Volume and Feature Preservation in Surface Mesh Optimization

Mesh optimization is critical in numerical simulations involving complex or evolving geometry. Because of the geometric constraints, such as preservation of sharp features and conservation of volume, optimizing a surface mesh poses significant challenges, especially when a CAD model is unavailable. In this paper, we introduce a formulation of volume conservation in a local sense for surface meshes under smoothing or other types of mesh motion, and propose a simple and efficient technique to solve it. We also present a simple and robust feature detection technique to enhance the effectiveness of local volume conservation and mesh optimization. We present the theoretical foundation of our techniques and experimental study to demonstrate their effectiveness.