Reinforcement strength reduction in FEM for mechanically stabilized earth structures

The factor of safety of mechanically stabilized earth(MSE) structures can be analyzed either using limit equilibrium method(LEM) or strength reduction method(SRM) in finite element/difference method. In LEM, the strengths of the reinforcement members and soils are reduced with the same factor. While using the SRM, only soil strength is reduced during the calculation of the factor of safety. This causes inconsistence in calculating the factor of safety of the MSE structures. To overcome this, an iteration method is proposed to consider the strength reduction of the reinforcements in SRM. The method is demonstrated by using PLAXIS, a finite element software. The results show that the factor of safety converges after a few iterations. The reduction of strength has different effects on the factor of safety depending on the properties of the reinforcements and the soil, and failure modes.

ERROR IMPROVEMENT OF TEMPORAL DISCRETIZATION IN TDFEM FOR ELECTROMAGNETIC ANALYSIS

Integral method is employed in this paper to alleviate the error accumulation of differential equation discretization about time variant t in Time Domain Finite Element Method (TDFEM) for electromagnetic simulation. The error growth and the stability condition of the presented method and classical central difference scheme are analyzed. The electromagnetic responses of 2D lossless cavities are investigated with TDFEM; high accuracy is validated with numerical results presented.

Numerical Homogenization of the Elliptic Problem with Rapidly Varying Tensor or Boundary Condition

Homogenization is concerned with obtaining the average properties of a material. The problem on its own has no easy solution, except in cases like the periodic case, when it can be obtained in closed form. In this paper we consider a numerical solution of the elliptic homogenization problem for the case of rapidly varying tensor or boundary conditions. The method makes use of an adaptive finite element method to correctly capture the rapid change in the tensor or boundary condition. In the numerical experiments we vary the mesh size and do a posteriori error analysis on test problems.

Spectral Methods for Two Dimensional Incompressible Flow

We take the two dimensional vorticity equations as models to describe spectral methods and their combinations with finite difference methods or finite element methods, which are applicable to other similar nonlinear problems. Some numerical results and error estimates of these methods are given.

AN ANISOTROPIC NONCONFORMING FINITE ELEMENT SCHEME WITH MOVING GRIDS FOR PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS

A Crank-Nicolson scheme based on nonconforming finite element with moving grids is dis- cussed for a class of parabolic integro-differential equations under anisotropic meshes. The corresponding convergence analysis is presented and the error estimates are obtained by using the interpolation operator instead of the conventional elliptic projection which is an indispensable tool in the convergence analysis of traditional finite element methods in previous literature.

On the use of the discontinuous Galerkin method for numerical simulation of two-dimensional compressible turbulence with shocks

In this paper,the discontinuous Galerkin(DG)method combined with localized artificial diffusivity is investigated in the context of numerical simulation of broadband compressible turbulent flows with shocks for under-resolved cases.Firstly,the spectral property of the DG method is analyzed using the approximate dispersion relation(ADR)method and compared with typical finite difference methods,which reveals quantitatively that significantly less grid points can be used with DG for comparable numerical error.Then several typical test cases relevant to problems of compressible turbulence are simulated,including one-dimensional shock/entropy wave interaction,two-dimensional decaying isotropic turbulence,and two-dimensional temporal mixing layers.Numerical results indicate that higher numerical accuracy can be achieved on the same number of degrees of freedom with DG than high order finite difference schemes.Furthermore,shocks are also well captured using the localized artificial diffusivity method.The results in this work can provide useful guidance for further applications of DG to direct and large eddy simulation of compressible turbulent flows.

Plasmonic-enhanced two-photon fluorescence with single gold nanoshell

Single gold nanoshell with mutilpolar plasmon resonances is proposed to enhance two-photon fluorescence efficiently.The single emitter single nanoshell configuration is studied systematically by employing the finite-difference time-domain method.The emitter located inside or outside the nanoshell at various positions leads to a significantly different enhancement effect.The fluorescent emitter placed outside the nanoshell can achieve large fluorescence intensity given that both the position and orientation of the emission dipole are optimally controlled.In contrast,for the case of the emitter placed inside the nanoshell,it can experience substantial two-photon fluorescence enhancement without strict requirements upon the position and dipole orientations.Metallic nanoshell encapsulating many fluorescent emitters should be a promising nanocomposite configuration for bright two-photon fluorescence label.The results provide a comprehensive understanding about the plasmonic-enhanced two-photon fluorescence behaviors,and the nanocomposite configuration has great potential for optical detecting,imaging and sensing in biological applications.

A new a priori error estimate of nonconforming finite element methods

This paper is devoted to a new error analysis of nonconforming finite element methods.Compared with the classic error analysis in literature,only weak continuity,the F-E-M-Test for nonconforming finite element spaces,and basic Hm regularity for exact solutions of 2m-th order elliptic problems under consideration are assumed.The analysis is motivated by ideas from a posteriori error estimates and projection average operators.One main ingredient is a novel decomposition for some key average terms on(n.1)-dimensional faces by introducing a piecewise constant projection,which defines the generalization to more general nonconforming finite elements of the results in literature.The analysis and results herein are conjectured to apply for all nonconforming finite elements in literature.

NONCONFORMING FINITE ELEMENT METHOD FOR NONLINEAR PARABOLIC EQUATIONS

A nonconforming finite element method for the nonlinear parabolic equations is studied inthis paper.The convergence analysis is presented and the optimal error estimate in L^2(‖·‖_h)norm isobtained through Ritz projection technique,where ‖·‖_h is a norm over the finite element space.

A POSTERIORI ERROR ANALYSIS OF NONCONFORMING METHODS FOR THE EIGENVALUE PROBLEM

This paper extends the unifying theory for a posteriori error analysis of the nonconformingfinite element methods to the second order elliptic eigenvalue problem.In particular,the authorproposes the a posteriori error estimator for nonconforming methods of the eigenvalue problems andprove its reliability and efficiency based on two assumptions concerning both the weak continuity andthe weak orthogonality of the nonconforming finite element spaces,respectively.In addition,the authorexamines these two assumptions for those nonconforming methods checked in literature for the Laplace,Stokes,and the linear elasticity problems.