References of "Johnen, Amaury"
     in
Bookmark and Share    
Peer Reviewed
See detailComputing Bounds on the Geometrical Quality of 2D Curvilinear Finite Elements
Johnen, Amaury ULg; Remacle, J.-F.; Toulorge, T. 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: 58 (12 ULg)
Full Text
Peer Reviewed
See detailGeometrical Validity of Curvilinear Finite Elements
Johnen, Amaury ULg; Remacle, J.-F.; Geuzaine, Christophe ULg

in Journal of Computational Physics (2013), 233

In this paper, we describe a way to compute accurate bounds on Jacobian de- terminants of curvilinear polynomial finite elements. Our condition enables to guarantee that an element is geometrically valid ... [more ▼]

In this paper, we describe a way to compute accurate bounds on Jacobian de- terminants 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 B ́ezier functions, that has both properties of boundedness and positivity. Numerical results show the sharpness of our estimates. [less ▲]

Detailed reference viewed: 86 (27 ULg)
Full Text
Peer Reviewed
See detailGeometrical Validity of High-Order Triangular Finite Elements
Johnen, Amaury ULg; Remacle, Jean-François; Geuzaine, Christophe ULg

in Engineering with Computers (2012)

This paper presents a method to compute accurate bounds on Jacobian determinants of high-order (curvilinear) triangular nite elements. This method can be used to guarantee that a curvilinear triangle is ... [more ▼]

This paper presents a method to compute accurate bounds on Jacobian determinants of high-order (curvilinear) triangular nite elements. This method can be used to guarantee that a curvilinear triangle is geometrically valid, i.e., that its Jacobian determinant is strictly positive everywhere in its reference domain. It also provides an e cient way to measure the quality the triangles. The key feature of the method is to expand the Jacobian determinant using a polynomial basis, built using B ezier functions, that has both properties of boundedness and positivity. Numerical results show the sharpness of our estimates. [less ▲]

Detailed reference viewed: 98 (24 ULg)
Full Text
Peer Reviewed
See detailBlossom-Quad: a non-uniform quadrilateral mesh generator using a minimum cost perfect matching algorithm
Remacle, J.-F.; Lambrechts, J.; Seny, B. et al

in International Journal for Numerical Methods in Engineering (2012), 89

Detailed reference viewed: 86 (10 ULg)
Peer Reviewed
See detailEfficient Evaluation of the Geometrical Validity of Curvilinear Finite Elements
Johnen, Amaury ULg; Remacle, Jean-François; Geuzaine, Christophe ULg

in Proceedings of the 5th international conference on Advanced COmputational Methods in ENgineering (ACOMEN 2011) (2011, November 14)

Detailed reference viewed: 32 (11 ULg)
Peer Reviewed
See detailGeometrical Validity of Curvilinear Finite Elements
Johnen, Amaury ULg; Remacle, Jean-François; Geuzaine, Christophe ULg

in William Roshan, Quadros (Ed.) Proceedings of the 20th International Meshing Roundtable (2011, October 25)

Detailed reference viewed: 23 (6 ULg)