Minimal surface-guided higher-order mesh generation for CAD models

Abstract

This paper presents a novel method for generating higher-order meshes for CAD surfaces by leveraging minimal surface theory to improve element shapes. We explore the concept of higher-order mesh distortion through deformation gradients and introduce an energy function designed to minimize the surface area of these meshes, providing a theoretical justification for its effectiveness in untangling. The process of mesh generation starts with segmenting CAD surfaces into linear elements, followed by the insertion of higher-order nodes within these elements. These nodes are then projected onto the CAD surface to form the initial higher-order elements. By optimizing energy functions related to minimal surfaces and the projection distances, we achieve high-quality, geometrically accurate higher-order surface meshes. Our method has been validated on complex geometries, showcasing its potential in creating effective higher-order meshes for industrial CAD models.