Local refinement of simplicial grids based on the skeleton
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Summary
A novel approach to the development of a class of local simplicial refinement strategies and the numerical results obtained appear to confirm that the measure of degeneracy of subtetrahedra is bounded, and converges asymptotically to a fixed value when the refinement proceeds.
- Type
- article
- Published
- 2000-02-01
- Cited by
- 118
- References
- 31
- OpenAlex
- https://openalex.org/W1963991060
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:53383471
Keywords
Mathematics, Tetrahedron, Triangulation, Degeneracy (biology), Division (mathematics)
References
- An algorithm for coarsening unstructured meshes
- Quality Local Refinement of Tetrahedral Meshes Based on Bisection
- Higher-dimensional voronoi diagrams in linear expected time
- NEW LONGEST-EDGE ALGORITHMS FOR THE REFINEMENT AND/OR IMPROVEMENT OF UNSTRUCTURED TRIANGULATIONS
- Relationship between tetrahedron shape measures
- Error Estimates for Adaptive Finite Element Computations
- On faster convergence of the bisection method for certain triangles
- A Posteriori Error Analysis of Finite Element Solutions for One-Dimensional Problems
- Algorithms in Combinatorial Geometry
- An improved derefinement algorithm of nested meshes
- Efficient refinement/derefinement algorithm of nested meshes to solve evolution problems
- The use of adaptive grid refinement for badly behaved elliptic partial differential equations
- Construction of Three-Dimensional Improved-Quality Triangulations Using Local Transformations
- Optimal Multilevel Iterative Methods for Adaptive Grids
- A mesh-refinement scheme for finite element computations
- A posteriori error analysis and adaptive processes in the finite element method: Part II—adaptive mesh refinement
- A 3-D refinement algorithm suitable for adaptive and multi-grid techniques
- On the shape of tetrahedra from bisection
- How to Construct the Skeleton of CSG Objects
- A recursive approach to local mesh refinement in two and three dimensions
Cited by
- An object oriented method for tetrahedral mesh refinement
- Mesh Refinement Based on the 8-Tetrahedra Longest- Edge Partition
- Asymptotic Behavior of the Average of the Adjacencies of the Topological Entities in Some Simplex Partitions
- Neural Nets for Mesh Assessment
- Longest-edge n-section algorithms: Properties and open problems
- Local Convergence of Adaptive Methods for Nonlinear Partial Differential Equations
- Parameter estimation in a 3-D wind field adaptive model using GAs
- The Basis Refinement Method
- A mathematical proof of how fast the diameters of a triangle mesh tend to zero after repeated trisection
- Strong regularity of a family of face-to-face partitions generated by the longest-edge bisection algorithm
- Refinement based on longest-edge and self-similar four-triangle partitions
- Average adjacencies for tetrahedral skeleton-regular partitions
- Hexing the Tet
- Graph‐based data structures for skeleton‐based refinement algorithms
- Simplex and Diamond Hierarchies: Models and Applications
- Nonobtuse Tetrahedral Partitions that Refine Locally Towards Fichera-Like Corners
- Optimal multilevel methods for graded bisection grids
- Fractality of refined triangular grids and space-filling curves
- Proving the non-degeneracy of the longest-edge trisection by a space of triangular shapes with hyperbolic metric
- A patch/subdomain iteration framework and algorithm class for error indicator and mesh reliability calculations
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