High-Order Mesh Morphing for Boundary and Interface Fitting to Implicit Geometries

TL;DR

This paper introduces a high-order mesh morphing technique that aligns mesh boundaries with implicit geometries, especially level set-defined interfaces, using a variational optimization approach with adaptive strategies.

Contribution

The method uniquely combines a source mesh representation of level set functions with adaptive penalty strategies within a variational framework for robust boundary and interface fitting.

Findings

Robust generation of boundary- and interface-fitted meshes in 2D and 3D.

Effective handling of curvilinear domains with different element types.

Adaptive strategies improve mesh alignment accuracy.

Abstract

We propose a method that morphs high-orger meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero isocontour of a smooth discrete function. Common examples of this scenario include using level set functions to represent material interfaces in multimaterial configurations, and evolving geometries in shape and topology optimization. The proposed method formulates the mesh optimization problem as a variational minimization of the sum of a chosen mesh-quality metric using the Target-Matrix Optimization Paradigm (TMOP) and a penalty term that weakly forces the selected faces of the mesh to align with the target surface. The distinct features of the method are use of a source mesh to represent the level set function with sufficient accuracy, and adaptive strategies for setting the penalization weight and selecting the faces of the mesh to be fit to the target isocontour of the level set field. We demonstrate that the proposed method is robust for generating boundary- and interface-fitted meshes for curvilinear domains using different element types in 2D and 3D.