A Comparison of High Order Interpolation Nodes for the Pyramid

TL;DR

This paper compares high order interpolation nodes for pyramids, aiming to improve mesh construction by adapting tetrahedral node optimization techniques to pyramids with face node constraints.

Contribution

It introduces adapted procedures for constructing optimized pyramid nodal sets, generalizing tetrahedral node construction methods for better mesh compatibility.

Findings

Enhanced pyramid nodal sets with optimized interpolation properties

Improved compatibility of pyramid faces with tetrahedral and hexahedral meshes

Generalized Warp and Blend construction for pyramids

Abstract

The use of pyramid elements is crucial to the construction of efficient hex-dominant meshes. For conforming nodal finite element methods with mixed element types, it is advantageous for nodal distributions on the faces of the pyramid to match those on the faces and edges of hexahedra and tetrahedra. We adapt existing procedures for constructing optimized tetrahedral nodal sets for high order interpolation to the pyramid with constrained face nodes, including two generalizations of the explicit Warp and Blend construction of nodes on the tetrahedron.