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  • Open Access


    Rigorous Joining of Asymptotic Beam Models to Three-Dimensional Finite Element Models

    Huimin Song1, Dewey H. Hodges1

    CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.3, pp. 239-278, 2012, DOI:10.3970/cmes.2012.085.239

    Abstract The present paper presents a rigorous approach that can accurately and efficiently capture the linear, static and free-vibration behaviors of a beam-like structure by the rigorous combination of a one-dimensional beam model with a three-dimensional continuum model. This study focuses on coupling these disparate finite element types, putting them both into a single finite element model while making use of the asymptotically exact information available as part of the beam model, which itself is obtained by asymptotic dimensional reduction. The coupling is undertaken by use of appropriate transformation matrices at the interface together with stress and displacement recovery relations that… More >

  • Open Access


    On Determination of a Finite Jacobi Matrix from Two Spectra

    Gusein Sh. Guseinov1

    CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 405-422, 2012, DOI:10.3970/cmes.2012.084.405

    Abstract In this work we study the inverse spectral problem for two spectra of finite order real Jacobi matrices (tri-diagonal matrices). The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by replacing the first diagonal element of the Jacobi matrix by some another number. The uniqueness and existence results for solution of the inverse problem are established and an explicit procedure of reconstruction of the matrix from the two spectra is given. More >

  • Open Access


    The Mode Relation for Open Acoustic Waveguide Terminated by PML with Varied Sound Speed

    Jianxin Zhu, Zengsi Chen, Zheqi Shen

    CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.5, pp. 547-560, 2012, DOI:10.3970/cmes.2012.083.547

    Abstract An acoustic waveguide with continuously varying sound speed is discussed in this paper. When the waveguide is open along the depth, the perfectly matched layer (PML) is used to terminate the infinite domain. Since the sound speed is gradually varied, the density is assumed as constant in each fluid layer. For this waveguide, it is shown that the mode relation is derived by using the differential transfer matrix method (DTMM). To solve leaky and PML modes, Newton's iteration is applied, and Chebyshev pseudospectral method is used for obtaining initial guesses. The solutions are with high accuracy. More >

  • Open Access


    T-Trefftz Voronoi Cell Finite Elements with Elastic/Rigid Inclusions or Voids for Micromechanical Analysis of Composite and Porous Materials

    L. Dong1, S. N. Atluri2

    CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.2, pp. 183-220, 2012, DOI:10.32604/cmes.2012.083.183

    Abstract In this paper, we develop T-Trefftz Voronoi Cell Finite Elements (VCF -EM-TTs) for micromechanical modeling of composite and porous materials. In addition to a homogenous matrix in each polygon-shaped element, three types of arbitrarily-shaped heterogeneities are considered in each element: an elastic inclusion, a rigid inclusion, or a void. In all of these three cases, an inter-element compatible displacement field is assumed along the element outer-boundary, and interior displacement fields in the matrix as well as in the inclusion are independently assumed as T-Trefftz trial functions. Characteristic lengths are used for each element to scale the T-Trefftz trial functions, in… More >

  • Open Access


    An Iterative Method for the Least-Squares Minimum-Norm Symmetric Solution

    Minghui Wang1, Musheng Wei2, Shanrui Hu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.77, No.3&4, pp. 173-182, 2011, DOI:10.3970/cmes.2011.077.173

    Abstract The mapping from the symmetric solution set to its independent parameter space is studied and an iterative method is proposed for the least-squares minimum-norm symmetric solution of AXB = E. Numerical results are reported that show the efficiency of the proposed methods. 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


    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


    Drug Delivery: From a Contact Lens to the Anterior Chamber

    J.A. Ferreira2,3, P. de Oliveira2, P. Silva4, J.N. Murta5

    CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.1, pp. 1-14, 2011, DOI:10.3970/cmes.2011.071.001

    Abstract Mathematical models to describe drug concentration profiles of topically administered drug in the anterior chamber aqueous humor have been proposed by several authors. The aim of this paper is to present a mathematical model to predict the drug concentration in the anterior chamber when a therapeutical contact lens with the drug entrapped in nanoparticles is used. More >

  • Open Access


    Novel Algorithms Based on the Conjugate Gradient Method for Inverting Ill-Conditioned Matrices, and a New Regularization Method to Solve Ill-Posed Linear Systems

    Chein-Shan Liu1, Hong-Ki Hong1, Satya N. Atluri2

    CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.3, pp. 279-308, 2010, DOI:10.3970/cmes.2010.060.279

    Abstract We propose novel algorithms to calculate the inverses of ill-conditioned matrices, which have broad engineering applications. The vector-form of the conjugate gradient method (CGM) is recast into a matrix-form, which is named as the matrix conjugate gradient method (MCGM). The MCGM is better than the CGM for finding the inverses of matrices. To treat the problems of inverting ill-conditioned matrices, we add a vector equation into the given matrix equation for obtaining the left-inversion of matrix (and a similar vector equation for the right-inversion) and thus we obtain an over-determined system. The resulting two modifications of the MCGM, namely the… More >

  • Open Access


    On Solving the Ill-Conditioned System Ax=b: General-Purpose Conditioners Obtained From the Boundary-Collocation Solution of the Laplace Equation, Using Trefftz Expansions With Multiple Length Scales

    Chein-Shan Liu1, Weichung Yeih2, Satya N. Atluri3

    CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.3, pp. 281-312, 2009, DOI:10.3970/cmes.2009.044.281

    Abstract Here we develop a general purpose pre/post conditionerT, to solve an ill-posed system of linear equations,Ax=b. The conditionerTis obtained in the course of the solution of the Laplace equation, through a boundary-collocation Trefftz method, leading to:Ty=x, whereyis the vector of coefficients in the Trefftz expansion, andxis the boundary data at the discrete points on a unit circle. We show that the quality of the conditionerTis greatly enhanced by using multiple characteristic lengths (Multiple Length Scales) in the Trefftz expansion. We further show thatTcan be multiplicatively decomposed into a dilationTDand a rotationTR. For an odd-orderedA, we develop four conditioners based on… More >

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