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120
A Delaunay Refinement Algorithm for Quality 2Dimensional Mesh Generation
, 1995
"... We present a simple new algorithm for triangulating polygons and planar straightline graphs. It provides "shape" and "size" guarantees: All triangles have a bounded aspect ratio. The number of triangles is within a constant factor of optimal. Such "quality" triangulations are desirable as meshes for ..."
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Cited by 194 (0 self)
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We present a simple new algorithm for triangulating polygons and planar straightline graphs. It provides "shape" and "size" guarantees: All triangles have a bounded aspect ratio. The number of triangles is within a constant factor of optimal. Such "quality" triangulations are desirable as meshes for the nite element method, in which the running time generally increases with the number of triangles, and where the convergence and stability may be hurt by very skinny triangles. The technique we use  successive refinement of a Delaunay triangulation  extends a mesh generation technique of Chew by allowing triangles of varying sizes. Compared with previous quadtreebased algorithms for quality mesh generation, the Delaunay refinement approach is much simpler and generally produces meshes with fewer triangles. We also discuss an implementation of the algorithm and evaluate its performance on a variety of inputs.
Mesh Generation And Optimal Triangulation
, 1992
"... We survey the computational geometry relevant to finite element mesh generation. We especially focus on optimal triangulations of geometric domains in two and threedimensions. An optimal triangulation is a partition of the domain into triangles or tetrahedra, that is best according to some cri ..."
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Cited by 180 (8 self)
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We survey the computational geometry relevant to finite element mesh generation. We especially focus on optimal triangulations of geometric domains in two and threedimensions. An optimal triangulation is a partition of the domain into triangles or tetrahedra, that is best according to some criterion that measures the size, shape, or number of triangles. We discuss algorithms both for the optimization of triangulations on a fixed set of vertices and for the placement of new vertices (Steiner points). We briefly survey the heuristic algorithms used in some practical mesh generators.
Voronoi Diagrams
 Handbook of Computational Geometry
"... Voronoi diagrams can also be thought of as lower envelopes, in the sense mentioned at the beginning of this subsection. Namely, for each point x not situated on a bisecting curve, the relation p x q defines a total ordering on S. If we construct a set of surfaces H p , p S,in3space such t ..."
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Cited by 143 (19 self)
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Voronoi diagrams can also be thought of as lower envelopes, in the sense mentioned at the beginning of this subsection. Namely, for each point x not situated on a bisecting curve, the relation p x q defines a total ordering on S. If we construct a set of surfaces H p , p S,in3space such that H p is below H q i# p x q holds, then the projection of their lower envelope equals the abstract Voronoi diagram.
Smooth Surface Reconstruction via Natural Neighbour Interpolation of Distance Functions
, 2000
"... We present an algorithm to reconstruct smooth surfaces of arbitrary topology from unorganised sample points and normals. The method uses natural neighbour interpolation, works in any dimension and allows to deal with non uniform samples. The reconstructed surface is a smooth manifold passing through ..."
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Cited by 119 (4 self)
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We present an algorithm to reconstruct smooth surfaces of arbitrary topology from unorganised sample points and normals. The method uses natural neighbour interpolation, works in any dimension and allows to deal with non uniform samples. The reconstructed surface is a smooth manifold passing through all the sample points. This surface is implicitly represented as the zeroset of some pseudodistance function. It can be meshed so as to satisfy a userdefined error bound. Experimental results are presented for surfaces in R³.
Optimistic parallelism requires abstractions
 In PLDI
, 2007
"... Irregular applications, which manipulate large, pointerbased data structures like graphs, are difficult to parallelize manually. Automatic tools and techniques such as restructuring compilers and runtime speculative execution have failed to uncover much parallelism in these applications, in spite o ..."
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Cited by 119 (20 self)
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Irregular applications, which manipulate large, pointerbased data structures like graphs, are difficult to parallelize manually. Automatic tools and techniques such as restructuring compilers and runtime speculative execution have failed to uncover much parallelism in these applications, in spite of a lot of effort by the research community. These difficulties have even led some researchers to wonder if there is any coarsegrain parallelism worth exploiting in irregular applications. In this paper, we describe two realworld irregular applications: a Delaunay mesh refinement application and a graphics application that performs agglomerative clustering. By studying the algorithms and data structures used in these applications, we show that there is substantial coarsegrain, data parallelism in these applications, but that this parallelism is very dependent on the input data and therefore cannot be uncovered by compiler analysis. In principle, optimistic techniques such as threadlevel speculation can be used to uncover this parallelism, but we argue that current implementations cannot accomplish this because they do not use the proper abstractions for the data structures in these programs. These insights have informed our design of the Galois system, an objectbased optimistic parallelization system for irregular applications. There are three main aspects to Galois: (1) a small number of syntactic constructs for packaging optimistic parallelism as iteration over ordered and unordered sets, (2) assertions about methods in class libraries, and (3) a runtime scheme for detecting and recovering from potentially unsafe accesses to shared memory made by an optimistic computation. We show that Delaunay mesh generation and agglomerative clustering can be parallelized in a straightforward way using the Galois approach, and we present experimental measurements to show that this approach is practical. These results suggest that Galois is a practical approach to exploiting data parallelism in irregular programs.
2000, ‘Delaunay triangulations and Voronoi diagrams for Riemannian manifolds
 ACM Symposium on Computational Geometry
"... For a sufficiently dense set of points in any closed Riemannian manifold, we prove that a unique Delannay triangulation exists. This triangulation has the same properties as in Euclidean space. Algorithms for constructing these triangulations will also be described. 1. ..."
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Cited by 59 (2 self)
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For a sufficiently dense set of points in any closed Riemannian manifold, we prove that a unique Delannay triangulation exists. This triangulation has the same properties as in Euclidean space. Algorithms for constructing these triangulations will also be described. 1.
Numerical Schemes for the HamiltonJacobi and Level Set Equations on Triangulated Domains
, 1997
"... Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the HamiltonJacobi (HJ), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the HJ equations. Unf ..."
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Cited by 56 (7 self)
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Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the HamiltonJacobi (HJ), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the HJ equations. Unfortunately, the basic scheme lacks proper Lipschitz continuity of the numerical Hamiltonian. By employing a "virtual" edge ipping technique, Lipschitz continuity of the numerical flux is restored on acute triangulations. Next, schemes are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous Hamiltonians. These schemes possess a discrete maximum principle on arbitrary triangulations and naturally exhibit proper Lipschitz continuity of the numerical Hamiltonian. Finally, a class of PetrovGalerkin approximations are considered. These schemes are stabilized via a leastsquares bilinear form. The PetrovGalerkin schemes do not possess a discrete...
Aspects of Unstructured Grids and FiniteVolume Solvers for the Euler and NavierStokes Equations (Part 4)
, 1995
"... this report, the model was tested on various subsonic and transonic flow problems: flat plates, airfoils, wakes, etc. The model consists of a single advectiondiffusion equation with source term for a field variable which is the product of turbulence Reynolds number and kinematic viscosity, e RT . ..."
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Cited by 56 (0 self)
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this report, the model was tested on various subsonic and transonic flow problems: flat plates, airfoils, wakes, etc. The model consists of a single advectiondiffusion equation with source term for a field variable which is the product of turbulence Reynolds number and kinematic viscosity, e RT . This variable is proportional to the eddy viscosity except very near a solid wall. The model equation is of the form: D( e RT ) Dt =(c ffl 2 f 2 (y + ) \Gamma c ffl 1 ) q e RT P +( + t oe R )r 2 ( e RT ) \Gamma 1 oe ffl (r t ) \Delta r( e RT ): (6:3:3) In this equation P is the production of turbulent kinetic energy and is related to the mean flow velocity rateofstrain and the kinematic eddy viscosity t . Equation (6.3.3) depends on distance to solid walls in two ways. First, the damping function f 2 appearing in equation (6.3.3) depends directly on distance to the wall (in wall units). Secondly, t depends on e R t and damping functions which require distance to the wall