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  • Open Access

    ARTICLE

    Improving Volume Element Methods by Meshless Radial Basis Function Techniques

    P. Orsini1, H. Power1,2, H. Morvan1

    CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.3, pp. 187-208, 2008, DOI:10.3970/cmes.2008.023.187

    Abstract In this work, we present a modified Control Volume (CV) method that uses a Radial Basis Function (RBF) interpolation to improve the prediction of the flux accuracy at the faces of the CV. The method proposed differs from classical CV methods in the way that the flux at the cell surfaces is computed. A local RBF interpolation of the field variable is performed at the centres of the cell being integrated and its neighbours. This interpolation is then used to reconstruct the solution and its gradient in the integration points which support the flux computation. More >

  • Open Access

    ARTICLE

    A Hybrid Multi-Region BEM / LBIE-RBF Velocity-Vorticity Scheme for the Two-Dimensional Navier-Stokes Equations

    E.J. Sellountos1, A. Sequeira1

    CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.2, pp. 127-148, 2008, DOI:10.3970/cmes.2008.023.127

    Abstract In this work a hybrid velocity-vorticity scheme for the solution of the 2D Navier-Stokes equations is presented. The multi-region Local Boundary Integral Equation (LBIE) combined with Radial Basis Functions (RBF) interpolation is used for the solution of the kinematics and the multi-region BEM for the solution of the transport kinetics. The final system of equations is in band form for both methods. The issue of RBF discontinuities is resolved by constructing the RBF matrix locally in every region. The kinematics integral equation is used in three different forms, for coupling the velocity field on the More >

  • Open Access

    ARTICLE

    Meshless Method with Enriched Radial Basis Functions for Fracture Mechanics

    P.H. Wen1, M.H. Aliabadi2

    Structural Durability & Health Monitoring, Vol.3, No.2, pp. 107-120, 2007, DOI:10.3970/sdhm.2007.003.107

    Abstract In the last decade, meshless methods for solving differential equations have become a promising alternative to the finite element and boundary element methods. Based on the variation of potential energy, the element-free Galerkin method is developed on the basis of finite element method by the use of radial basis function interpolation. An enriched radial basis function is formulated to capture the stress singularity at the crack tip. The usual advantages of finite element method are retained in this method but now significant improvement of accuracy. Neither the connectivity of mesh in the domain by the More >

  • Open Access

    ABSTRACT

    A comparison of the RBF-based meshfree boundary knot and the boundary particle methods

    W. Chen1

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 177-188, 2007, DOI:10.3970/icces.2007.003.177

    Abstract This paper is concerned with the two new boundary-type radial basis function collocation schemes, boundary knot method (BKM) and boundary particle method (BPM). The BKM is developed based on the dual reciprocity theorem, while the BKM employs the multiple reciprocity technique. Unlike the method of fundamental solution, the two methods use the non-singular general solution instead of the singular fundamental solution to circumvent the controversial artificial boundary outside the physical domain. Compared with the boundary element method, both BKM and BPM are meshfree, super-convergent, integration-free, symmetric, and mathematically simple collocation techniques for general PDEs. In More >

  • Open Access

    ARTICLE

    Geometrically Nonlinear Analysis of Reissner-Mindlin Plate by Meshless Computation

    P. H. Wen1, Y. C. Hon2

    CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.3, pp. 177-192, 2007, DOI:10.3970/cmes.2007.021.177

    Abstract In this paper, we perform a geometrically nonlinear analysis of Reissner-Mindlin plate by using a meshless collocation method. The use of the smooth radial basis functions (RBFs) gives an advantage to evaluate higher order derivatives of the solution at no cost on extra-interpolation. The computational cost is low and requires neither the connectivity of mesh in the domain/boundary nor integrations of fundamental/particular solutions. The coupled nonlinear terms in the equilibrium equations for both the plane stress and plate bending problems are treated as body forces. Two load increment schemes are developed to solve the nonlinear More >

  • Open Access

    ARTICLE

    An Unconditionally Time-Stable Level Set Method and Its Application to Shape and Topology Optimization

    S.Y. Wang1,2, K.M. Lim2,3, B.C. Khoo2,3, M.Y. Wang4

    CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 1-40, 2007, DOI:10.3970/cmes.2007.021.001

    Abstract The level set method is a numerical technique for simulating moving interfaces. In this paper, an unconditionally BIBO (Bounded-Input-Bounded-Output) time-stable consistent meshfree level set method is proposed and applied as a more effective approach to simultaneous shape and topology optimization. In the present level set method, the meshfree infinitely smooth inverse multiquadric Radial Basis Functions (RBFs) are employed to discretize the implicit level set function. A high level of smoothness of the level set function and accuracy of the solution to the Hamilton-Jacobi partial differential equation (PDE) can be achieved. The resulting dynamic system of… More >

  • Open Access

    ARTICLE

    Computation of transient viscous flows using indirect radial basis function networks

    N. Mai-Duy1, L. Mai-Cao2, T. Tran-Cong3

    CMES-Computer Modeling in Engineering & Sciences, Vol.18, No.1, pp. 59-78, 2007, DOI:10.3970/cmes.2007.018.059

    Abstract In this paper, an indirect/integrated radial-basis-function network (IRBFN) method is further developed to solve transient partial differential equations (PDEs) governing fluid flow problems. Spatial derivatives are discretized using one- and two-dimensional IRBFN interpolation schemes, whereas temporal derivatives are approximated using a method of lines and a finite-difference technique. In the case of moving interface problems, the IRBFN method is combined with the level set method to capture the evolution of the interface. The accuracy of the method is investigated by considering several benchmark test problems, including the classical lid-driven cavity flow. Very accurate results are More >

  • Open Access

    ARTICLE

    A Numerical Study of Strain Localization in Elasto-Thermo-Viscoplastic Materials using Radial Basis Function Networks

    P. Le1, N. Mai-Duy1, T. Tran-Cong1, G. Baker2

    CMC-Computers, Materials & Continua, Vol.5, No.2, pp. 129-150, 2007, DOI:10.3970/cmc.2007.005.129

    Abstract This paper presents a numerical simulation of the formation and evolution of strain localization in elasto-thermo-viscoplastic materials (adiabatic shear band) by the indirect/integral radial basis function network (IRBFN) method. The effects of strain and strain rate hardening, plastic heating, and thermal softening are considered. The IRBFN method is enhanced by a new coordinate mapping which helps capture the stiff spatial structure of the resultant band. The discrete IRBFN system is integrated in time by the implicit fifth-order Runge-Kutta method. The obtained results are compared with those of the Modified Smooth Particle Hydrodynamics (MSPH) method and More >

  • Open Access

    ARTICLE

    Computation of Laminated Composite Plates using Integrated Radial Basis Function Networks

    N. Mai-Duy1, A. Khennane2, T. Tran-Cong3

    CMC-Computers, Materials & Continua, Vol.5, No.1, pp. 63-78, 2007, DOI:10.3970/cmc.2007.005.063

    Abstract This paper reports a meshless method, which is based on radial-basis-function networks (RBFNs), for the static analysis of moderately-thick laminated composite plates using the first-order shear deformation theory. Integrated RBFNs are employed to represent the field variables, and the governing equations are discretized by means of point collocation. The use of integration rather than conventional differentiation to construct the RBF approximations significantly stabilizes the solution and enhances the quality of approximation. The proposed method is verified through the solution of rectangular and non-rectangular composite plates. Numerical results obtained show that the method achieves a very More >

  • Open Access

    ARTICLE

    Performance of Multiquadric Collocation Method in Solving Lid-driven Cavity Flow Problem with Low Reynolds Number

    S. Chantasiriwan1

    CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 137-146, 2006, DOI:10.3970/cmes.2006.015.137

    Abstract The multiquadric collocation method is the collocation method based on radial basis function known as multiquadrics. It has been successfully used to solve several linear and nonlinear problems. Although fluid flow problems are among problems previously solved by this method, there is still an outstanding issue regarding the influence of the free parameter of multiquadrics (or the shape parameter) on the performance of the method. This paper provides additional results of using the multiquadric collocation method to solve the lid-driven cavity flow problem. The method is used to solve the problem in the stream function-vorticity More >

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