Adaptive Surface Fitting and Tangential Relaxation for High-Order Mesh Optimization

Abstract

We propose a new approach for controlling the characteristics of certain mesh faces during optimization of high-order curved meshes. The practical goals are tangential relaxation along initially aligned curved boundaries and internal surfaces, and mesh fitting to initially non-aligned surfaces. The distinct feature of the method is that it utilizes discrete finite element functions (for example level set functions) to define implicit surfaces, which are used to adapt the positions of certain mesh nodes. The algorithm does not require CAD descriptions or analytic parametrizations, and can be beneficial in computations with dynamically changing geometry, for example shape optimization and moving mesh multimaterial simulations. The main advantage of this approach is that it completely avoids geometric operations (e.g., surface projections), and all calculations can be performed through finite element operations.

Hex-Mesh Generation and Processing: a Survey

“…In particular, while the higher-order elements in the meshes it obtains may be inversion-free and high quality, the underlying linear mesh elements may remain inverted. Most recently, Knupp et al [2021] proposed a high-order hex-mesh optimization method that targets objects with no underlying CAD representation but using on the fly computed implicit surface representations. It specifically targets conforming meshes with interior surfaces and is advertised as well suited for computations with dynamically changing geometry.…”