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.

翻译：细化森林方法能以可忽略的成本实现动态自适应网格细化（AMR）。该方法最初为四边形和六面体单元开发，前期研究已建立了针对单纯形和棱柱形单元非结构网格的理论与算法。为充分发挥基于树的AMR在三维混合单元网格中的潜力，本文引入金字塔作为新型功能单元类型，其主要功能是在不产生悬挂边的条件下连接四面体与六面体单元。我们提出了一种定义明确的金字塔单元空间填充曲线（SFC），并详细阐述了如何解决金字塔细化在单元层面和森林层面带来的独特挑战。我们提出了必要的功能设计方案，并将细化、粗化、分区及面层幽灵单元交换等核心全局并行算法进行泛化，以全面支持这种新型单元。实验验证了这套完整的混合单元动态AMR框架在效率与可扩展性方面的优越性。