Direct discretization of planar div-curl problems
SIAM Journal on Numerical Analysis
Discrete exterior calculus
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Generating the Voronoi-Delaunay Dual Diagram for Co-Volume Integration Schemes
ISVD '07 Proceedings of the 4th International Symposium on Voronoi Diagrams in Science and Engineering
On Nonobtuse Simplicial Partitions
SIAM Review
There Is No Face-to-Face Partition of R5 into Acute Simplices
Discrete & Computational Geometry
SIAM Journal on Scientific Computing
Well-centered meshing
PyDEC: Software and Algorithms for Discretization of Exterior Calculus
ACM Transactions on Mathematical Software (TOMS)
Technical note: Delaunay Hodge star
Computer-Aided Design
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An n-simplex is said to be n-well-centered if its circumcenter lies in its interior. We introduce several other geometric conditions and an algebraic condition that can be used to determine whether a simplex is n-well-centered. These conditions, together with some other observations, are used to describe restrictions on the local combinatorial structure of simplicial meshes in which every simplex is well-centered. In particular, it is shown that in a 3-well-centered (2-well-centered) tetrahedral mesh there are at least 7 (9) edges incident to each interior vertex, and these bounds are sharp. Moreover, it is shown that, in stark contrast to the 2-dimensional analog, where there are exactly two vertex links that prevent a well-centered triangle mesh in R^2, there are infinitely many vertex links that prohibit a well-centered tetrahedral mesh in R^3.