Automatic Grid Generation Using Spatially Based Trees

15.1 1ntroduction 15.2 Recursive Domain Subdivisions to Define Spatially Based Trees 15.3 Quadtrees and Octrees for Automatic Mesh Generation 15.4 Tree Construction for Automatic Mesh Generation Preliminaries • Mesh Control and Octant Sizes • Definitions of Octree • Information Stored in the Tree 15.5 Mesh Generation within the Tree Cells Meshing Interior Cells • Meshing Boundary Cells 15.6 Mesh Finalization Processes Node Point Repositioning • Elimination of Poorly Sized and Shaped Elements Caused by Interactions of the Object Boundary and the Tree • Three-Dimensional Mesh Modifications to Improve Mesh Quality • A Couple of Examples 15.7 Closing Remarks

[1]  Mark S. Shephard,et al.  Automatic mesh generation allowing for efficient a priori and a posteriori mesh refinement , 1986 .

[2]  Mark S. Shephard,et al.  Automatic three‐dimensional mesh generation by the finite octree technique , 1984 .

[3]  Paul-Louis George,et al.  Optimization of Tetrahedral Meshes , 1995 .

[4]  Moshe Shpitalni,et al.  Finite element mesh generation via switching function representation , 1989 .

[5]  K. R. Grice,et al.  Robust, geometrically based, automatic two‐dimensional mesh generation , 1987 .

[6]  Mark S. Shephard,et al.  The versatility of automatic mesh generators based on tree structures and advanced geometric constructs , 1988 .

[7]  Mukul Saxena,et al.  Automatic mesh generation from solid models based on recursive spatial decompositions , 1989 .

[8]  Renato Perucchio,et al.  Toward automatic finite element analysis , 1987 .

[9]  Chris L. Jackins,et al.  Oct-trees and their use in representing three-dimensional objects , 1980 .

[10]  N. Sapidis,et al.  Combining recursive spatial decompositions and domain Delaunay tetrahedrizations for meshing arbitrarily shaped curved solid models , 1993 .

[11]  M. D. Mikhailov.  On problems with boundary conditions of the u= unknown constant , 1988 .

[12]  Ajay Kela.  Hierarchical octree approximations for boundary representation-based geometric models , 1989 .

[13]  Hanan Samet,et al.  Applications of spatial data structures , 1989 .

[14]  M. Shephard,et al.  A combined octree/delaunay method for fully automatic 3‐D mesh generation , 1990 .

[15]  M. Shephard,et al.  Reliability of automatic 3D mesh generation , 1992 .

[16]  E. K. Buratynski.  A fully automatic three-dimensional mesh generator for complex geometries , 1990 .

[17]  M. Saxena,et al.  Parallel fem algorithms based on recursive spatial decomposition—I. Automatic mesh generation , 1992 .

[18]  B Wördenweber.  Finite element mesh generation , 1984 .

[19]  Moshe Shpitalni,et al.  Switching Function Based Representation — an Alternative to Quadtree Encoding for Manufacturing Systems , 1985 .

[20]  Mark S. Shephard.  Update to: Approaches to the Automatic Generation and Control of Finite Element Meshes , 1996 .

[21]  Rolf Bünten,et al.  Automatic generation of hexahedral finite element meshes , 1995, Comput. Aided Geom. Des..