Geometric Constrained Scalable Algorithm for PDE-Constrained Shape Optimization

In this project, the parallel performance of shape optimization schemes is investigated using varying core counts for several levels of refinement. Weak scalability results are presented for up to 49 152 cores on the national supercomputer HAWK, and the effects on performance related to a high number of cores-per-node is discussed. The algorithm developed during the project is benchmarked in an optimal design problem oriented towards fluid dynamics applications. This work is concerned with situations where it is necessary to retain certain geometric properties, such as volume and barycenter. Therefore, the optimization process solves a PDE-constrained optimization problem that incorporates the imposed geometric constraints in the descent directions. It is done by solving the corresponding minimization problem in appropriate Banach spaces. 2d and 3d results are presented where the domain needs a high number of elements to be properly defined. The system of equations consists of a very large number of degrees of freedom, thus it can only be solved efficiently via the most modern distributed-memory systems, such as HAWK at HLRS.