Conforming to interface structured adaptive mesh refinement: 3D algorithm and implementation

Abstract

A new non-iterative mesh generation algorithm named conforming to interface structured adaptive mesh refinement (CISAMR) is introduced for creating 3D finite element models of problems with complex geometries. CISAMR transforms a structured mesh composed of tetrahedral elements into a conforming mesh with low element aspect ratios. The construction of the mesh begins with the structured adaptive mesh refinement of elements in the vicinity of material interfaces. An r-adaptivity algorithm is then employed to relocate selected nodes of nonconforming elements, followed by face-swapping a small fraction of them to eliminate tetrahedrons with high aspect ratios. The final conforming mesh is constructed by sub-tetrahedralizing remaining nonconforming elements, as well as tetrahedrons with hanging nodes. In addition to studying the convergence and analyzing element-wise errors in meshes generated using CISAMR, several example problems are presented to show the ability of this method for modeling 3D problems with intricate morphologies.