A Morton-Type Space-Filling Curve for Pyramid Subdivision and Hybrid Adaptive Mesh Refinement

TL;DR

This paper introduces a new space-filling curve for pyramids to enable efficient, scalable hybrid adaptive mesh refinement connecting tetrahedral and hexahedral elements.

Contribution

It develops a novel Morton-type space-filling curve for pyramids and extends AMR algorithms to support hybrid meshes with pyramidal elements.

Findings

Efficient and scalable hybrid AMR framework demonstrated.

New space-filling curve effectively connects tetrahedral and hexahedral elements.

Algorithms for refinement, coarsening, and partitioning successfully generalized.

Abstract

The forest-of-refinement-trees approach allows for dynamic adaptive mesh refinement (AMR) at negligible cost. While originally developed for quadrilateral and hexahedral elements, previous work established the theory and algorithms for unstructured meshes of simplicial and prismatic elements. To harness the full potential of tree-based AMR for three-dimensional mixed-element meshes, this paper introduces the pyramid as a new functional element type; its primary purpose is to connect tetrahedral and hexahedral elements without hanging edges. We present a well-defined space-filling curve (SFC) for the pyramid and detail how the unique challenges on the element and forest level associated with the pyramidal refinement are resolved. We propose the necessary functional design and generalize the fundamental global parallel algorithms for refinement, coarsening, partitioning, and face ghost exchange to fully support this new element. Our demonstrations confirm the efficiency and scalability of this complete, hybrid-element dynamic AMR framework.