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Overhauser triangular elements for three-dimensional potential problems using boundary element methods

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 1996年第24期39卷 4183-4198页

作者： Durodola, JF Fenner, RT UNIV LONDON IMPERIAL COLL SCI TECHNOL & MED DEPT MECH ENGNLONDON SW7 2BXENGLAND

Interpolation to boundary data and one-dimensional Overhauser parabola blending methods are used to derive Overhauser triangular elements. The elements are C-1-continuous at inter-element nodes and no functional derivatives are required as nodal parameters. These efficient parametric representation elements are used to solve three-dimensional potential problems using the Boundary Element Method (BEM). Results obtained are generally as accurate as those obtained using Overhauser quadrilateral elements.

关键词： Overhauser triangular elements boundary element three-dimensional potential problems

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Introduction to Mesh Based Generated Lumped Parameter Models for Electromagnetic Problems using triangular elements

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CES Transactions on Electrical Machines and Systems 2023年第1期7卷 21-34页

作者： Haidar Y.Diab Salim Asfirane Nicolas Bracikowski Frédéric Gillon Yacine Amara UniversitéLe Havre Normandie Le Havre76600France Département Génie Industriel et Maintenance Nantes UniversitéSt-Nazaire44602France Ecole Centrale de Lille Hauts-de-France59651France IEEE

This paper is an introduction to mesh based generated reluctance network modeling using triangular *** contributions on mesh based generated reluctance networks using rectangular shaped elements have been published,but very few on those generated from a mesh using triangular *** use of triangular elements is aimed at extending the application of the approach to any shape of modeled *** concepts of the approach are presented in the case of electromagnetic *** procedure for coding the approach in the case of a flat linear permanent magnet machine is *** developed under MATLAB environment are also included.

关键词： Lumped parameter modeling Finite element method Mesh triangular elements Electromagnetic devices Modeling

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Advantages of cubic arcs for approximating curved boundaries by subparametric transformations for some higher order triangular elements

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APPLIED MATHEMATICS AND COMPUTATION 2013年第12期219卷 6893-6910页

作者： Naidu, V. Kesavulu Nagaraja, K. V. Amrita Vishwa Vidyapeetham Amrita Sch Engn Dept Math Bangalore 560035 Karnataka India

In the finite element method, the most popular technique for dealing with curved boundaries is that of isoparametric coordinate transformations. In this paper, the 10-node (cubic), 15-node (quartic) and 21-node (quintic) curved boundary triangular elements having one curved side and two straight sides are analyzed using the isoparametric coordinate transformations. By this method, these curved triangles in the global coordinate system are mapped into a isosceles right angled unit triangle in the local coordinate system and the curved boundary of these triangular elements are implicitly replaced by cubic, quartic, and quintic arcs. The equations of these arcs involve parameters, which are the coordinates of points on the curved side. Relations are deduced for choosing the parameters in quartic and quintic arcs in such a way that each arc is always a cubic arc which passes through four points of the original curve, thus ensuring a good approximation. The point transformations thus determined with the above choice of parameters on the curved boundary and also in turn the other parameters in the interior of curved triangles will serve as a powerful subparametric coordinate transformation for higher order curved triangular elements. Numerical examples are given to demonstrate the accuracy and efficiency of the method. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Finite element method Numerical integration triangular elements Point transformations

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Time efficiency and error estimation in generating element stiffness matrices of plane triangular elements using Universal Matrix Method and Gauss-Quadrature

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AIN SHAMS ENGINEERING JOURNAL 2018年第4期9卷 965-972页

作者： Jeyakarthikeyan, P., V Yogeshwaran, R. Abdullahi, Hamza Sulayman SRM Univ Sch Mech Engn Madras Tamil Nadu India

This paper is aimed at generating element stiffness matrices for the family of triangular elements using Universal Matrix Method and performing a CPU time efficiency analysis and comparison of stiffness coefficients deviation (error). The interpolation functions of the field variable function (displacement) are to be integrated explicitly once and for all when geometric transformation function is linear, to give the constant universal matrices. This makes the generation of stiffness matrix a simple addition of universal matrices rather than integration of functions. (C) 2016 AM Shams University.

关键词： Stiffness matrix Gauss Quadrature Error estimation CPU time ratio Closed-form triangular elements

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A New Class of High-Order Energy Stable Flux Reconstruction Schemes for triangular elements

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JOURNAL OF SCIENTIFIC COMPUTING 2012年第1期51卷 224-256页

作者： Castonguay, P. Vincent, P. E. Jameson, A. Stanford Univ Dept Aeronaut & Astronaut Stanford CA 94305 USA

The flux reconstruction (FR) approach allows various well-known high-order schemes, such as collocation based nodal discontinuous Galerkin (DG) methods and spectral difference (SD) methods, to be cast within a single unifying framework. Recently, the authors identified a new class of FR schemes for 1D conservation laws, which are simple to implement, efficient and guaranteed to be linearly stable for all orders of accuracy. The new schemes can easily be extended to quadrilateral elements via the construction of tensor product bases. However, for triangular elements, such a construction is not possible. Since numerical simulations over complicated geometries often require the computational domain to be tessellated with simplex elements, the development of stable FR schemes on simplex elements is highly desirable. In this article, a new class of energy stable FR schemes for triangular elements is developed. The schemes are parameterized by a single scalar quantity, which can be adjusted to provide an infinite range of linearly stable high-order methods on triangular elements. Von Neumann stability analysis is conducted on the new class of schemes, which allows identification of schemes with increased explicit time-step limits compared to the collocation based nodal DG method. Numerical experiments are performed to confirm that the new schemes yield the optimal order of accuracy for linear advection on triangular grids.

关键词： High-order methods Flux reconstruction Nodal discontinuous Galerkin method triangular elements Stability

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Stabilized mixed triangular elements with area bubble functions at small and large deformations

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COMPUTERS & STRUCTURES 2014年 138卷 172-182页

作者： Caylak, Ismail Mahnken, Rolf Univ Paderborn Chair Engn Mech D-33098 Paderborn Germany

A well known approach for stabilization of mixed finite triangular elements are volume bubble functions. In this paper a new concept of area bubble functions in geometrically linear (elastic and elasto-plastic) and geometrically non-linear elastic regimes is presented. These functions are used in order to enrich the displacement field. In the numerical examples, simulations for Cook's membrane problem and a block under central pressure demonstrate, that the proposed formulation avoids locking and reduces stress oscillations for incompressible materials. Furthermore, the results reveal that area bubble functions are superior to volume bubble functions. This paper is an extension of the works published by the authors regarding tetrahedral elements. (c) 2014 Elsevier Ltd. All rights reserved.

关键词： Finite elements triangular elements Mixed elements Area bubble functions

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A new formulation of the mixed finite element method for solving elliptic and parabolic PDE with triangular elements

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JOURNAL OF COMPUTATIONAL PHYSICS 1999年第1期149卷 148-167页

作者： Younes, A Mose, R Ackerer, P Chavent, G Univ Strasbourg 1 CNRS UMR 7507 Inst Mecan Fluides F-67000 Strasbourg France Inst Natl Rech Informat & Automat F-78153 Le Chesnay France

For the groundwater flow problem (which corresponds to the Darcy flow model), we show how to produce a scheme with one unknown per element, starting from a mixed formulation discretized with the Raviart Thomas triangular elements of lowest order. The aim is here to obtain a new formulation with one unknown per element by elimination of the velocity variables q = -k grad P, without any restriction concerning the computation of the velocity field. In the first part, we describe the triangular mixed finite element method used for solving Darcy's and mass balance equations. In the second part, we study the elliptic-parabolic problem;we describe the new formulation of the problem in order to use mixed finite elements (MFE) with less unknowns without any specific numerical integration. Finally, we compare the computational effort of the MFE method with the new formulation for different triangulations using numerical experiments. In this work, we show that the new formulation can be seen as a general formulation which can be equivalent to the finite volume or the finite difference methods in some particular cases. (C) 1999 Academic Press.

关键词： mixed finite element method finite volume method elliptic-parabolic problem triangular elements

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ON ADAPTIVITY FOR DIFFUSION-PROBLEMS USING triangular elements

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ENGINEERING COMPUTATIONS 1995年第1期12卷 75-84页

作者： PADRA, C VENERE, MJ División Mecánica Computacional DIA Centro Atómico Bariloche CNEA 8400 San Carlos de Bariloche Argentina División Mecánica Computacional DIA Centro Atómico Bariloche CNEA 8400 San Carlos de Bariloche Argentina

In this work an adaptive scheme to solve diffusion problems, using linear and quadratic triangles, is presented. The densification algorithm, based on the subdivision of the selected elements, and the error estimator used are described first. We pay special attention to the behaviour of the estimator. It has two contributions: the residual term and the flux-jump term. Babuska and co-workers have shown that for bilinear quadrilterals, the first term is negligible, but for biquadratic, it is the dominant term. We show evidence suggesting that these results cannot be extended to triangular elements when the problem has a singular solution. We found, in this case, that if the flux-jump term is neglected, the expected rate of convergence cannot be obtained. Finally, some remarks about the whole adaptive process are discussed.

关键词： ADAPTION DIFFUSION PROBLEMS triangular elements

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The use of parabolic arcs in matching curved boundaries by point transformations for some higher order triangular elements

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FINITE elements IN ANALYSIS AND DESIGN 2008年第15期44卷 920-932页

作者： Rathod, H. T. Nagaraja, K. V. Naidu, V. Kesavulu Venkatesudu, B. Amrita Sch Engn Dept Math Bangalore 560035 Karnataka India Bangalore Univ Dept Math Bangalore 560001 Karnataka India

This paper is concerned with curved boundary triangular elements having one curved side and two straight sides. The curved elements considered here are the 6-node (quadratic), 10-node (cubic), 15-node (quartic) and 21-node (quintic) triangular elements. On using the isoparametric coordinate transformation, these curved triangles in the global (x, y) coordinate system are mapped into a standard triangle: {(xi, eta)/ 0 <=, xi <= 1, xi + eta <= 1} in the local coordinate system (xi, eta). Under this transformation curved boundary of these triangular elements is implicitly replaced by quadratic, cubic, quartic and quintic arcs. The equations of these arcs involve parameters, which are the coordinates of points on the curved side. This paper deduces relations for choosing the parameters in quartic and quintic arcs in such a way that each arc is always a parabola which passes through four points of the original curve, thus ensuring a good approximation. The point transformations which are thus determined with the above choice of parameters on the curved boundary and also in turn the other parameters in the interior of curved triangles will serve as a powerful subparametric coordinate transformation for higher order curved triangular elements with one curved side and two straight sides. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Finite element method Numerical integration triangular elements Point transformations

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An adaptive least-squares spectral collocation method with triangular elements for the incompressible Navier-Stokes equations

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JOURNAL OF ENGINEERING MATHEMATICS 2006年第3期56卷 337-350页

作者： Heinrichs, Wilhelm Univ Duisburg Essen D-45117 Essen Germany

A least-squares spectral collocation scheme for the incompressible Navier-Stokes equations is proposed. Grid refinement is performed by means of adaptive triangular elements. On each triangle the Fekete nodes are employed for the collocation of the differential equation. On the element interfaces continuity of the functions is enforced in the least-squares sense. Equal-order Dubiner polynomials are used to obtain a stable spectral scheme. The collocation conditions and the interface conditions lead to an overdetermined system that can be solved efficiently by least-squares. The solution technique only involves symmetric positive-definite linear systems. The approach is first applied to the Poisson equation and then extended to singular perturbation problems where least-squares have a stabilizing effect. By adaptivity, a suitable decomposition of the domain is found where the boundary layer is well resolved. Finally, the method is successfully applied to the regularized driven-cavity flow problem. Numerical simulations confirm the high accuracy of the proposed spectral least-squares scheme.

关键词： least-squares spectral collocation adaptivity triangular elements Navier-Stokes

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