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

TL;DR

This paper introduces a novel mesh optimization method that uses finite element functions to control high-order curved meshes, enabling surface fitting and tangential relaxation without geometric operations, suitable for dynamic geometries.

Contribution

The method uniquely employs implicit surface definitions via finite element functions, eliminating the need for CAD or analytic parametrizations in mesh optimization.

Findings

Avoids geometric surface projections

Applicable to dynamic and complex geometries

Enhances mesh quality for high-order curved meshes

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.