Parallel 3d shape optimization for cellular composites on large distributed-memory clusters

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.