Parallel SFCbased mesh partitioning and load balancing Modern supercomputers allow the simulation of complex phenomena with increased accuracy. Eventually, this requires finer geometric discretizations with larger numbers of mesh elements. In this context, and extrapolating to the Exascale paradigm, meshing operations such as generation, adaptation or partition, become a critical issue within the simulation workflow. In this paper, we focus on mesh partitioning. In particular, we present some improvements carried out on an inhouse parallel mesh partitioner based on the Hilbert SpaceFilling Curve. Additionally, taking advantage of its performance, we present the application of the SFCbased partitioning for dynamic load balancing. This method is based on the direct monitoring of the imbalance at runtime and the subsequent repartitioning of the mesh. The target weights for the optimized partitions are evaluated using a leastsquares approximation considering all measurements from previous iterations. In this way, the final partition corresponds to the average performance of the computing devices engaged.

Parametrization quantization with free boundaries for trimmed quad meshing The generation of quad meshes based on surface parametrization techniques has proven to be a versatile approach. These techniques quantize an initial seamless parametrization so as to obtain an integer grid map implying a pure quad mesh. Stateoftheart methods following this approach have to assume that the surface to be meshed either has no boundary, or has a boundary which the resulting mesh is supposed to be aligned to. In a variety of applications this is not desirable and nonboundaryaligned meshes or gridparametrizations are preferred. We thus present a technique to robustly generate integer grid maps which are either boundaryaligned, nonboundaryaligned, or partially boundaryaligned, just as required by different applications. We thereby generalize previous work to this broader setting. This enables the reliable generation of trimmed quad meshes with partial elements along the boundary, preferable in various scenarios, from tiled texturing over design and modeling to fabrication and architecture, due to fewer constraints and hence higher overall mesh quality and other benefits in terms of aesthetics and flexibility.