  Geometrical Validity of High-Order Triangular Finite ElementsJohnen, Amaury  ; ; Geuzaine, Christophe in Engineering with Computers (in press) 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: 64 (10 ULg)Geometrical Validity of Curvilinear Finite ElementsJohnen, Amaury ; ; Geuzaine, Christophe in Journal of Computational Physics (in press) 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: 63 (16 ULg) Blossom-Quad: a non-uniform quadrilateral mesh generator using a minimum cost perfect matching algorithm; ; et al in International Journal for Numerical Methods in Engineering (2012), 89 Detailed reference viewed: 62 (8 ULg)Efficient Evaluation of the Geometrical Validity of Curvilinear Finite ElementsJohnen, Amaury ; ; Geuzaine, Christophe in Proceedings of the 5th international conference on Advanced COmputational Methods in ENgineering (ACOMEN 2011) (2011, November 14) Detailed reference viewed: 23 (11 ULg)Geometrical Validity of Curvilinear Finite ElementsJohnen, Amaury ; ; Geuzaine, Christophe in William Roshan, Quadros (Ed.) Proceedings of the 20th International Meshing Roundtable (2011, October 25) Detailed reference viewed: 19 (5 ULg) |
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