A geometric mesh smoothing algorithm related to damped oscillations
It provides a new smoothing method for mesh quality improvement in computational geometry and finite element analysis, but the results are only shown on example meshes without quantitative benchmarks.
The paper introduces a mesh smoothing algorithm for various element types, derived from a geometric transformation modeled as damped oscillations, and demonstrates its numerical performance on example meshes.
We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral and hexahedral meshes whose centerpiece is a simple geometric triangle transformation. The first part focuses on the mathematical properties of the element transformation. In particular, the transformation gives rise directly to a continuous model given by a system of coupled damped oscillations. Derived from this physical model, adaptive parameters are introduced and their benefits presented. The second part discusses the mesh smoothing algorithm based on the element transformation and its numerical performance on example meshes.