Concrete mathematics: a foundation for computer science
Concrete mathematics: a foundation for computer science
On the shape of tetrahedra from bisection
Mathematics of Computation
Physically-based mesh generation: automated triangulation of surfaces and volumes via bubble packing
Physically-based mesh generation: automated triangulation of surfaces and volumes via bubble packing
A recursive approach to local mesh refinement in two and three dimensions
Journal of Computational and Applied Mathematics
Quality local refinement of tetrahedral meshes based on bisection
SIAM Journal on Scientific Computing
The 4-triangles longest-side partition of triangles and linear refinement algorithms
Mathematics of Computation
A 3D refinement/derefinement algorithm for solving evolution problems
Applied Numerical Mathematics - Special issue on numerical grid generation-technologies for advanced simulations
Non-equivalent partitions of d-triangles with Steiner points
Applied Numerical Mathematics - Special issue: Applied scientific computing - Grid generation, approximated solutions and visualization
Average adjacencies for tetrahedral skeleton-regular partitions
Journal of Computational and Applied Mathematics
Non-degeneracy study of the 8-tetrahedra longest-edge partition
Applied Numerical Mathematics
Block-balanced meshes in iterative uniform refinement
Computer Aided Geometric Design
Computational aspects of the refinement of 3D tetrahedral meshes
Journal of Computational Methods in Sciences and Engineering
Non-degeneracy study of the 8-tetrahedra longest-edge partition
Applied Numerical Mathematics
Average adjacencies for tetrahedral skeleton-regular partitions
Journal of Computational and Applied Mathematics
An overview of procedures for refining triangulations
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part I
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For any 2D triangulation τ, the 1-skeleton mesh of τ is the wireframe mesh defined by the edges of τ, while that for any 3D triangulation τ, the 1-skeleton and the 2-skeleton meshes, respectively, correspond to the wireframe mesh formed by the edges of τ and the "surface" mesh defined by the triangular faces of τ. A skeleton-regular partition of a triangle or a tetrahedra, is a partition that globally applied over each element of a conforming mesh (where the intersection of adjacent elements is a vertex or a common face, or a common edge) produce both a refined conforming mesh and refined and conforming skeleton meshes. Such a partition divides all the edges (and all the faces) of an individual element in the same number of edges (faces). We prove that sequences of meshes constructed by applying a skeleton-regular partition over each element of the preceding mesh have an associated set of difference equations which relate the number of elements, faces, edges and vertices of the nth and (n - 1)th meshes. By using these constitutive difference equations we prove that asymptotically the average number of adjacencies over these meshes (number of triangles by node and number of tetrahedra by vertex) is constant when n goes to infinity. We relate these results with the non-degeneracy properties of longest-edge based partitions in 2D and include empirical results which support the conjecture that analogous results hold in 3D.