Numerical integration over simplexes and cones

Hammer, Preston C.; Marlowe, O.J.; Stroud, A. H.

doi:10.1090/s0025-5718-1956-0086389-6

Cited by 86 publications

(56 citation statements)

References 2 publications

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“…La position des connecteurs sur chaque face triangulaire étant libre, il est intéressant pour la suite de les placer aux trois points définis par Hammer pour l'intégration exacte d'une fonction quadratique sur un domaine triangulaire (Hammer et al, 1956).…”

Section: Choix Des Connecteursunclassified

Modèles équilibre pour l'analyse duale

Kempeneers

Beckers

Almeida³

et al. 2003

Revue Européenne des Éléments Finis

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L'analyse duale pure a été l'une des premières méthodes utilisées pour estimer l'erreur de discrétisation globale commise lors d'un calcul par éléments finis. Elle repose sur la comparaison de deux solutions éléments finis, la première obtenue à partir d'un modèle cinématiquement admissible classique et la seconde issue d'un modèle statiquement admissible (approche de type équilibre). Nous présentons dans ce travail deux méthodes permettant de créer des éléments équilibre. La première qui peut être qualifiée d'hybride, permet d'étudier des problèmes bidimensionnels avec des éléments équilibre de degré élevé. La seconde, pour laquelle nous présentons dans ce travail l'extension récente aux problèmes 3D à maillages tétraédriques, est de type équilibre pur. Ces deux approches nous ont permis de présenter quelques résultats d'estimation de l'erreur globale par analyse duale.ABSTRACT. The pure dual analysis is one of the first methods developed to perform the estimation of the global discretization error of finite elements analysis. It is based on the comparison of two finite elements solutions, one of which being of the displacement type (kinematically admissible), the second one being of the equilibrium type (statically admissible). This work presents two methods allowing to create equilibrium elements. The first one which can be seen as an hybrid method, allows to compute high-order equilibrium solutions of 2D problems. The second method is of the pure equilibrium type. Its recent extension to 3D problems with tetrahedral mesh is presented here. Those approaches enabled us to present some results of global error estimation by dual analysis. MOTS-CLÉS : estimation d'erreur globale, analyse duale, modèles équilibre.

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Section: Choix Des Connecteursunclassified

Modèles équilibre pour l'analyse duale

Kempeneers

Beckers

Almeida³

et al. 2003

Revue Européenne des Éléments Finis

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“…Np NpitM JC (r) = N I PjP (r) + I lnij (r) n-l n=NP+l (4) where Np is the number of half basis functions jP, Ni the number of full basis functions jt, and IP and II the unknown current coefficients on the conducting surface.…”

Section: Ill Mom and Numerical Implementationmentioning

confidence: 99%

“…In this work, fully symmetric quadrature formulas have been used to perform the surface and volume integrations. In the former case, a 13-point (7-degree) rule [4] has been successfully used even in the case of triangles of aspect ratio greater than 10. In the latter case, various rules have been tested in order to assure a sufficient accuracy when distorted tetrahedrons are utilized.…”

Section: Ill Mom and Numerical Implementationmentioning

confidence: 99%

A Galerkin Method Solution for Arbitrary Electromagnetic Problems using a Surface-Volume Formulation

Rodriguez

Cuevas

Krozer

1999

29th European Microwave Conference, 1999

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An efficient numerical method to analyze the electromagnetic field in presence of bodies of arbitrary shape and material is presented. The method has been applied to the problem of the field distribution in the far field of a mobile phone antenna near a head and a hand of a person. Resonant microwave circuits and scattering applications demonstrate the versatility and effectiveness of the present method. Other problems have also been studied, which can be conductors, dielectrics or and arbitrary combinations of both. The procedure is based on the surface and volume equivalence principles and a Galerkin method is used to solve the integral equations. I On partial leave from:

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“…We get then the matrices R.. , from which we draw the stiffness matrix. ID To estimate numerically the integrals G , we use the 7-points formula given in [23]. We found a satisfying accuracy on using these formulas on 64 subtriangles by dividing each side of the unit triangle in 8 equal parts.…”

Section: Derivation Of the Stiffness Matrix Of An Elementmentioning

confidence: 99%

A Curved Finite Element for Thin Elastic Shells

Dupuis¹,

Goël²

1969

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This paper is concerned with a curved triangular finite shell element, which represents the rigid-body motions exactly and assures convergence in energy. The stiffness matrix is derived in a general way that is valid for all mathematical models which accept Kirchhoff's assumption. A numerical example is presented to indicate the quality of results that can be obtained with 9 or 18 degrees of freedom at each meshpoint and basic functions of 1 2 classes C or C .

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Numerical integration over simplexes and cones

Cited by 86 publications

References 2 publications

Modèles équilibre pour l'analyse duale

Modèles équilibre pour l'analyse duale

A Galerkin Method Solution for Arbitrary Electromagnetic Problems using a Surface-Volume Formulation

A Curved Finite Element for Thin Elastic Shells

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