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  • Open Access

    ARTICLE

    On the Numerical Solution of the Laplace Equation with Complete and Incomplete Cauchy Data Using Integral Equations

    Christina Babenko1, Roman Chapko2, B. Tomas Johansson3

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.5, pp. 299-317, 2014, DOI:10.3970/cmes.2014.101.299

    Abstract We consider the numerical solution of the Laplace equations in planar bounded domains with corners for two types of boundary conditions. The first one is the mixed boundary value problem (Dirichlet-Neumann), which is reduced, via a single-layer potential ansatz, to a system of well-posed boundary integral equations. The second one is the Cauchy problem having Dirichlet and Neumann data given on a part of the boundary of the solution domain. This problem is similarly transformed into a system of ill-posed boundary integral equations. For both systems, to numerically solve them, a mesh grading transformation is employed together with trigonometric quadrature… More >

  • Open Access

    ARTICLE

    A Corrected 3D Parallel SPH Method for Simulating the Polymer Free Surface Flows Based on the XPP Model

    Tao Jiang1,2, Yuan-Sheng Tang1, Jin-Lian Ren1,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.4, pp. 249-297, 2014, DOI:10.3970/cmes.2014.101.249

    Abstract In this work, a corrected three-dimensional smoothed particle hydrodynamics (CSPH-3D) method is proposed to simulate the polymer free surface flows in the filling process based on the eXtended Pom-Pom (XPP) model, and some complex deformation phenomena are also numerically predicted. The proposed CSPH-3D method is mainly motivated by a coupled concept that an extended kernel-gradient-corrected SPH (KGC-SPH) method is used in the interior of fluid flow and the traditional SPH (TSPH) method is used near the boundary domain. The present 3D particle method has higher accuracy and better stability than the TSPH-3D method. Meanwhile, a density diffusive term is introduced… More >

  • Open Access

    ARTICLE

    Improved MPS-FE Fluid-Structure Interaction Coupled Method with MPS Polygon Wall Boundary Model

    N. Mitsume1, S. Yoshimura1, K. Murotani1, T. Yamada1

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.4, pp. 229-247, 2014, DOI:10.3970/cmes.2014.101.229

    Abstract The MPS-FE method, which adopts the Finite Element (FE) method for structure computation and the Moving Particle Simulation (MPS) method for fluid computation involving free surfaces, was developed to solve fluid-structure interaction problems with free surfaces. The conventional MPS-FE method, in which MPS wall boundary particles and finite elements are overlapped in order to exchange information at a fluid-structure interface, is not versatile and reduces the advantages of the software modularity. In this study, we developed a nonoverlapping approach in which the interface in the fluid computation corresponds to the interface in the structure computation through an MPS polygon wall… More >

  • Open Access

    ARTICLE

    Dynamic Response of Borehole in Poroelastic Medium with Disturbed Zone

    W. Kaewjuea1, T. Senjuntichai2, R.K.N.D. Rajapakse3

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.3, pp. 207-228, 2014, DOI:10.3970/cmes.2014.101.207

    Abstract Dynamic response of an infinite cylindrical borehole in a poroelastic medium with an excavation disturbed zone is investigated in this paper. The borehole is subjected to axisymmetric time-harmonic loads and fluid sources applied to its surface, which is either fully permeable or impermeable. The governing equations based on Biot’s poroelastodynamics theory are solved by using two scalar potentials and two vector potentials. The general solutions are then derived through the application of Fourier integral transform with respect to the vertical coordinate. An exact stiffness matrix scheme is established from the derived general solutions to include the excavation disturbed zone. Boundary… More >

  • Open Access

    ARTICLE

    Time-Domain BEM Analysis for Three-dimensional Elastodynamic Problems with Initial Conditions

    Yuan Li1, Jianming Zhang1,2, Guizhong Xie1, Xingshuai Zheng1, Shuaiping Guo1

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.3, pp. 187-206, 2014, DOI:10.3970/cmes.2014.101.187

    Abstract In this paper, a time-domain boundary element method formulation for the analysis of three-dimensional elastodynamic problems with arbitrary, non-null initial conditions is presented. The formulation is based on the convolution quadrature method, by which the numerical stability is improved significantly. In order to take into account the non-null initial conditions in this formulation, a general method is developed to replace the initial conditions by equivalent pseudo-forces based on the pseudo-force method. The original governing equation is transformed into a new one subjected to null initial conditions. In the numerical examples, longitudinal vibrations of a free beam and a cantilevered beam… More >

  • Open Access

    ARTICLE

    On Solving Linear and Nonlinear Sixth-Order Two Point Boundary Value Problems Via an Elegant Harmonic Numbers Operational Matrix of Derivatives

    W.M. Abd- Elhameed1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.3, pp. 159-185, 2014, DOI:10.3970/cmes.2014.101.159

    Abstract This paper is concerned with developing two new algorithms for direct solutions of linear and nonlinear sixth-order two point boundary value problems. These algorithms are based on the application of the two spectral methods namely, collocation and Petrov-Galerkin methods. The suggested algorithms are completely new and they depend on introducing a novel operational matrix of derivatives which is expressed in terms of the well-known harmonic numbers. The basic idea for the suggested algorithms rely on reducing the linear or nonlinear sixth-order boundary value problem governed by its boundary conditions to a system of linear or nonlinear algebraic equations which can… More >

  • Open Access

    ARTICLE

    Prediction of Fracture Parameters of High Strength and Ultra-high Strength Concrete Beam using Gaussian Process Regression and Least Squares

    Shantaram Parab1, Shreya Srivastava2, Pijush Samui3, A. Ramachandra Murthy4

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.2, pp. 139-158, 2014, DOI:10.3970/cmes.2014.101.139

    Abstract This paper studies the applicability of Gaussian Process Regression (GPR) and Least Squares Support Vector Machines (LSSVM) to predict fracture parameters and failure load (Pmax) of high strength and ultra-high strength concrete beams. Fracture characteristics include fracture energy (GF), critical stress intensity factor (KIC) and critical crack tip opening displacement (CTODC) Mathematical models have been developed in the form of relation between several input variables such as beam dimensions, water cement ratio, compressive strength, split tensile strength, notch depth, modulus of elasticity and output fracture parameters. Four GPR and four LSSVM models have been developed using MATLAB software for training… More >

  • Open Access

    ARTICLE

    A Meshless Method for Solving the 2D Brusselator Reaction-Diffusion System

    M. Mohammadi1, R. Mokhtari2,3, R. Schaback4

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.2, pp. 113-138, 2014, DOI:10.3970/cmes.2014.101.113

    Abstract In this paper, the two-dimensional (2D) Brusselator reaction-diffusion system is simulated numerically by the method of lines. The proposed method is implemented as a meshless method based on spatial trial functions in the reproducing kernel Hilbert spaces. For efficiency and stability reasons, we use the Newton basis introduced recently by Müller and Schaback. The method is shown to work in all interesting situations described by Hopf bifurcations and Turing patterns. More >

  • Open Access

    ARTICLE

    Legendre Polynomials Method for Solving a Class of Variable Order Fractional Differential Equation

    Lifeng Wang1, Yunpeng Ma1,2, Yongqiang Yang1

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.2, pp. 97-111, 2014, DOI:10.3970/cmes.2014.101.097

    Abstract In this paper, a numerical method based on the Legendre polynomials is presented for a class of variable order fractional differential equation. We adopt the Coimbra variable order fractional operator, which can be viewed as a Caputo-type definition. Three different kinds of operational matrixes with Legendre polynomials are derived. A truncated the Legendre polynomials series together with the products of several dependent matrixes are utilized to reduce the variable order fractional differential equation to a system of algebraic equations. The solution of this system gives the approximation solution for the truncated limited n. An error analysis technique is also given.… More >

  • Open Access

    ARTICLE

    Coupled ABC and Spline Collocation Approach for a Class of Nonlinear Boundary Value Problems over Semi-Infinite Domains

    S.A. Khuri1, A. Sayfy1

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.2, pp. 81-96, 2014, DOI:10.3970/cmes.2014.101.081

    Abstract In this article, we introduce a numerical scheme to solve a class of nonlinear two-point BVPs on a semi-infinite domain that arise in engineering applications and the physical sciences. The strategy is based on replacing the boundary condition at infinity by an asymptotic boundary condition (ABC) specified over a finite interval that approaches the given value at infinity. Then, the problem complimented with the resulting ABC is solved using a fourth order spline collocation approach constructed over uniform meshes on the truncated domain. A number of test examples are considered to confirm the accuracy, efficient treatment of the boundary condition… More >

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