Results 1  10
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24
An anglebased approach to twodimensional mesh smoothing
 In Proceedings, 9th International Meshing Roundtable
, 2000
"... We present an effective and easytoimplement anglebased smoothing scheme for triangular, quadrilateral and triquad mixed meshes. For each mesh node our algorithm compares all the pairs of adjacent angles incident to the node and adjusts these angles so that they become equal in the case of a tria ..."
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Cited by 43 (1 self)
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We present an effective and easytoimplement anglebased smoothing scheme for triangular, quadrilateral and triquad mixed meshes. For each mesh node our algorithm compares all the pairs of adjacent angles incident to the node and adjusts these angles so that they become equal in the case of a triangular mesh and a quadrilateral mesh, or they form the ideal ratio in the case of a triquad mixed mesh. The size and shape quality of the mesh after this smoothing algorithm is much better than that after Laplacian smoothing. The proposed method is superior to Laplacian smoothing by reducing the risk of generating inverted elements and increasing the uniformity of element sizes. The computational cost of our smoothing method is yet much lower than optimizationbased smoothing. To prove the effectiveness of this algorithm, we compared errors in approximating a given analytical surface by a set of bilinear patches corresponding to a mesh with Laplacian smoothing and a mesh with the proposed smoothing method. The experiments show that a mesh smoothed with our method has roughly 20 % less approximation error.
High Quality Compatible Triangulations
 PROCEEDINGS OF 11TH INTERNATIONAL MESHING ROUNDTABLE
, 2002
"... Compatible meshes are isomorphic meshing of the interiors of two polygons having a correspondence between their vertices. Compatible meshing may be used for constructing sweeps, suitable for finite element analysis, between two base polygons. They may also be used for meshing a given sequence of pol ..."
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Cited by 12 (2 self)
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Compatible meshes are isomorphic meshing of the interiors of two polygons having a correspondence between their vertices. Compatible meshing may be used for constructing sweeps, suitable for finite element analysis, between two base polygons. They may also be used for meshing a given sequence of polygons forming a sweep. We present a method to compute compatible triangulations of planar polygons with a very small number of Steiner (interior) vertices. Being close to optimal in terms of the number of Steiner vertices, these compatible triangulations are usually not of high quality, i.e., do not have wellshaped triangles. We show how to increase the quality of these triangulations by adding Steiner vertices in a compatible manner, using several novel techniques for remeshing and mesh smoothing. The total scheme results in highquality compatible meshes with a small number of triangles. These meshes may then be morphed to obtain the intermediate triangulated sections of a sweep, if needed.
Anisotropic mesh adaptation for transient flows simulations
 In Proc. of 12th Int. Meshing Rountable (Santa Fe
, 2003
"... Unstructured mesh adaptation has already revealed very efficient for computing an accurate solution in a reasonnable amount of time on current PC architectures. Two features are still missing in the adaptation scheme: (i) the creation of arbitrary anisotropic meshes and (ii) the capture of transient ..."
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Cited by 6 (1 self)
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Unstructured mesh adaptation has already revealed very efficient for computing an accurate solution in a reasonnable amount of time on current PC architectures. Two features are still missing in the adaptation scheme: (i) the creation of arbitrary anisotropic meshes and (ii) the capture of transient phenomena. Therefore, in this paper, we propose a global scheme suitable to compute steadystate as well as transient problems, based on anisotropic mesh adaptation. Several examples of numerical simulations in CFD are provided to emphasize the efficiency of the proposed approach.
Mesh and Solver Coadaptation in Finite Element Methods for Anisotropic Problems, Numerical Methods for Differential Equations
"... Mesh generation and algebraic solver are two important aspects of the finite element methodology. In this article, we are concerned with the joint adaptation of the anisotropic triangular mesh and the iterative algebraic solver. Using generic numerical examples pertaining to the accurate and efficie ..."
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Cited by 5 (2 self)
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Mesh generation and algebraic solver are two important aspects of the finite element methodology. In this article, we are concerned with the joint adaptation of the anisotropic triangular mesh and the iterative algebraic solver. Using generic numerical examples pertaining to the accurate and efficient finite element solution of some anisotropic problems, we hereby demonstrate that the processes of geometric mesh adaptation and the algebraic solver construction should be adapted simultaneously. We also propose some techniques applicable to the coadaptation of both anisotropic meshes and linear solvers. © 2005 Wiley
Gridfields: ModelDriven Data Transformation in the Physical Sciences
, 2006
"... Scientists’ ability to generate and store simulation results is outpacing their ability to analyze them via ad hoc programs. We observe that these programs exhibit an algebraic structure that can be used to facilitate reasoning and improve performance. In this dissertation, we present a formal data ..."
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Cited by 4 (2 self)
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Scientists’ ability to generate and store simulation results is outpacing their ability to analyze them via ad hoc programs. We observe that these programs exhibit an algebraic structure that can be used to facilitate reasoning and improve performance. In this dissertation, we present a formal data model that exposes this algebraic structure, then implement the model, evaluate it, and use it to express, optimize, and reason about data transformations in a variety of scientific domains. Simulation results are defined over a logical grid structure that allows a continuous domain to be represented discretely in the computer. Existing approaches for manipulating these gridded datasets are incomplete. The performance of SQL queries that manipulate large numeric datasets is not competitive with that of specialized tools, and the upfront effort required to deploy a relational database makes them unpopular for dynamic scientific applications. Tools for processing multidimensional arrays can only capture regular, rectilinear grids. Visualization libraries accommodate arbitrary grids, but no algebra has been developed to simplify their use and afford optimization. Further, these libraries are data dependent—physical
Accurate and high quality triangle models from D grey scale images
 Utrecht University
, 2002
"... Visualization of medical data requires the extraction of surfaces that represent the boundaries of objects of interest. This paper describes a method that combines finding these boundaries accurately and ensuring that this surface consists of high quality triangles. The latter is important for su ..."
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Cited by 3 (1 self)
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Visualization of medical data requires the extraction of surfaces that represent the boundaries of objects of interest. This paper describes a method that combines finding these boundaries accurately and ensuring that this surface consists of high quality triangles. The latter is important for subsequent visualization and simulation. We show that the surfaces created using this method are both accurate and have good quality triangles.
Evaporation: a Technique for Visualizing Mesh Quality
 Proceedings of the 8th International Meshing Roundtable, South Lake Tahoe
, 1999
"... The work described here addresses information generated during mesh preprocessing, specifically mesh quality indicators derived on a perelement basis. A technique is introduced for visualizing perelement quality indicators which allows the researcher to see the spatial distribution of the indicato ..."
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Cited by 3 (2 self)
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The work described here addresses information generated during mesh preprocessing, specifically mesh quality indicators derived on a perelement basis. A technique is introduced for visualizing perelement quality indicators which allows the researcher to see the spatial distribution of the indicator across the entire mesh. The technique uses time as a display axis, creating a succession of images in which the mesh is gradually eroded down to its “worst ” elements. The technique is described algorithmically here and is applied to an example. In addition to supplying the user with the locations of the worst mesh elements, the technique appears to provide its user with a good highlevel understanding of the relationship between mesh geometry and quality. This may also prove to be a useful technique for observing successive refinements of a mesh.
Geometrical Mesh Improvement Properties of Delaunay Terminal Edge Refinement
, 2006
"... The use of edge based refinement in general, and Delaunay terminal edge refinement in particular are well established for planar meshing, but largely on a heuristic basis. In this paper, we present a series of theoretical results on the geometric mesh improvement properties of these methods. The dis ..."
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Cited by 3 (1 self)
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The use of edge based refinement in general, and Delaunay terminal edge refinement in particular are well established for planar meshing, but largely on a heuristic basis. In this paper, we present a series of theoretical results on the geometric mesh improvement properties of these methods. The discussion is based on refining a mesh to meet a specified angle tolerance. 1
Mesh Quality for Threedimensional Finite Element Solutions on Anisotropic Meshes
 Proceedings of FEM3D, Kr ' izek
, 2001
"... The concept of solutionbased mesh quality is driven by the need not only to consider whether a good solution can be produced on a given mesh, but also whether a mesh can be considered appropriate for a given solution. The aim of this paper is to look at different ways in which such a mesh can be ..."
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Cited by 2 (1 self)
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The concept of solutionbased mesh quality is driven by the need not only to consider whether a good solution can be produced on a given mesh, but also whether a mesh can be considered appropriate for a given solution. The aim of this paper is to look at different ways in which such a mesh can be produced for a model hyperbolic problem, which may be regarded as typical of flow problems with directional solutions. Given an error estimate, standard hrefinement schemes can reduce this error to below userspecified levels by increasing the resolution where the error is large, however in three dimensions such an approach can lead to excessively large meshes. In particular, for problems containing strongly directional features it may be possible to reduce the error by refining the mesh in a directional manner, and thus with greater efficiency than uniform hrefinement. The approach adopted is to consider an rrefinement scheme combined with an existing isotropic hrefinement appro...
Geometric Error Estimation
 in "ADVCOMP 2010: The Fourth International Conference on Advanced Engineering Computing and Applications in Sciences, IARIA conference
"... Abstract—An essential prerequisite for the numerical finite element simulation of physical problems expressed in terms of PDEs is the construction of an adequate mesh of the domain. This first stage, which usually involves a fully automatic mesh generation method, is then followed by a computational ..."
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Abstract—An essential prerequisite for the numerical finite element simulation of physical problems expressed in terms of PDEs is the construction of an adequate mesh of the domain. This first stage, which usually involves a fully automatic mesh generation method, is then followed by a computational step. One can show that the quality of the solution strongly depends on the shape quality of the mesh of the domain. At the second stage, the numerical solution obtained with the initial mesh is generally analyzed using an appropriate a posteriori error estimator which, based on the quality of the solution, indicates whether or not the solution is accurate. The quality of the solution is closely related to how well the mesh corresponds to the underlying physical phenomenon, which can be quantified by the element sizes of the mesh. An a posteriori error estimation based on the interpolation error depending on the Hessian of the solution seems to be well adapted to the purpose of adaptive meshing. In this paper, we propose a new interpolation error estimation based on the local deformation of the Cartesian surface representing the solution. This methodology is generally used in the context of surface meshing. In our example, the proposed methodology is applied to minimize the interpolation error on an image whose grey level is considered as being the solution. Keywordsa posteriori error estimation; interpolation error; mesh adaptation; surface curvature. I.