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

2026-02-24

AI Summary

This work addresses a critical bottleneck in dynamic adaptive mesh refinement (AMR) on three-dimensional hybrid meshes containing tetrahedral and hexahedral elements: the inefficient handling of pyramid elements due to the absence of an effective connectivity mechanism and hierarchical tree-based management. The paper presents the first Morton-type space-filling curve tailored for pyramid elements, establishing a comprehensive framework that supports both element-level and forest-level refinement while consistently resolving hanging edges across heterogeneous element types. By introducing a forest-of-refinement-trees data structure, parallel refinement/coarsening algorithms, partitioning strategies, and face-based ghost exchange techniques, the authors develop a highly efficient and scalable AMR system for hybrid meshes. Experimental results demonstrate excellent performance and strong scalability in large-scale parallel environments, significantly extending the applicability of tree-based AMR frameworks to complex hybrid grid configurations.

Technology Category

• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Responsible Web: Data and user privacy-enhancing technologies for the Web

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.

Problem

• adaptive mesh refinement
• pyramid element
• space-filling curve
• hybrid mesh
• hanging edges

Innovation

• pyramid element
• space-filling curve
• adaptive mesh refinement
• hybrid mesh
• parallel algorithms