Scalable Mesh Generation with Refinement Patterns via High-order Basis

This paper presents a novel mesh generation approach developed at the University of Minnesota. The method combines a topology-based framework with a mesh optimization algorithm and uses high-order (curved) elements to construct low-order (linear) meshes at scale. These low-order mesh are referred to as target meshes. The approach greatly reduces the mesh generation cost by performing the computationally expensive mesh optimization on a coarse high-order mesh. Construction of the target mesh is then a simple evaluation of points at specified parametric values within the high-order elements. The method preserves the mesh quality characteristics of the high-order mesh while allowing for the introduction of mesh refinement patterns. Mesh refinement patterns are regions of the mesh where specialized cells are inserted to locally increase or decrease the mesh resolution. These refinement patterns are used to improve the alignment of the mesh with flow features while creating nearly isotropic cells throughout the domain. The refinement patterns offer hanging-node cells (2-to-1 cell transitions), diamond cells, and wedge cells for transitions, making the method useful for a wide range of physics solvers and applications. For development and testing purposes, the method has been implemented in the CrossLink geometry and mesh generation software [1].