Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Automatic triangular mesh generation of trimmed parametric surfaces for finite element analysis
Computer Aided Geometric Design
Improved adaptive quadrilateral mesh generation using fission elements
Advances in Engineering Software
Advances in Engineering Software
Topology-reducing surface simplification using a discrete solid representation
ACM Transactions on Graphics (TOG)
Surface Modeling for CAD - Cam
Surface Modeling for CAD - Cam
An improved procedure for 2D unstructured Delaunay mesh generation
Advances in Engineering Software
Mesh generation for implicit geometries
Mesh generation for implicit geometries
Journal of Computational Physics
Finite Element Mesh Generation
Finite Element Mesh Generation
Adaptive triangular element generation and optimization-based smoothing: Part 2. On the surface
Advances in Engineering Software
Computer Aided Geometric Design
Delaunay refinement algorithms for triangular mesh generation
Computational Geometry: Theory and Applications
Finite Elements in Analysis and Design
Adaptive triangular element generation and optimization-based smoothing: Part 2. On the surface
Advances in Engineering Software
Three-dimensional simulation of forging using tetrahedral and hexahedral elements
Finite Elements in Analysis and Design
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A systematic approach to adaptive triangular element generation and optimization-based smoothing on the plane is presented in this paper. The approach starts from the input geometry of a rough triangular element that needs to be remeshed in order to meet the desired mesh density. Several density specifying geometries are proposed to specify the desired mesh density distribution in a closed form. To reduce the geometrical error that is inevitable in remeshing, the boundary edges are interpolated by the third-order chord-length spline curves. A virtual grid method is employed in calculating the desired mesh density at an arbitrary point. In order to improve mesh quality, triangular elements are recursively modified through the local transformation processes including face splitting, edge splitting, edge collapsing and edge swapping together with the physically-based smoothing process. Finally, optimization of local mesh quality is carried out by an optimal nodal smoothing scheme. Several application examples are given to show the characteristics of the presented approach.