A new space-filling curves for adaptive mesh refinement
This work introduces a new discrete space-filling curve (SFC) for elements that can be represented by a set of inequalities x_i ≤ x_j and 0 ≤ x_i ≤ 1. This includes the most often used elements in 2D (quadrilaterals and triangles) and 3D (hexahedrons, prisms, pyramids, tetrahedrons). The new SFC combines ideas from the Freudenthal-Kuhn triangulation and the Morton SFC. By representing the inequalities as directed edges in a graph on the coordinates, a refinement scheme can be represented as a graph. The cyclefree orientations of this graph represent the valid types in the refinement scheme. This new space-filling curve can be used for tree-based refinement of hybrid coarse meshes, i.e. meshes consisting of different element shapes. It allows for a compact representation of the refined elements and a fast computation of hierarchical, geometrical and topological features. Its structure enables a templated implementation of the interface functionality needed for adaptive mesh refinement by the AMR library t8code. Thus, maintenance and code readability is increased and code duplication minimized. t8code is a mesh refinement library for scalable dynamic adaptive mesh refinement on hybrid meshes. Its modular approach provides high-level functionality (New, Adapt, Partition, Ghost, Balance) to the application, using low-level space-filling curve functionality.
