Structure-aware Structured Mesh Optimization

In order to use finite element analysis in industrial product analysis and verification,we should divide the domain of the problem into a collection of finite elements.The quality of finite element meshes is one of the key factors that affects the efficiency and accuracy of finite element analysis.So we should optimize the finite element meshes after mesh generation and editing to meet the requirements of finite element analysis.The existing mesh optimization methods improve mesh quality to a certain degree,while they still cannot get perfect results.This paper provides a structure-aware mesh optimization method that improves the quality of structured meshes.The contributions of this paper are as follows:(1)We present a structure-aware optimization technique considering structure information of the surface for quadrilateral meshes.First,we obtain key structure vertices and key structure lines based on 2D cross field.And then we obtain the grid points which should be constrained by key structure lines.Finally we improve quadrilateral mesh element quality by minimizing objective function defined in terms of shape metric of quadrilateral mesh elements and extracted structure information.(2)We present a structure-aware optimization technique considering structure information of the solid model for hexahedral meshes.First,we obtain key structure edge and key structure surfaces based on 3D frame field.And then we obtain the grid points which should be constrained by key structure surfaces.Finally we improve hexahedral mesh element quality by minimizing objective function defined in terms of shape metric of hexahedral mesh elements and extracted structure information.(3)We develop a graphical application providing mesh optimization,quality evaluation and mesh element retrieval.And we use this application to verify our algorithms.Experimental results show that our structure-aware optimization method can improve complex mesh quality significantly.