Showing papers on "Extended finite element method published in 1997"
TL;DR: In this article, a new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved, which can therefore be more efficient than the usual finite element methods.
Abstract: A new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved This new method can therefore be more efficient than the usual finite element methods An additional feature of the partition-of-unity method is that finite element spaces of any desired regularity can be constructed very easily This paper includes a convergence proof of this method and illustrates its efficiency by an application to the Helmholtz equation for high wave numbers The basic estimates for a posteriori error estimation for this new method are also proved © 1997 by John Wiley & Sons, Ltd
2,387 citations
TL;DR: This paper studies a multiscale finite element method for solving a class of elliptic problems arising from composite materials and flows in porous media, which contain many spatial scales and proposes an oversampling technique to remove the resonance effect.
1,825 citations
01 Jan 1997
TL;DR: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems and discusses the main points in the application to electromagnetic design, including formulation and implementation.
Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.
1,820 citations
TL;DR: This paper extends a discontinuous finite element discretization originally considered for hyperbolic systems such as the Euler equations to the case of the Navier?Stokes equations by treating the viscous terms with a mixed formulation, and finds the method is ideally suited to compute high-order accurate solution of theNavier?
1,750 citations
TL;DR: This paper focuses its attention on two-dimensional steady-state problems and presents higher order accurate discontinuous finite element solutions on unstructured grids of triangles and shows that, in the presence of curved boundaries, a meaningful high-order accurate solution can be obtained only if a corresponding high- order approximation of the geometry is employed.
780 citations
TL;DR: In this paper, various time-domain finite-element methods for the simulation of transient electromagnetic wave phenomena are discussed, including nodal and edge/facet element basis functions, along with the numerical stability properties of the different methods.
Abstract: Various time-domain finite-element methods for the simulation of transient electromagnetic wave phenomena are discussed. Detailed descriptions of test/trial spaces, explicit and implicit formulations, nodal and edge/facet element basis functions are given, along with the numerical stability properties of the different methods. The advantages and disadvantages of mass lumping are examined. Finally, the various formulations are compared on the basis of their numerical dispersion performance.
419 citations
TL;DR: In this article, a locking-free finite element model using the form of the exact solution of the Timoshenko beam theory is developed, which yields exact nodal values for the generalized displacements for constant material and geometric properties of beams.
315 citations
TL;DR: It is demonstrated how a block-iteration allows a simple and efficient implementation of the method and how finite element meshes can be constructed adaptively on the local and the global scales.
241 citations
TL;DR: In this article, the analysis of bolted steel connections by means of finite elements is presented, where elementary tee stub connections are endowed with different plastic failure mechanisms and can be used as benchmarks in the validation process of finite element software packages.
188 citations
TL;DR: In this paper, a virtual finite element method for the Navier-Stokes equations in enclosures containing internal parts which may be moving is presented, which is based upon optimization techniques and belongs to the class of fictitious domain methods.
Abstract: A new Galerkin finite element method for the solution of the Navier–Stokes equations in enclosures containing internal parts which may be moving is presented. Dubbed the virtual finite element method, it is based upon optimization techniques and belongs to the class of fictitious domain methods. Only one volumetric mesh representing the enclosure without its internal parts needs to be generated. These are rather discretized using control points on which kinematic constraints are enforced and introduced into the mathematical formulation by means of Lagrange multipliers. Consequently, the meshing of the computational domain is much easier than with classical finite element approaches.
First, the methodology will be presented in detail. It will then be validated in the case of the two-dimensional Couette cylinder problem for which an analytical solution is available. Finally, the three-dimensional fluid flow inside a mechanically agitated vessel will be investigated. The accuracy of the numerical results will be assessed through a comparison with experimental data and results obtained with a standard finite element method. © 1997 John Wiley & Sons, Ltd.
182 citations
TL;DR: In this article, the authors summarized and reviewed several finite element formulations used to solve structural acoustics and fluid-structure interaction problems, which can be applied to a variety of applications, including acoustic cavity analyis, acoustic radiation and scattering from elastic structures vibrations of submerged structures, dynamics of fluid-filled piping systems, underwater shock analyis and transient acoustic.
TL;DR: In this article, the analysis of bolted steel connections by means of finite elements was performed using the ABAQUS software package and a three-dimensional finite element model was proposed to simulate the stiffness and strength behavior of isolated extended end-plate steel connections.
TL;DR: The ideas of algebraic topology are applied to the analysis of the finite volume and finite element methods, illuminating the similarity between the discretization strategies adopted by the two methods, in the light of a geometric interpretation proposed for the role played by the weighting functions in finite elements.
TL;DR: In this paper, a displacement finite element model is derived using the Lagrangian approach together with an analogy with solid elements to solve the 3D poroelasticity problem in acoustics based on the isotropic Biot-Allard theory.
Abstract: In this paper, the finite element method (FEM) is used to solve the three-dimensional poroelasticity problem in acoustics based on the isotropic Biot–Allard theory A displacement finite element model is derived using the Lagrangian approach together with an analogy with solid elements From this model, it is seen that the “damping” and “stiffness” matrices of the poroelastic media are complex and frequency dependent This leads to cumbersome calculations for large finite element models and spectral analyses To overcome this difficulty, an efficient algorithm is proposed It is based on low-frequency approximations of the frequency-dependent dissipation mechanisms in poroelastic media This efficient algorithm allows the poroelastic materials to be modeled with classical FEM codes Also, the acoustic–poroelastic and the poroelastic–poroelastic coupling conditions are presented The proposed model is compared to existing literature for both two-dimensional and three-dimensional problems Excellent compari
TL;DR: Presents recent advances obtained by the authors in the development of enhanced strain finite elements for finite deformation problems, showing in particular a mode‐free response, while maintaining a simple and efficient (strain driven) numerical implementation.
Abstract: Presents recent advances obtained by the authors in the development of enhanced strain finite elements for finite deformation problems. Discusses two options, both involving simple modifications of the original enhancement strategy of the deformation gradient as proposed in previous works. The first new strategy is based on a full symmetrization of the original enhanced interpolation fields; the second involves only the transposed part of these fields. Both modifications lead to a significant improvement of the performance in problems involving high compressive stresses, showing in particular a mode‐free response, while maintaining a simple and efficient (strain driven) numerical implementation. Demonstrates these properties with a number of numerical benchmark simulations, including a complete modal analysis of the elements.
TL;DR: A new approach to automatic derivation of formulas needed in nonlinear finite element analysis is presented, combining several techniques: symbolic capabilities of Mathematica, automatic differentiation technique, simultaneous optimization of expressions and a stochastic evaluation of the formulas instead of a conventional pattern matching technique.
TL;DR: In this article, a stochastic heat transfer variational principle is suggested for transient and steady-state heat problems, which allows incorporation of system uncertainties into the conventional finite element equations, which are solved for the first two probabilistic moments of the nodal random temperature field.
TL;DR: In this paper, finite element methods of least-squares type for the stationary, incompressible Navier-Stokes equations in two and three dimensions were studied and optimal error estimates for conforming finite element approximations and analysis of some nonstandard boundary conditions were obtained.
Abstract: In this paper we study finite element methods of least-squares type for the stationary, incompressible Navier--Stokes equations in two and three dimensions. We consider methods based on velocity-vorticity-pressure form of the Navier--Stokes equations augmented with several nonstandard boundary conditions. Least-squares minimization principles for these boundary value problems are developed with the aid of the Agmon--Douglis--Nirenberg (ADN) elliptic theory. Among the main results of this paper are optimal error estimates for conforming finite element approximations and analysis of some nonstandard boundary conditions. Results of several computational experiments with least-squares methods which illustrate, among other things, the optimal convergence rates are also reported.
TL;DR: In this article, a numerical method is developed using a discontinuous finite element method for the discretization of the advective terms using one-dimensional approximate Riemann solvers.
Abstract: SUMMARY When transport is advection-dominated, classical numerical methods introduce excessive artificial diffusion and spurious oscillations. Special methods are required to overcome these phenomena. To solve the advection‐ diffusion equation, a numerical method is developed using a discontinuous finite element method for the discretization of the advective terms. At the discontinuities of the approximate solution, numerical advective fluxes are calculated using one-dimensional approximate Riemann solvers. The method is stabilized with a multidimensional slope limiter which introduces small amounts of numerical diffusion when sharp concentration fronts occur. In addition, the diffusive term is discretized using a mixed hybrid finite element method. With this approach, numerical oscillations are completely avoided for a full range of cell Peclet numbers. The combination of discontinuous and mixed finite elements can be easily applied to 2D and 3D models using various types of elements in regular and irregular meshes. Numerical tests show good agreement with 1D and 2D analytical solutions. This approach is compared at the same time with two different numerical methods, a standard mixed finite method and a finite volume approach with high-resolution upwind terms. Regular and irregular meshes are used for the numerical tests to study the mesh effects on the numerical results. Our data show that in all cases this approach performs well. 1997 by John Wiley & Sons, Ltd.
TL;DR: A survey of effective finite element formulations for the analysis of shell structures is presented in this article, where the basic requirements for shell elements are discussed, in which it is emphasized that generality and reliability are most important items.
Abstract: A survey of effective finite element formulations for the analysis of shell structures is presented. First, the basic requirements for shell elements are discussed, in which it is emphasized that generality and reliability are most important items. A general displacement-based formulation is then briefly reviewed. This formulation is not effective, but it is used as a starting point for developing a general and effective approach using the mixed interpolation of the tensorial components. The formulation of various MITC elements (that is, elements based on Mixed Interpolation of Tensorial Components) are presented. Theoretical results (applicable to plate analysis) and various numerical results of analyses of plates and shells are summarized. These illustrate some current capabilities and the potential for further finite element developments.
TL;DR: In this article, a numerical algorithm using equal-order linear finite element and fractional four-step methods is presented for the analyses of incompressible fluid flow and heat transfer problems, where the SUPG (streamline upwind Petrov-Galerkin) method is used for the weighted formulation of Navier-Stokes equations.
TL;DR: In this paper, the authors proposed a technique to search for the critical slip surface as well as to define and calculate the factor of safety for the slope, when the finite element method is used to model its formation.
TL;DR: This paper addresses finite element-based computational models for the three-dimensional, (3-D) nonlinear analysis of soft hydrated tissues, such as the articular cartilage in diarthrodial joints, under physiologically relevant loading conditions.
Abstract: This paper addresses finite element-based computational models for the three-dimensional, (3-D) nonlinear analysis of soft hydrated tissues, such as the articular cartilage in diarthrodial joints, under physiologically relevant loading conditions. A biphasic continuum description is used to represent the soft tissue as a two-phase mixture of incompressible, inviscid fluid and a hyperelastic solid. Alternate mixed-penalty and velocity-pressure finite element formulations are used to solve the nonlinear biphasic governing equations, including the effects of a strain-dependent permeability and a hyperelastic solid phase under finite deformation. The resulting first-order nonlinear system of equations is discretized in time using an implicit finite difference scheme, and solved using the Newton-Raphson method. Using a discrete divergence operator, an equivalence is shown between the mixed-penalty method and a penalty method previously derived by Suh et al. [1]. In Part II [2], the mixed-penalty and velocity-p...
TL;DR: In this paper, the authors derived the Kirchhoff plate-elastic foundation interaction by mixed-type formulation using the Gâteaux differential instead of well-known variational principles of Hellinger-Reissner and Hu-Washizu.
Abstract: The main objective of the present work is to give the systematic way for derivation of Kirchhoff plate-elastic foundation interaction by mixed-type formulation using the Gâteaux differential instead of well-known variational principles of Hellinger–Reissner and Hu–Washizu. Foundation is a Pasternak foundation, and as a special case if shear layer is neglected, it converges to Winkler foundation in the formulation. Uniform variation of the thickness of the plate is also included into the mixed finite element formulation of the plate element PLTVE4 which is an isoparametric C0 class conforming element discretization. In the dynamic analysis, the problem reduces to solution of the standard eigenvalue problem and the mixed element is based upon a consistent mass matrix formulation. The element has four nodes and at each node transverse displacement two bending and one torsional moment is the basic unknowns. Proper geometric and dynamic boundary conditions corresponding to the plate and the foundation is given by the functional. Performance of the element for bending and free vibration analysis is verified with a good accuracy on the numerical examples and analytical solutions present in the literature. © 1997 by John Wiley & Sons, Ltd.
TL;DR: In this article, an element geometric mapping scheme based on blending the exact shape of the domain boundary is described that can either be used directly during element integrations, or used to construct element-level geometric approximations of required accuracy.
TL;DR: In this paper, the convergence analysis of an efficient numerical method for the solution of an initial-boundary value problem for a scalar nonlinear conservation law equation with a diffusion term is presented.
Abstract: We present the convergence analysis of an efficient numerical method for the solution of an initial-boundary value problem for a scalar nonlinear conservation law equation with a diffusion term. Nonlinear convective terms are approximated with the aid of a monotone finite volume scheme considered over the finite volume mesh dual to a triangular grid, whereas the diffusion term is discretized by piecewise linear conforming triangular elements. Under the assumption that the triangulations are of weakly acute type, with the aid of the discrete maximum principle, a priori estimates, and some compactness arguments based on the use of the Fourier transform with respect to time, the convergence of the approximate solutions to the exact solution is proved, provided that the mesh size tends to zero. c 1997 John Wiley & Sons, Inc.
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01 Jul 1997
TL;DR: In this paper, a beam propagation method based on the finite element method (FEM) is described for longitudinally varying three-dimensional (3-D) optical waveguides.
Abstract: A beam propagation method (BPM) based on the finite element method (FEM) is described for longitudinally varying three-dimensional (3-D) optical waveguides. In order to avoid nonphysical reflections from the computational window edges, the transparent boundary condition is introduced. The present algorithm using the Pade approximation is, to our knowledge, the first wide-angle finite element beam propagation method for 3-D waveguide structures. To show the validity and usefulness of this approach, numerical results are shown for Gaussian-beam excitation of a straight rib waveguide and guided-mode propagation in a Y-branching rib waveguide.
TL;DR: In this article, a highly accurate and rapidly converging hybrid approach for the Quadrature Element Method (QEM) solution of plate free vibration problems is presented, which essentially consists of a collocation method in conjunction with a Galerkin finite element technique, to combine the high accuracy of DQM for the efficient solution of differential equations with the generality of the finite element formulation.