Optimal Subparametric Finite Elements for Elliptic Partial Differential Equations Using Higher-Order Curved Triangular Elements

Nagaraja, K.V.; Naidu, V. Kesavulu; Siddheshwar, P. G.

doi:10.1080/15502287.2013.870256

Cited by 20 publications

(5 citation statements)

References 19 publications

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“…Hereafter, the interpreted work is anticipated to extend the use of the HO discretization process together with the HOSFEM for resolving some of these problems. Thus, this technique obviously reduces computing duration compared with the approach where conventional isoparametric mapping is employed [34]. Thus, automated HO mesh generators are proposed to calculate the eigenfrequencies, particularly for curved geometries, using a HOSFEM technique.…”

Section: Discussionmentioning

confidence: 99%

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An Efficient Automatic Mesh Generator With Parabolic Arcs in Julia for Computation of TE and TM Modes for Waveguides

Kannan

Nagaraja

2020

IEEE Access

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An enriched finite element method is presented to numerically solve the eigenvalue problem on electromagnetic waveguides governed by the Helmholtz equation. In this work, a highly efficient, simple and precise higher order subparametric method was developed using a 2D automated mesh generator performed with JuliaFEM. The transcendence computerized discretization code in Julia is developed for the present work. For curved waveguide structures, meshes with one side and curving higher orders are proposed with triangular elements with parabolic arcs. The technique is shown for distinct waveguide constructions, and the results are compared with the strongest numerical or analytical results available. The results demonstrate that the proposed methodology is effective and accurate for generating finite element simulations for complex structures with black holes and irregular topology due to no curvature loss. This article presents a finding cutoff frequency performed with JuliaFEM-an open-source program. Analysis results produced by commercial software are considered for the comparison and show that the calculation results between the two programs do not differ significantly. This procedure can be used to achieve the most effective transmission of energy for electromagnetic applications.

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Section: Discussionmentioning

confidence: 99%

“…• n-Sided polygonal smoothed finite element method Various finite elements have been proposed for engineering analysis. These elements have been proposed to facilitate meshing of the problem domain, to facilitate the analysis of physical phenomena, and to overcome drawbacks or limitations in the existing methods [34], [35].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Automatic Mesh Generator With Parabolic Arcs in Julia for Computation of TE and TM Modes for Waveguides

Kannan

Nagaraja

2020

IEEE Access

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“…(2) where refers to Lagrange shape functions, refers to the unknown nodal values and represents the order of the curved triangular elements. The underlying mathematical basis of FEM is very well explained by the theories of Galerkin weak formulation [6,7]. A key feature of this method is that the integrals of functions can be evaluated on any arbitrary domains.…”

Section: Mathematical Formulation Of Finite Element Methodsmentioning

confidence: 99%

“…We use [1] as the starting mesh by defining the nodal points on the interior and boundary by subparametric transformations matching parabolic arcs given in [6]. The investigation states that various endeavours where made on subparametric transformations by several authors [6,7]. As a part of this section, the way to generate curved cubic order triangular meshing is discussed.…”

Section: Mathematical Formulation For Meshing Of Cubic Order Curved Triangular Elementmentioning

confidence: 99%

“…Generally, usage of isoparametric transformations encounters a complex rational integral function whose denominator and Jacobian are bivariate polynomial of higher order. Thus the difficulty arising in solving such an integral of an arbitrary curved boundaries can be overcome by the use of subparametric transformations by parabolic or cubic arcs for higher order curved triangular elements developed in the works [6,7]. Hence, the Jacobian acquired will always be bivariate polynomial of linear order.…”

Section: Introductionmentioning

confidence: 99%

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A new finite element method using MATLAB for Poisson’s Equation in axisymmetric domain

Shylaja¹

2021

TURCOMAT

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This paper demonstrates finite element procedure for two-dimensional axisymmetric domains. For many engineering applications like structural engineering, aerospace engineering, geo-mechanics etc., the solution domain and boundary conditions are axisymmetric. Henceforth, we can illuminate just the axisymmetric part of the solution domain that gives the data of the entire domain. This paper demonstrates the effectiveness of using MATLAB programming demonstrated by Persson et.al (2004) as the initial mesh for discretization of axisymmetric domains for higher order meshing. Further, solving some class of partial differential equations using finite element method with nodal relation given by subparametric transformations Rathod et.al (2008). In this paper a cubic order curved triangular meshing for some of the domains like ellipse and circle are demonstrated. These in turn finds its applications in the fields like stress analysis in mechanical engineering, torsion twist (shear strength) analysis in civil engineering, evaluation of stress intensity factor for quarter elliptical crack in pressure vessels in equipment industry etc,. The output data from the meshing scheme like meshing of the domain, nodal position, element connectivity and boundary edges are been used in the finite element procedures. The efficiency of the method is achieved by p-refinement scheme i.e., fixing the number of elements and increasing the polynomial order.

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A Simple and Efficient Higher Order Finite Element Scheme for Helmholtz Waveguides

Panda

Nagaraja

Naidu

2017

Lecture Notes in Electrical Engineering

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Optimal Subparametric Finite Elements for Elliptic Partial Differential Equations Using Higher-Order Curved Triangular Elements

Cited by 20 publications

References 19 publications

An Efficient Automatic Mesh Generator With Parabolic Arcs in Julia for Computation of TE and TM Modes for Waveguides

An Efficient Automatic Mesh Generator With Parabolic Arcs in Julia for Computation of TE and TM Modes for Waveguides

A new finite element method using MATLAB for Poisson’s Equation in axisymmetric domain

A Simple and Efficient Higher Order Finite Element Scheme for Helmholtz Waveguides

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