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  • Open Access

    ARTICLE

    Solution of Two-dimensional Linear and Nonlinear Unsteady Schrödinger Equation using “Quantum Hydrodynamics” Formulation with a MLPG Collocation Method

    V. C. Loukopoulos1, G. C. Bourantas2

    CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.1, pp. 49-70, 2014, DOI:10.3970/cmes.2014.103.049

    Abstract A numerical solution of the linear and nonlinear time-dependent Schrödinger equation is obtained, using the strong form MLPG Collocation method. Schrödinger equation is replaced by a system of coupled partial differential equations in terms of particle density and velocity potential, by separating the real and imaginary parts of a general solution, called a quantum hydrodynamic (QHD) equation, which is formally analogous to the equations of irrotational motion in a classical fluid. The approximation of the field variables is obtained with the Moving Least Squares (MLS) approximation and the implicit Crank-Nicolson scheme is used for time discretization. For the two-dimensional nonlinear… More >

  • Open Access

    ARTICLE

    Space-time Discontinuous Galerkin Method Based on a New Generalized Flux Vector Splitting Method for Multi-dimensional Nonlinear Hyperbolic Systems

    P.A. Trapper1, P.Z. Bar-Yoseph2

    CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.1, pp. 19-47, 2014, DOI:10.3970/cmes.2014.103.019

    Abstract The space-time discontinuous Galerkin method for multi-dimensional nonlinear hyperbolic systems is enhanced with a generalized technique for splitting a flux vector that is not limited to the homogeneity property of the flux. This technique, based on the flux’s characteristic decomposition, extends the scope of the method’s applicability to a wider range of problems, including elastodynamics. The method is used for numerical solution of a number of representative problems based on models of vibrating string and vibrating rod that involve the propagation of a sharp front through the solution domain. More >

  • Open Access

    ARTICLE

    Approximate Analytical Solution of Time-fractional order Cauchy-Reaction Diffusion equation

    H. S. Shukla1, Mohammad Tamsir1, Vineet K. Srivastava2, Jai Kumar3

    CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.1, pp. 1-17, 2014, DOI:10.3970/cmes.2014.103.001

    Abstract The objective of this article is to carry out an approximate analytical solution of the time fractional order Cauchy-reaction diffusion equation by using a semi analytical method referred as the fractional-order reduced differential transform method (FRDTM). The fractional derivative is illustrated in the Caputo sense. The FRDTM is very efficient and effective powerful mathematical tool for solving wide range of real world physical problems by providing an exact or a closed approximate solution of any differential equation arising in engineering and allied sciences. Four test numerical examples are provided to validate and illustrate the efficiency of FRDTM. More >

  • Open Access

    ARTICLE

    MLPG Refinement Techniques for 2D and 3D Diffusion Problems

    Annamaria Mazzia1, Giorgio Pini1, Flavio Sartoretto2

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.6, pp. 475-497, 2014, DOI:10.3970/cmes.2014.102.475

    Abstract Meshless Local Petrov Galerkin (MLPG) methods are pure meshless techniques for solving Partial Differential Equations. One of pure meshless methods main applications is for implementing Adaptive Discretization Techniques. In this paper, we describe our fresh node–wise refinement technique, based upon estimations of the “local” Total Variation of the approximating function. We numerically analyze the accuracy and efficiency of our MLPG–based refinement. Solutions to test Poisson problems are approximated, which undergo large variations inside small portions of the domain. We show that 2D problems can be accurately solved. The gain in accuracy with respect to uniform discretizations is shown to be… More >

  • Open Access

    ARTICLE

    On the Formulation of Three-Dimensional Inverse Catenary for Embedded Mooring Line Modeling

    M.A.L. Martins1, E.N. Lages1

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.6, pp. 449-474, 2014, DOI:10.3970/cmes.2014.102.449

    Abstract Embedded anchors have been widely used in offshore operations, and they are known to be effective and economical solutions to anchoring problems. Aiming at contributing to the definition and understanding of the embedded mooring line behavior, this paper expands the formulation adopted at DNV Recommended Practices, for two-dimensional modeling of the interaction between the seabed and the anchor line, to three-dimensional analysis. The formulation here presented, within an elegant differential geometry approach, can now model even out of plane lines. A reference problem is then defined and solved using the obtained governing equations. Corresponding equations are implemented and solved numerically… More >

  • Open Access

    ARTICLE

    The Boundary Integral Equation for 3D General Anisotropic Thermoelasticity

    Y.C. Shiah1, C.L. Tan2,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.6, pp. 425-447, 2014, DOI:10.3970/cmes.2014.102.425

    Abstract Green’s functions, or fundamental solutions, are necessary items in the formulation of the boundary integral equation (BIE), the analytical basis of the boundary element method (BEM). In the formulation of the BEM for 3D general anisotropic elasticity, considerable attention has been devoted to developing efficient algorithms for computing these quantities over the years. The mathematical complexity of this Green’s function has also posed an obstacle in the development of this numerical method to treat problems of 3D anisotropic thermoelasticity. This is because thermal effects manifest themselves as an additional domain integral in the integral equation; this has implications for the… More >

  • Open Access

    ARTICLE

    Voxel-based Analysis of Electrostatic Fields in Virtual-human Model Duke using Indirect Boundary Element Method with Fast Multipole Method

    S. Hamada1

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.5, pp. 407-424, 2014, DOI:10.3970/cmes.2014.102.407

    Abstract The voxel-based indirect boundary element method (IBEM) combined with the Laplace-kernel fast multipole method (FMM) is capable of analyzing relatively large-scale problems. A typical application of the IBEM is the electric field analysis in virtual-human models such as the model called Duke provided by the foundation for research on information technologies in society (IT’IS Foundation). An important property of voxel-version Duke models is that they have various voxel sizes but the same structural feature. This property is useful for examining the O(N) and O(D2) dependencies of the calculation times and the amount of memory required by the FMM-IBEM, where NMore >

  • Open Access

    ARTICLE

    Free-Space Fundamental Solution of a 2D Steady Slow Viscous MHD Flow

    A. Sellier1, S. H. Aydin2, M. Tezer-Sezgin3

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.5, pp. 393-406, 2014, DOI:10.3970/cmes.2014.102.393

    Abstract The fundamental free-space 2D steady creeping MHD flow produced by a concentrated point force of strength g located at a so-called source point x0 in an unbounded conducting Newtonian liquid with uniform viscosity µ and conductivity σ > 0 subject to a prescribed uniform ambient magnetic field B = Be1 is analytically obtained. More precisely, not only the produced flow pressure p and velocity u but also the resulting stress tensor field σ are expressed at any observation point x ≠ x0 in terms of usual modified Bessel functions, the vectors g, x-x0 and the so-called Hartmann layer thickness d… More >

  • Open Access

    ARTICLE

    An Improved Isogeometric Boundary Element Method Approach in Two Dimensional Elastostatics

    Vincenzo Mallardo1, Eugenio Ruocco2

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.5, pp. 373-391, 2014, DOI:10.3970/cmes.2014.102.373

    Abstract The NURBS based isogeometric analysis offers a novel integration between the CAD and the numerical structural analysis codes due to its superior capacity to describe accurately any complex geometry. Since it was proposed in 2005, the approach has attracted rapidly growing research interests and wide applications in the Finite Element context. Only recently, in 2012, it was successfully tested together with the Boundary Element Method. The combination of the isogeometric approach and the Boundary Element Method is efficient since both the NURBS geometrical representation and the Boundary Element Method deal with quantities entirely on the boundary of the problem. Actually,… More >

  • Open Access

    ARTICLE

    Analysis of 3D Anisotropic Solids Using Fundamental Solutions Based on Fourier Series and the Adaptive Cross Approximation Method

    R. Q. Rodríguez1,2, C. L. Tan2, P. Sollero1, E. L. Albuquerque3

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.5, pp. 359-372, 2014, DOI:10.3970/cmes.2014.102.359

    Abstract The efficient evaluation of the fundamental solution for 3D general anisotropic elasticity is a subject of great interest in the BEM community due to its mathematical complexity. Recently, Tan, Shiah, andWang (2013) have represented the algebraically explicit form of it developed by Ting and Lee (Ting and Lee, 1997; Lee, 2003) by a computational efficient double Fourier series. The Fourier coefficients are numerically evaluated only once for a specific material and are independent of the number of field points in the BEM analysis. This work deals with the application of hierarchical matrices and low rank approximations, applying the Adaptive Cross… More >

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