A space-filling curve for pyramidal adaptive mesh refinement

Abstract

In this thesis we present a space-filling curve for pyramid elements. We use the new approach for the formulation of discrete space-filling curves presented by Holke and develop a space-filling curve for pyramids that is based on the Morton-code for tetrahedra. We prove, that our curve fits the task of adaptive mesh refinement (AMR), namely that local operations on the mesh change the curve only locally. Furthermore, we develop the algorithms to use pyramids for AMR and implement them in the t8code library. We enable the support of pyramidal elements for the New, Partition, Adapt, Ghost and Balance high-level algorithms of t8code, which also results in a modified version of t8code. Using the JUWELS Supercomputer we achieve very good to ideal scaling behaviour for adaptive mesh refinement, partitioning, computing the ghost elements and for computing a mesh that fulfils a 2:1 balance condition. We achieve fast run times for the initial refinement of a mesh. Further runtime analysis shows, that except for the initial refinement, our modified version of t8code is as fast as the state-of-the-art version of t8code without pyramids. We present runtime results for meshes with up to 5.1e10 elements, and prove that our approach scales perfectly in that case.