scispace - formally typeset
Search or ask a question

Showing papers on "Smoothed finite element method published in 1993"


Book
01 Mar 1993
TL;DR: The Finite Element Method in Electromagnetics, Third Edition as discussed by the authors is a leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetic engineering.
Abstract: A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagneticsThe finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration.The Finite Element Method in Electromagnetics, Third Edition explains the methods processes and techniques in careful, meticulous prose and covers not only essential finite element method theory, but also its latest developments and applicationsgiving engineers a methodical way to quickly master this very powerful numerical technique for solving practical, often complicated, electromagnetic problems.Featuring over thirty percent new material, the third edition of this essential and comprehensive text now includes:A wider range of applications, including antennas, phased arrays, electric machines, high-frequency circuits, and crystal photonicsThe finite element analysis of wave propagation, scattering, and radiation in periodic structuresThe time-domain finite element method for analysis of wideband antennas and transient electromagnetic phenomenaNovel domain decomposition techniques for parallel computation and efficient simulation of large-scale problems, such as phased-array antennas and photonic crystalsAlong with a great many examples, The Finite Element Method in Electromagnetics is an ideal book for engineering students as well as for professionals in the field.

3,705 citations


Book ChapterDOI
TL;DR: A brief overview of stabilized finite element methods and their application to the advection-diffusion equation is given in this paper, along with a discussion of the developments applied to these methods.

457 citations


Journal ArticleDOI
TL;DR: A priori and a posteriori error estimates are proved for a finite element method for linear second order hyperbolic equations based on a space-time finite element discretization with the basis functions being continuous in space and discontinuous in time.

245 citations


Book
30 Sep 1993

153 citations


Book
21 Dec 1993
TL;DR: In this paper, a unified approach to the variational and computational mechanics of solids and structures is presented, including transfer, stiffness, and flexibility methods, finite elements, weighted residuals, finite differences, and boundary element methods.
Abstract: Mechanics of Structures presents a unified approach to the variational and computational mechanics of solids and structures. The fundamentals of the theory of elasticity and variational theorems are covered, as are generalized variational theorems and applications. Matrix structural mechanics (including transfer, stiffness, and flexibility methods), finite elements, weighted residuals, finite differences, and boundary element methods are presented in a rational, unified manner. The book also includes comprehensive chapters on stability and dynamics of structural systems.Mechanics of Structures provides solid information for students and professionals in civil, mechanical, and aerospace engineering. It is an excellent text for courses offering the fundamentals of finite elements; advanced strength of materials; matrix structural analysis; computational solid mechanics; variational methods of mechanics; and rods, plates, and shells.

130 citations



Journal ArticleDOI
TL;DR: In this article, a new quadrilateral element using isoparametric bilinear basis functions for both components of the rotation vector and the deflection is introduced, which is a stable modification of the MITC4 element.

94 citations


Book ChapterDOI
01 May 1993
TL;DR: In this paper, the authors discuss the solution of the Navier-Stokes equations by numerical methods combining operator splitting for the time discretization and finite elements for the space discretisation.
Abstract: In this article we discuss the solution of the Navier-Stokes equations modelling unsteady incompressible viscous flow, by numerical methods combining operator splitting for the time discretization and finite elements for the space discretization. The discussion includes the description of conjugate gradient algorithms which are used to solve the advection-diffusion and Stokes type problems produced at each time step by the operator splitting methods. Introduction and Synopsis The main goal of this article is to review several issues associated to the numerical solution of the Navier-Stokes equations modelling incompressible viscous flow. The methodology to be discussed relies systematically on variational priciples and is definitely oriented to Galerkin approximations. Also, we shall take advantage of time discretizations by operator splitting to decouple the two main difficulties occuring in the Navier-Stokes model, namely the incompressibility condition Δ u=0 and the advection term (u.Δ)u, u being here the velocity field. The space approximation will be based on finite element methods and we shall discuss with some details the compatibility conditions existing between the velocity and pressure spaces; the practical implementation of these finite element methods will also be addressed. This article relies heavily on [1]-[7] and does not have the pretention to cover the full field of finite element methods for the Navier-Stokes equations; concentrating on books only, pertinent references in this direction are [8]-[14] (see also the references therein). This article is organized in sections whose list is given just below. The Navier-Stokes equations for incompressible viscous flow Operator splitting methods for initial value problems. Application to the Navier- Stokes equations Iterative solution of the advection-diffusion sub-problems […]

74 citations


Journal ArticleDOI
P. Carnevali1, R. B. Morris1, Y. Tsuji1, G. Taylor1
TL;DR: Using two sample applications, it is shown that, using the techniques proposed here, p-version finite element analysis can have a substantially lower computational cost, for given accuracy, than standard finite element methods.
Abstract: New basis functions and solution procedures for p-version finite element analysis are described. They are used in a highly efficient p-version finite element solver for linear elastostatics and dynamics, which has been used in an industrial environment for over two years. Using two sample applications it is shown that, using the techniques proposed here, p-version finite element analysis can have a substantially lower computational cost, for given accuracy, than standard finite element methods. This makes the industrial applicability of p-version finite element analysis much wider than is commonly believed.

73 citations


Journal ArticleDOI
TL;DR: A new treatment of macromolecular electrostatics has been developed using the 3‐D finite element method to numerically solve the linear Poisson–Boltzmann equation, and is able to give an accurate description of the electrostatic potential distribution in a macromolescular system.
Abstract: A new treatment of macromolecular electrostatics has been developed using the 3-D finite element method to numerically solve the linear Poisson–Boltzmann equation. The procedure is based upon a model where the macromolecule is represented at an atomic level of detail, while the solvent is treated in a continuum approximation. The finite element method has two major advantages over previous methods based upon the finite difference approach. First, charges are located on atomic centers rather than being distributed onto grid points. Second, an isoparameter model allows the use of noncubic grids, providing a more accurate description of molecular shape. The principal disadvantage of the finite element method has been its computational complexity, which arises from the use of large matrices. To overcome this difficulty, a new matrix representation has been formulated and an iterative solution procedure has been adopted. The combination of these two techniques drastically reduces the size of the system matrix and increases the overall computational efficiency of the algorithm, making the new treatment computationally competitive with the finite difference approach. Because of the mathematical rigor and physical sophistication of the finite element algorithm, the new treatment is able to give an accurate description of the electrostatic potential distribution in a macromolecular system. Results on test cases with simple geometries show that the new treatment is able to reach the same level of accuracy achieved by the finite difference method while using a lower grid density. Near changes and surfaces, our method is more accurate than the finite difference method. The overall maximum deviation between computed and analytic potentials is less than 3% except in regions surrounding charges. The applicaions of both the finite element and finite difference methods to the same biomolecular systems produce similar potential distributions that would become identical in the limit of infinitely fine grids. © 1993 John Wiley & Sons, Inc.

70 citations


Journal ArticleDOI
TL;DR: In this article, the Stokes problem is approximated by a mixed finite element method using a new finite el- ement, which has properties analogous to the finite volume methods, namely, the local conservation of the momentum and the mass.
Abstract: The Stokes problem is approximated by a mixed finite element method using a new finite el- ement, which has properties analogous to the finite volume methods, namely, the local conservation of the momentum and the mass. Estimates of optimal order are derived for the errors in the velocity, the pressure, and the gradient of the velocity. This new finite element also works for the elasticity problem, and all estimates are valid uniformly with respect to the compressibility. Finally, some numerical results for the incompressible Navier-Stokes equations are presented.


Journal ArticleDOI
TL;DR: In this article, a geometrically exact, finite strain rod model is derived from basic kinematical assumptions, incorporating shear distortion in bending and taking account of torsion warping.
Abstract: Department of Structural and Foundation Engineering, Escola Politecnica Universidade de Sao Paulo, CP 61548, 05424-970 Sao Paulo, SP, Brazil A fully nonlinear, geometrically exact, finite strain rod model is derived from basic kinematical assumptions. The model incorporates shear distortion in bending and can take account of torsion warping. Rotation in 3D space is handled with the aid of the Euler-Rodrigues formula. The accomplished parametrization is simple and does not require update algorithms based on quaternions parameters. Weak and strong forms of the equilibrium equations are derived in terms of cross section strains and stresses, which are objective and suitable for constitutive description. As an example, an invariant linear elastic constitutive equation based on the small strain theory is presented. The attained formulation is very convenient for numerical procedures employing Galerkin projection like the finite element method and can be readily implemented in a finite element code. A mixed formulation of Hu-Washizu type is also derived, allowing for independent interpolation of the displacement, strain and stress fields within a finite element. An exact expression for the Frechet derivative of the weak form of equilibrium is obtained in closed form, which is always symmetric for conservative loading, even far from an equilibrium state and is very helpful for numerical procedures like the Newton method as well as for stability and bifurcation analysis. Several numerical examples illustrate the usefulness of the formulation in the lateral stability analysis of spatial frames. These examples were computed with the code FENOMENA, which is under development at the Computational Mechanics Laboratory of the Escola Politecnica. INTRODUCTION The interest on geometrically nonlinear analysis of struc­tures has increased in the recent few years. Besides the practical importance of nonlinear static and dynamic analysis of flexible rod and shell assemblages, the de­velopment of convenient geometrically exact models has contributed to this fact. These models show many ben­efits, which have been emphasized by many authors, as one can verify in a non-exhaustive list reproduced in the references. This work derives a geometrically exact rod model from the kinematic assumption that cross sections, which are initially orthogonal to the axis, remain plane and undistorted during the deformation. The theory accom­modates finite strains, large displacements and rotations, and accounts for shear distortion in bending. Torsion warping can be effortlessly acquainted for, provided elas­tic behavior is assumed. On the other hand, the intro­duction of elastic-plastic, visco-plastic and visco-elastic constitutive equations in terms of cross section general­ized strains and stresses is straightforward. The consid­eration of cross section inertia is direct as well. The accomplished formulation can be readily applied to the nonlinear analysis of spatial frames through the finite element method and presents the following advan­tages: (a) rotations in 3D space are treated in a consistent but convenient way through the Euler-Rodrigues for­mula: update algorithms based on quaternion pa­rameters are not required; (b) there is no need of approximate strain-displacement relationships or additional assumptions like moder­ate rotations, small curvatures and small cross sec­tion dimensions; (c) generalized cross section strains and stresses, which are energetically conjugate, can be consistently de­fined; (d) generalized cross section displacements and external loadings, which are energetically conjugate, can be consistently defined; (e) equilibrium and motion equations are consistently derived in weak form as well as in strong form; (f) boundary conditions are obtained by variational ar­guments;

Proceedings ArticleDOI
19 Apr 1993
TL;DR: In this paper, a finite element was developed for use in the vibration analysis of fluid-conveying pipes, represented as a Timoshenko beam possessing stiffness and mass while the fluid was iciealized as incompressible and inviscid.
Abstract: A finite element was developed for use in the vibration analysis of fluid-conveying pipes. The pipe was represented as a Timoshenko beam possessing stiffness and mass while the fluid was iciealized as incompressible and inviscid. With these simplifications the equations of motion were derived by the use of Hamilton's principle. Coriolis and centripetal terms in the equation of motion were the result of the fluid flowing in a moving frame of reference (Le. the vibrating pipe). Formulation of a two-node, Co continuous, fluid-conveying beam element followed from the weak form of the equation of motion. Inclusion of the Coriolis term is what made this element unique with respect to previous work. Verification of the element was accomplished by modeling Coriolis mass flowmeters and then predicting their frequency and relative phase delay for the mode of operation. Results compared favorably to experimental data for commercially available Coriolis mass flowmeters.

Proceedings ArticleDOI
01 Sep 1993
TL;DR: Two algorithms, derived from the finite element method, are described and analyzed and can incorporate an interpolation function directly into the authors' form factor computation.
Abstract: Many of the current radiosity algorithms create a piecewise constant approximation to the actual radiosity. Through interpolation and extrapolation, a continuous solution is obtained. An accurate solution is found by increasing the number of patches which describe the scene. This has the effect of increasing the computation time as well as the memory requirements. By using techniques found in the finite element method, we can incorporate an interpolation function directly into our form factor computation. We can then use less elements to achieve a more accurate solution. Two algorithms, derived from the finite element method, are described and analyzed.

Journal ArticleDOI
TL;DR: A comparison of the total and orbital energies for two diatomic systems demonstrates that the finite basis set approach can afford an accuracy approaching that achieved in finite difference and finite element methods provided that the large and flexible basis sets are systematically constructed.

Journal ArticleDOI
TL;DR: In this paper, a three-step finite element method has been used to simulate unsteady incompressible flows, such as the vortex pairing in mixing layer, and the properties of the flow fields are displayed by the marker and cell technique.
Abstract: This paper describes a three-step finite element method and its applications to unsteady incompressible fluid flows. The stability analysis of the one-dimensional purely convection equation shows that this method has third-order accuracy and an extended numerical stability domain in comparison with the Lax-Wendroff finite element method. The method is cost effective for incompressible flows, because it permits less frequent updates of the pressure field with good accuracy. In contrast with the Taylor-Galerkin method, the present three-step finite element method does not contain any new higher-order derivatives, and is suitable for solving non-linear multi-dimensional problems and flows with complicated outlet boundary conditions. The three-step finite element method has been used to simulate unsteady incompressible flows, such as the vortex pairing in mixing layer. The properties of the flow fields are displayed by the marker and cell technique. The obtained numerical results are in good agreement with the literature.


Journal ArticleDOI
TL;DR: In this paper, the mixed finite element method is applied to construct a two-dimensional membrane element with drilling rotations for geometrically nonlinear elasticity, which yields rather stiff but indeed convergent results.

Journal ArticleDOI
TL;DR: This paper discretizes the equations in space using Galerkin methods and analyzes semidiscrete as well as second and fourth-order accurate in time fully discrete methods for the approximation of the solution of the problem and proves optimal-order L2 error estimates.
Abstract: In this paper we study finite element methods for a class of problems of nonlinear elastodynamics. We discretize the equations in space using Galerkin methods. For the temporal discretization, the construction of our schemes is based on rational approximations of cos x and ex. We analyze semidiscrete as well as secondand fourth-order accurate in time fully discrete methods for the approximation of the solution of the problem and prove optimal-order L2 error estimates. For some schemes a Taylor-type technique is used so that only linear systems of equations need be solved at each time step. In the proofs we need various estimates for a nonlinear elliptic projection, the proofs of which are also established in the paper.

Journal ArticleDOI
TL;DR: In this paper, an efficient and accurate finite element procedure for the solution directly in the time domain of transient problems involving structures submerged in an infinite acoustic fluid is proposed. But the complexity of the finite element software for interior structural acoustics problems is not addressed.
Abstract: This paper is concerned with the development of an efficient and accurate finite element procedure for the solution directly in the time domain of transient problems involving structures submerged in an infinite acoustic fluid The central feature of the procedure is a novel impedance, or, absorbing boundary, element that is used to render the computational domain finite This element is local in both time and space, and is completely defined by a pair of symmetric stiffness and damping matrices It thus can be attached directly to the adjoining fluid elements within the computational domain using standard assembly procedures Due to its local nature, it also preserves the overall structure of the global equations of motion, including symmetry and sparseness Thus the new impedance element makes it possible to solve complex transient exterior structural acoustics problems via existing finite element software for interior problems by just incorporating this element into current finite element libraries St


Journal ArticleDOI
TL;DR: In this paper, a two-dimensional transient model for the removal of metal using a high power laser is developed, and the non-dimensional forms of the governing equation and the boundary conditions are derived by using a finite element method.

Journal ArticleDOI
TL;DR: In this article, a class of extraction techniques is developed to recover stresses as well as displacements from finite element solutions, with particular emphasis on the extraction of boundary stresses along slope continuous portions of the boundary.
Abstract: A class of extraction techniques is developed to recover stresses as well as displacements from finite element solutions. Particular emphasis is placed on the extraction of boundary stresses along slope continuous portions of the boundary. The techniques are superconvergent in that the convergence of the recovered quantities is equal to that of the strain energy. Numerical examples are used to demonstrate that the techniques are efficient and reliable, and can be easily implemented in the finite element analysis environment.

Book ChapterDOI
01 Jan 1993
TL;DR: In this paper, the concept of finite element analysis in nonlinear solid mechanics using material (Lagrangian) and spatial (Eulerian) coordinates has been discussed and a brief introduction in stability analysis and the associated numerical algorithms are given.
Abstract: This three lectures course will give a modern concept of finite-element- analysis in nonlinear solid mechanics using material (Lagrangian) and spatial (Eulerian) coordinates. Elastic response of solids is treated as an essential example for the geometrically and material nonlinear behavior. Furthermore a brief introduction in stability analysis and the associated numerical algorithms will be given.

01 Jan 1993
TL;DR: In this article, the authors proposed a method for solving scalar nonlinear conservation laws using discontinuous elements in one or in several dimensions, where the standard first order difference scheme is obtained with piecewise constant approximations, while higher degree piecewise polynomial approximation gives more accurate schemes.
Abstract: Solutions of scalar nonlinear conservation laws are calculated by using discontinuous finite elements in one or in several dimensions. The standard first order finite difference scheme is obtained with piecewise constant approximations, while higher degree piecewise polynomial approximations give more accurate schemes. At discontinuities of the approximate solution, numerical fluxes are calculated by one-dimensional approximate Riemann solvers. The method is stabilized with truely multidimensional slope limiters. Special attention is given to piecewise linear approximation which is shown to be total variation diminishing and con-vergent. In two dimensions numerical experiments are presented on structural as well as on unstructured meshes.


Journal ArticleDOI
TL;DR: In this article, a finite element method based on a least-squares variational principle is developed for the velocity-vorticity-pressure formulation of the Navier-Stokes equations.


Journal ArticleDOI
TL;DR: A class of nonstandard finite element methods, which are based on the use of nonconforming finite elements and the projection of coefficients into finite element spaces, produce symmetric and positive definite systems of algebraic equations.
Abstract: In this paper, a class of nonstandard finite element methods, which we call projection finite element methods, is introduced to numerically solve the stationary drift-diffusion semiconductor device equations in two and three space dimensions The methods are based on the use of nonconforming finite elements and the projection of coefficients into finite element spaces, produce symmetric and positive definite systems of algebraic equations, allow to design optimal order multigrid methods for the solution of the linear systems, and yield error estimates of high order Numerical results are presented to show the performance of the methods