRS的分布式内存簇HEN上采用并测试了一种梯度拟化的形状优化算法。在两个基准测试中研究了该算法的性能。首先，相对于纯几何方面优化了细胞结构。然后将模型扩展，以便将复合材料优化以承受应用的变形。在这两种情况下，都根据弱和强可伸缩性研究了该算法。几何测试的结果反映了开尔文的猜想，即四甲苯二酚具有最小表面细胞的最佳填充空间设计。选择了PDE受限的测试用例，以证明变形梯度惩罚对复合材料中细胞间通道的影响及其对多族收敛的影响。提出了一项扩展研究，最多可用于12,288个核心和30亿座DOF。
Skin modeling is an ongoing research area that highly benefits from modern parallel algorithms. This article aims at applying shape optimization to compute cell size and arrangement for elastic energy minimization of a cellular composite material model for the upper layer of the human skin. A gradient-penalized shape optimization algorithm is employed and tested on the distributed-memory cluster Hazel Hen, HLRS, Germany. The performance of the algorithm is studied in two benchmark tests. First, cell structures are optimized with respect to purely geometric aspects. The model is then extended such that the composite is optimized to withstand applied deformations. In both settings, the algorithm is investigated in terms of weak and strong scalability. The results for the geometric test reflect Kelvin's conjecture that the optimal space-filling design of cells with minimal surface is given by tetrakaidecahedrons. The PDE-constrained test case is chosen in order to demonstrate the influence of the deformation gradient penalization on fine inter-cellular channels in the composite and its influence on the multigrid convergence. A scaling study is presented for up to 12,288 cores and 3 billion DoFs.
