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Hex-dominant meshing approach based on frame field smoothness ; ; et al in Procedia Engineering (2014), 82 Detailed reference viewed: 19 (1 ULg)Computing bounds on the geometrical quality of 2D curvilinear finite elements Johnen, Amaury ; ; et al Conference (2013, April 25) The development of high-order computational methods for solving partial differen- tial equations on unstructured grids has been underway for many years. Such meth- ods critically depend on the ... [more ▼] The development of high-order computational methods for solving partial differen- tial equations on unstructured grids has been underway for many years. Such meth- ods critically depend on the availability of high-quality curvilinear meshes, as one badly-shaped element can degrade the solution in the whole domain (J. Shewchuk, “What Is a Good Linear Finite Element? Interpolation, Conditioning, Anisotropy, and Quality Measures”, Preprint, 2002). The usual way of generating curved meshes is to first generate a straight sided mesh and to curve mesh entities that are classified on the boundaries of the domain. The latter operation introduces a “shape-distortion” that should be controlled if we suppose that the straight sided mesh is composed of well-shaped elements. Quality measures allow to quantify to which point an element is well-shaped. They also provide tools to improve the quality of meshes through optimization opera- tions. Many quality measures has been proposed for quadratic triangular finite element. Recently, X. Roca et al. (“Defining Quality Measures for High-Order Planar Triangles and Curved Mesh Generation”, Proceedings of the 20th Interna- tional Meshing Roundtable, 2011) proposed a technique that allows extending any Jacobian based quality measure for linear elements to high-order iso-parametric planar triangles of any interpolation degree. In this work we propose an efficient method to provide accurate bounds on the mag- nitude of the shape distortion of any triangular and quadrangular curved element. The shape distortion is measured with respect to an ideal element, which can e.g. be an equilateral triangle or the element from the original straight-sided mesh. The key feature of the method is that we can adaptively expand functions based on the Jacobian matrix and its determinant in terms of Be ́zier functions. Be ́zier functions have both properties of boundedness and positivity, which allow sharp computation of minimum or maximum of the interpolated functions. [less ▲] Detailed reference viewed: 81 (20 ULg)Geometrical validity of curvilinear finite elements Johnen, Amaury ; ; Geuzaine, Christophe in Journal of Computational Physics (2013), 233 In this paper, we describe a way to compute accurate bounds on Jacobian determinants of curvilinear polynomial finite elements. Our condition enables to guarantee that an element is geometrically valid, i ... [more ▼] In this paper, we describe a way to compute accurate bounds on Jacobian determinants of curvilinear polynomial finite elements. Our condition enables to guarantee that an element is geometrically valid, i.e., that its Jacobian determinant is strictly positive everywhere in its reference domain. It also provides an efficient way to measure the distortion of curvilinear elements. The key feature of the method is to expand the Jacobian determinant using a polynomial basis, built using Bézier functions, that has both properties of boundedness and positivity. Numerical results show the sharpness of our estimates. [less ▲] Detailed reference viewed: 94 (32 ULg)A Frontal Delaunay Quad Mesh Generator Using the L ∞ Norm ; ; et al in International Journal for Numerical Methods in Engineering (2013), 94(5), 494-512 Detailed reference viewed: 108 (38 ULg)ONELAB: Open Numerical Engineering LABoratory Geuzaine, Christophe ; ; et al in Proceedings of the 7th European Conference on Numerical Methods in Electromagnetism (NUMELEC2012) (2012, July) Detailed reference viewed: 134 (14 ULg)Quality open source mesh generation for cardiovascular flow simulations ; ; Geuzaine, Christophe et al in Ambrosi, D.; Quarteroni, A.; Rozza, G. (Eds.) Modelling Physiological Flow (2012) Detailed reference viewed: 103 (3 ULg)Discontinuous Galerkin Method for Computing Induced Fields in Superconducting Materials ; ; et al in IEEE Transactions on Magnetics (2012), 48(2), 591-594 Detailed reference viewed: 74 (10 ULg)Mesh influence on cardiovascular simulations ; ; et al in Proceedings of the 5th international conference on Advanced COmputational Methods in ENgineering (ACOMEN 2011) (2011, November) Detailed reference viewed: 14 (1 ULg)Robust generation of curvilinear hybrid meshes for CFD ; ; et al in Proceedings of the 5th international conference on Advanced COmputational Methods in ENgineering (ACOMEN 2011) (2011, November) Detailed reference viewed: 17 (0 ULg)A Frontal Delaunay Quad Mesh Generator Using the L ∞ Norm ; ; et al in Proceedings of the 20th International Meshing Roundtable (2011, October) Detailed reference viewed: 54 (11 ULg)Quality Surface Meshing Using Discrete Parametrizations ; ; Geuzaine, Christophe in Proceedings of the 20th International Meshing Roundtable (2011, October) Detailed reference viewed: 6 (0 ULg)Impact of the mesh on the accuracy and efficiency of cardiovascular simulations ; Geuzaine, Christophe ; et al in Proceedings of the ECCOMAS Thematic International Conference on Simulation and Modeling of Biological Flows (SIMBIO 2011) (2011, September) Detailed reference viewed: 17 (0 ULg)Discontinuous Galerkin Method for Computing Induced Fields in Superconducting Materials" ; ; et al in Proceedings of the 18th Conference on the Computation of Electromagnetic Fields (COMPUMAG 2011) (2011, July) Detailed reference viewed: 8 (0 ULg)Quality meshing algorithms for accurate and efficient cardiovascular simulations ; ; et al in Nithiarasu, P.; Lohner, R. (Eds.) Procedings of the 2nd International Conference on Mathematical and Computational Biomedical Engineering (CMBE2011) (2011, April) Detailed reference viewed: 12 (0 ULg)Quality surface meshing using discrete parametrizations ; ; et al in Proceedings of the 16th International Conference on Finite Elements in Flow Problems (FEF 2011) (2011, March) Detailed reference viewed: 10 (0 ULg)Blossom-Quad: a non-uniform quadrilateral mesh generator using a minimum cost perfect macthing algorithm ; Geuzaine, Christophe ; in Wall, W. A.; Gravemeier, V. (Eds.) Proceedings of the 16th International Conference on Finite Elements in Flow Problems (FEF 2011) (2011, March) Detailed reference viewed: 30 (0 ULg)High Quality Surface Remeshing Using Harmonic Maps. Part II: Surfaces with High Genus and of Large Aspect Ratio ; ; et al in International Journal for Numerical Methods in Engineering (2011), 86(11), 1303-1321 Detailed reference viewed: 36 (1 ULg)High Quality Surface Remeshing Using Harmonic Maps: Surfaces with High Genus and of Large Aspect Ratio ; Geuzaine, Christophe ; in Proceedings of the Third Workshop on Grid Generation for Numerical Computations, Tetrahedron III (2010, September) Detailed reference viewed: 30 (1 ULg)High-quality remeshing using harmonic maps Geuzaine, Christophe ; ; in Proceedings of the 5th Advanced Computational Electromagnetics workshop (2010, July) Detailed reference viewed: 8 (1 ULg)Méthode de Galerkin discontinue appliqué à la diffusion non linéaire dans les supraconducteurs Kameni Ntichi, Abelin ; ; et al in Proceedings of the 40e Congrès National d'Analyse Numérique (CANUM 2010) (2010) Detailed reference viewed: 85 (13 ULg) |
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