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Edge Elements (edge + element)

Distribution by Scientific Domains
Mathematics and Statistics66%

Selected Abstracts

Crack edge element of three-dimensional displacement discontinuity method with boundary division into triangular leaf elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2001
H. Li
Abstract In this paper, the existing Displacement Discontinuity Method (DDM) for three-dimensional elastic analysis with boundary discretized into triangular elements, which is purely based on analytical integrals, is extended from the constant element to the square-root crack edge element. In order to evaluate the singular integral when the receiver point falls into the remitter element, i.e., the observed point (x,y) ,,, a part analytical and part numerical integration procedure is adopted effectively. The newly developed codes prove valid in estimating the Stress Intensity Factor (SIF) KI. Furthermore, for the sake of keeping the advantages of high-speed and high-accuracy in developing the numerical system, a novel method to realize pure analytical integration of influence function is found by the aid of symbolic computation technology of Mathematica. Copyright © 2001 John Wiley & Sons, Ltd. [source]

A time-marching finite element method for an electromagnetic scattering problem

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2003
Tri Van
Abstract In this paper, Newmark time-stepping scheme and edge elements are used to numerically solve the time-dependent scattering problem in a three-dimensional polyhedral cavity. Finite element methods based on the variational formulation derived in Van and Wood (Adv. Comput. Math., to appear) are considered. Existence and uniqueness of the discrete problem is proved by using Babuska,Brezzi theory. Finite element error estimate and stability of the Newmark scheme are also established. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Convergence of adaptive edge finite element methods for H(curl)-elliptic problems

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2-3 2010
Liuqiang Zhong
Abstract The standard adaptive edge finite element method (AEFEM), using first/second family Nédélec edge elements with any order, for the three-dimensional H(curl)-elliptic problems with variable coefficients is shown to be convergent for the sum of the energy error and the scaled error estimator. The special treatment of the data oscillation and the interior node property are removed from the proof. Numerical experiments indicate that the adaptive meshes and the associated numerical complexity are quasi-optimal. Copyright © 2010 John Wiley & Sons, Ltd. [source]

An algebraic multigrid method for finite element discretizations with edge elements

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 3 2002
S. Reitzinger
Abstract This paper presents an algebraic multigrid method for the efficient solution of the linear system arising from a finite element discretization of variational problems in H0(curl,,). The finite element spaces are generated by Nédélec's edge elements. A coarsening technique is presented, which allows the construction of suitable coarse finite element spaces, corresponding transfer operators and appropriate smoothers. The prolongation operator is designed such that coarse grid kernel functions of the curl-operator are mapped to fine grid kernel functions. Furthermore, coarse grid kernel functions are ,discrete' gradients. The smoothers proposed by Hiptmair and Arnold, Falk and Winther are directly used in the algebraic framework. Numerical studies are presented for 3D problems to show the high efficiency of the proposed technique. Copyright © 2002 John Wiley & Sons, Ltd. [source]