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Numerical Solutions of the Euler Equations by Finite Volume Methods Using RungeKutta TimeStepping Schemes
, 1981
"... A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used to deter ..."
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Cited by 517 (78 self)
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to determine the steady transonic flow past an airfoil using an O mesh. Convergence to a steady state is accelerated by the use of a variable time step determined by the local Courant member, and the introduction of a forcing term proportional to the difference between the local total enthalpy and its free
Surface Reconstruction by Voronoi Filtering
 Discrete and Computational Geometry
, 1998
"... We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled ..."
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Cited by 405 (11 self)
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surfaces, where density depends on "local feature size", the output is topologically valid and convergent (both pointwise and in surface normals) to the original surface. We describe an implementation of the algorithm and show example outputs. 1 Introduction The problem of reconstructing a
Computing Geodesic Paths on Manifolds
 Proc. Natl. Acad. Sci. USA
, 1998
"... The Fast Marching Method [8] is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity. A ..."
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Cited by 294 (28 self)
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. As an application, we provide an optimal time algorithm for computing the geodesic distances and thereby extracting shortest paths on triangulated manifolds. 1 Introduction Sethian`s Fast Marching Method [8], is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M
Tetrahedral Mesh Generation by Delaunay Refinement
 Proc. 14th Annu. ACM Sympos. Comput. Geom
, 1998
"... Given a complex of vertices, constraining segments, and planar straightline constraining facets in E 3 , with no input angle less than 90 ffi , an algorithm presented herein can generate a conforming mesh of Delaunay tetrahedra whose circumradiustoshortest edge ratios are no greater than two ..."
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Cited by 133 (6 self)
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angles, although they are not all covered by the theoretical guarantee. 1 Introduction Meshes of triangles or tetrahedra have many applications, including interpolation, rendering, and numerical methods such as the finite element method. Most such applications demand more than just a triangulation
A Comparison of Mesh Simplification Algorithms
 Computers & Graphics
, 1997
"... In many applications the need for an accurate simplification of surface meshes is becoming more and more urgent. This need is not only due to rendering speed reasons, but also to allow fast transmission of 3D models in networkbased applications. Many different approaches and algorithms for mesh sim ..."
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Cited by 167 (8 self)
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of different topologypreserving methods, were run on a set of sample surfaces. We compared empirical computational complexities and the approximation accuracy of the resulting output meshes. 1 Introduction Triangles are the most popular drawing primitive. They are managed by all graphics libraries
Discontinuity Meshing for Radiosity
 Third Eurographics Workshop on Rendering
, 1992
"... The radiosity method is the most popular algorithm for simulating interreflection of light between diffuse surfaces. Most existing radiosity algorithms employ simple meshes and piecewise constant approximations, thereby constraining the radiosity function to be constant across each polygonal element ..."
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Cited by 92 (2 self)
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mesh, shadow. 1 Introduction One of the most challenging tasks of image synthesis in computer ...
A General Framework for Mesh Decimation
 in Proceedings of Graphics Interface
, 1998
"... The decimation of highly detailed meshes has emerged as an important issue in many computer graphics related fields. A whole library of different algorithms has been proposed in the literature. By carefully investigating such algorithms, we can derive a generic structure for mesh reduction schemes w ..."
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Cited by 94 (19 self)
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quality meshes while observing global error bounds. Introduction In several areas of computer graphics and geometric modeling, the representation of surface geometry by polygonal meshes is a well established standard. However, the complexity of the object models has increased much faster than the through
Optimal Point Placement for Mesh Smoothing
, 1997
"... We study the problem of moving a vertex in a finite element mesh to optimize the shapes of adjacent triangles. We show that many such problems can be solved in linear time using generalized linear programming. We also give efficient algorithms for some mesh smoothing problems that do not fit into th ..."
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Cited by 89 (5 self)
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into the generalized linear programming paradigm. 1 Introduction Unstructured mesh generation, a key step in the finite element method, can be divided into two stages. In point placement, the input domain is augmented by Steiner points and a preliminary mesh is formed, typically by Delaunay triangulation. In mesh
Quality Mesh Generation in Three Dimensions
, 1992
"... We show how to triangulate a three dimensional polyhedral region with holes. Our triangulation is optimal in the following two senses. First, our triangulation achieves the best possible aspect ratio up to a constant. Second, for any other triangulation of the same region into m triangles with b ..."
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Cited by 84 (3 self)
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with bounded aspect ratio, our triangulation has size n = O(m). Such a triangulation is desired as an initial mesh for a finite element mesh refinement algorithm. Previous three dimensional triangulation schemes either worked only on a restricted class of input, or did not guarantee wellshaped tetrahedra
WormHole Gossiping on Meshes
 In Second International EuroPar Conference, Volume I, number 1123 in LNCS
, 1996
"... Several algorithms for performing gossiping on one and higher dimensional meshes are presented. As a routing model, we assume the practically important wormhole routing. For onedimensional arrays, we give a novel lower bound and an asymptotically optimal gossiping algorithm. For twodimensional m ..."
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Cited by 6 (0 self)
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on the Paragon. For higher dimensional meshes, we give algorithms which are based on a generalized notion of a diagonal. 1 Introduction Meshes. One of the most thoroughly investigated interconnection schemes for parallel computation is the n \Theta n mesh, in which n 2 processing units, PUs, are connected
Results 1  10
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1,905