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  • Open Access


    Computation of Nonlinear Schrödinger Equation on an Open Waveguide Terminated by a PML

    Jianxin Zhu1, Zheqi Shen1

    CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.4, pp. 347-362, 2011, DOI:10.3970/cmes.2011.071.347

    Abstract It is known that the perfectly matched layer (PML) is a powerful tool to truncate the unbounded domain. Recently, the PML technique has been introduced in the computation of nonlinear Schrödinger equations (NSE), in which the nonlinearity is separated by some efficient time-splitting methods. A major task in the study of PML is that the original equation is modified by a factor c which varies fast inside the layer. And a large number of grid points are needed to capture the profile of c in the discretization. In this paper, the possibility is discussed for using some nonuniform finite difference… More >

  • Open Access


    The Superconvergence of Certain Two-Dimensional Cauchy Principal Value Integrals

    Jin Li 1, De-hao Yu 2

    CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.4, pp. 331-346, 2011, DOI:10.3970/cmes.2011.071.331

    Abstract The composite rectangle (midpoint) rule for the computation of multi-dimensional singular integrals is discussed, and the superconvergence results is obtained. When the local coordinate is coincided with certain priori known coordinates, we get the convergence rate one order higher than the global one. At last, numerical examples are presented to illustrate our theoretical analysis which agree with it very well. More >

  • Open Access


    Finite Element Approximate Inverse Preconditioning for solving 3D Biharmonic Problems on Shared Memory Systems

    G.A. Gravvanis1, K.M. Giannoutakis2

    CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.4, pp. 305-330, 2011, DOI:10.3970/cmes.2011.071.305

    Abstract In this paper we present parallel explicit approximate inverse matrix techniques for solving sparse linear systems on shared memory systems, which are derived using the finite element method for biharmonic equations in three space variables. Our approach for solving such equations is by considering the biharmonic equation as a coupled equation approach (pair of Poisson equation), using a FE approximation scheme, yielding an inner-outer iteration method. Additionally, parallel approximate inverse matrix algorithms are introduced for the efficient solution of sparse linear systems, based on an anti-diagonal computational approach that eliminates the data dependencies. Parallel explicit preconditioned conjugate gradient-type schemes in… More >

  • Open Access


    Simple "Residual-Norm" Based Algorithms, for the Solution of a Large System of Non-Linear Algebraic Equations, which Converge Faster than the Newton’s Method

    Chein-Shan Liu1, Satya N. Atluri2

    CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.3, pp. 279-304, 2011, DOI:10.3970/cmes.2011.071.279

    Abstract For solving a system of nonlinear algebraic equations (NAEs) of the type: F(x)=0, or Fi(xj) = 0, i,j = 1,...,n, a Newton-like algorithm has several drawbacks such as local convergence, being sensitive to the initial guess of solution, and the time-penalty involved in finding the inversion of the Jacobian matrix ∂Fi/∂xj. Based-on an invariant manifold defined in the space of (x,t) in terms of the residual-norm of the vector F(x), we can derive a gradient-flow system of nonlinear ordinary differential equations (ODEs) governing the evolution of x with a fictitious time-like variable t as an independent variable. We can prove… More >

  • Open Access


    Recent Developments on Thermo-Mechanical Simulations of Ductile Failure by Meshfree Method

    B. Ren1,2, J. Qian1, X. Zeng1, A. K. Jha3, S. Xiao4, S. Li1,5

    CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.3, pp. 253-278, 2011, DOI:10.3970/cmes.2011.071.253

    Abstract Ductile failure is a complex multi-scale phenomenon evolved from the micro-voids to macro-crack. There are three main failure mechanisms behinds a ductile failure: adiabatic shear band (ASB), spall fracture, and crack. Since this type of thermo-mechanical phenomena involves large deformation and large scale plastic yielding, a meshfree method has intrinsic advantages in solving this kind of problems over the conventional finite element method. In this paper, the numerical methodologies including multi-physics approach for ASB, parametric visibility condition for crack propagation, and multi-scale approach to determine spall strength in simulating ductile failure have been reviewed. A thermo-mechanical coupling algorithm is proposed… More >

  • Open Access


    A High-Fidelity Cable-Analogy Continuum Triangular Element for the Large Strain, Large Deformation, Analysis of Membrane Structures

    P.D.Gosling1,2, L. Zhang2

    CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.3, pp. 203-252, 2011, DOI:10.3970/cmes.2011.071.203

    Abstract The analysis of a continuum membrane by means of a discrete network of cables or bars is an efficient and readily tractable approach to the solution of a complex mechanics problem. However, is so doing, compromises are made in the quality of the approximation of the strain field. It is shown in this paper that the original form of the cable-analogy continuum triangle formulation is degraded by an inherent assumption of small strains in the underlying equations, in which the term ßmall" is shown to be "negligibly small". A revised version of this formulation is proposed in which a modification… More >

  • Open Access


    Assessment and Computational Improvement of Thermal Lattice Boltzmann Models Based Benchmark Computations

    R. Djebali1, M. El Ganaoui2

    CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.3, pp. 179-202, 2011, DOI:10.3970/cmes.2011.071.179

    Abstract The Lattice Boltzmann method (LBM) became, today, a powerful tool for simulating fluid flows. Its improvements for different applications and configurations offers more flexibility and results in several schemes such as in presence of external/internal forcing term. However, we look for the suitable model that gives correct informations, matches the hydrodynamic equations and preserves some features like coding easily, preserving computational cost, stability and accuracy. In the present work, high order incompressible models and equilibrium distribution functions for the advection-diffusion equations are analyzed. Boundary conditions, acceleration, stability and preconditioning with initial fields are underlined which permit to rigorously selecting two… More >

  • Open Access


    A New Insight into the Differential Quadrature Method in Solving 2-D Elliptic PDEs

    Ying-Hsiu Shen1, Chein-Shan Liu1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.2, pp. 157-178, 2011, DOI:10.3970/cmes.2011.071.157

    Abstract When the local differential quadrature (LDQ) has been successfully applied to solve two-dimensional problems, the global method of DQ still has a problem by requiring to solve the inversions of ill-posed matrices. Previously, when one uses (n-1)th order polynomial test functions to determine the weighting coefficients with n grid points, the resultant n ×n Vandermonde matrix is highly ill-conditioned and its inversion is hard to solve. Now we use (m-1)th order polynomial test functions by n grid points that the size of Vandermonde matrix is m×n, of which m is much less than n. We find that the (m-1)th order… More >

  • Open Access


    Turbulentlike Quantitative Analysis on Energy Dissipation in Vibrated Granular Media

    Zhi Yuan Cui1, Jiu Hui Wu1, Di Chen Li1

    CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.2, pp. 149-156, 2011, DOI:10.3970/cmes.2011.071.149

    Abstract A quantitative rule of the vibrated granular media's energy dissipation is obtained by adopting the turbulence theory in this letter. Our results show that, similar to the power spectrum in fully developed fluid turbulence as described in Kolmogorov's theory, the power spectrum of vibrated granular media also exhibits a k - 5 / 3 (k is the wave number) power which characterizes the local isotropic flow. What's more, the mean energy dissipation rate in vibrated granular media rises with the increase of particle size and volume ratio. The theoretical results in this letter can be verified by the previous experimental… More >

  • Open Access


    Accurate Time Integration of Linear Elastodynamics Problems

    A. Idesman 1

    CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.2, pp. 111-148, 2011, DOI:10.3970/cmes.2011.071.111

    Abstract The paper deals with the following issues of existing time-integration methods for a semi-discrete system of elastodynamics equations: a) the quantification and the suppression of spurious high frequencies; b) the selection of the amount of numerical dissipation for a time-integration method; and c) accurate time integration of low modes. The finite element method used in the paper or other methods can be applied for the space discretization. A new two-stage time-integration procedure consisting of basic computations and the filtering stage is developed. For accurate integration of all frequencies, a time-integration method with zero (or small) numerical dissipation is applied for… More >

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