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  • Open Access

    ARTICLE

    Weak Coupling of the Symmetric Galerkin BEM with FEM for Potential and Elastostatic Problems

    R. Springhetti1, G. Novati1, M. Margonari2

    CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.1, pp. 67-80, 2006, DOI:10.3970/cmes.2006.013.067

    Abstract With reference to potential and elastostatic problems, a BEM-FEM coupling procedure, based on the symmetric Galerkin version of the BEM, is developed; the continuity conditions at the interface of the BE and FE subdomains are enforced in weak form; the global linear system is characterized by a symmetric coefficient matrix. The procedure is numerically tested with reference first to 2D potential problems and successively to 3D elastoplastic problems (with plastic strains confined to the FE subdomain). More >

  • Open Access

    ARTICLE

    A New High-order Time-kernel BIEM for the Burgers Equation

    N. Mai-Duy1,2, T. Tran-Cong2, R.I. Tanner3

    CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.3, pp. 177-186, 2006, DOI:10.3970/cmes.2006.016.177

    Abstract This paper presents a new high-order time-kernel boundary-integral-equation method (BIEM) for numerically solving transient problems governed by the Burgers equation. Instead of using high-order Lagrange polynomials such as quadratic and quartic interpolation functions, the proposed method employs integrated radial-basis-function networks (IRBFNs) to represent the unknown functions in boundary and volume integrals. Numerical implementations of ordinary and double integrals involving time in the presence of IRBFNs are discussed in detail. The proposed method is verified through the solution of diffusion and convection-diffusion problems. A comparison of the present results and those obtained by low-order BIEMs and More >

  • Open Access

    ARTICLE

    Distributed Finite Element Normalized Approximate Inverse Preconditioning

    G.A. Gravvanis1, K.M. Giannoutakis1

    CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 69-82, 2006, DOI:10.3970/cmes.2006.016.069

    Abstract A new class of normalized explicit optimized approximate inverse finite element matrix techniques, based on normalized finite element approximate factorization procedures, for solving sparse linear systems resulting from the finite element discretization of partial differential equations in three space variables are introduced. A new parallel normalized explicit preconditioned conjugate gradient square method in conjunction with normalized approximate inverse finite element matrix techniques for solving efficiently sparse finite element linear systems on distributed memory systems is also presented along with theoretical estimates on speedups and efficiency. The performance on a distributed memory machine, using Message Passing More >

  • Open Access

    ARTICLE

    Meshless Local Petrov-Galerkin Method for Linear Coupled Thermoelastic Analysis

    J. Sladek1, V. Sladek1, Ch. Zhang2, C.L. Tan3

    CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.1, pp. 57-68, 2006, DOI:10.3970/cmes.2006.016.057

    Abstract The Meshless Local Petrov-Galerkin (MLPG) method for linear transient coupled thermoelastic analysis is presented. Orthotropic material properties are considered here. A Heaviside step function as the test functions is applied in the weak-form to derive local integral equations for solving two-dimensional (2-D) problems. In transient coupled thermoelasticity an inertial term appears in the equations of motion. The second governing equation derived from the energy balance in coupled thermoelasticity has a diffusive character. To eliminate the time-dependence in these equations, the Laplace-transform technique is applied to both of them. Local integral equations are written on small More >

  • Open Access

    ARTICLE

    The Lie-Group Shooting Method for Singularly Perturbed Two-Point Boundary Value Problems

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 179-196, 2006, DOI:10.3970/cmes.2006.015.179

    Abstract This paper studies the numerical computations of the second-order singularly perturbed boundary value problems (SPBVPs). In order to depress the singularity we consider a coordinate transformation from the x-domain to the t-domain. The relation between singularity and stiffness is demonstrated, of which the coordinate transformation parameter λ plays a key role to balance these two tendencies. Then we construct a very effective Lie-group shooting method to search the missing initial condition through a weighting factor r ∈ (0,1) in the t-domain formulation. For stabilizing the new method we also introduce two new systems by a translation of More >

  • Open Access

    ARTICLE

    Remeshing and Refining with Moving Finite Elements. Application to Nonlinear Wave Problems

    A. Wacher1, D. Givoli2

    CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 147-164, 2006, DOI:10.3970/cmes.2006.015.147

    Abstract The recently proposed String Gradient Weighted Moving Finite Element (SGWMFE) method is extended to include remeshing and refining. The method simultaneously determines, at each time step, the solution of the governing partial differential equations and an optimal location of the finite element nodes. It has previously been applied to the nonlinear time-dependent two-dimensional shallow water equations, under the demanding conditions of large Coriolis forces, inducing large mesh and field rotation. Such effects are of major importance in geophysical fluid dynamics applications. Two deficiencies of the original SGWMFE method are (1) possible tangling of the mesh… More >

  • Open Access

    ARTICLE

    Topology Optimization of 2D Potential Problems Using Boundary Elements

    Adrián P. Cisilino1

    CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.2, pp. 99-106, 2006, DOI:10.3970/cmes.2006.015.099

    Abstract Topological Optimization provides a powerful framework to obtain the optimal domain topology for several engineering problems. The Topological Derivative is a function which characterizes the sensitivity of a given problem to the change of its topology, like opening a small hole in a continuum or changing the connectivity of rods in a truss.
    A numerical approach for the topological optimization of 2D potential problems using Boundary Elements is presented in this work. The formulation of the problem is based on recent results which allow computing the topological derivative from potential and flux results. The… More >

  • Open Access

    ARTICLE

    The Application of a Hybrid Inverse Boundary Element Problem Engine for the Solution of Potential Problems

    S. Noroozi1, P. Sewell1, J. Vinney1

    CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.3, pp. 171-180, 2006, DOI:10.3970/cmes.2006.014.171

    Abstract A method that combines a modified back propagation Artificial Neural Network (ANN) and Boundary Element Analysis (BEA) was introduced and discussed in the author's previous papers. This paper discusses the development of an automated inverse boundary element problem engine. This inverse problem engine can be applied to both potential and elastostatic problems.
    In this study, BEA solutions of a two-dimensional potential problem is utilised to test the system and to train a back propagation Artificial Neural Network (ANN). Once training is completed and the transfer function is created, the solution to any subsequent or new… More >

  • Open Access

    ARTICLE

    Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method For Elasticity Problems

    S. N. Atluri1, H. T. Liu2, Z. D. Han2

    CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.3, pp. 141-152, 2006, DOI:10.3970/cmes.2006.014.141

    Abstract The Meshless Local Petrov-Galerkin (MLPG) mixed collocation method is proposed in this paper, for solving elasticity problems. In the present MLPG approach, the mixed scheme is applied to interpolate the displacements and stresses independently, as in the MLPG finite volume method. To improve the efficiency, the local weak form is established at the nodal points, for the stresses, by using the collocation method. The traction boundary conditions are also imposed into the stress equations directly. It becomes very simple and straightforward to impose various boundary conditions, especially for the high-order PDEs. Numerical examples show that More >

  • Open Access

    ARTICLE

    The Applications of Meshless Local Petrov-Galerkin (MLPG) Approaches in High-Speed Impact, Penetration and Perforation Problems

    Z. D. Han1, H. T. Liu1, A. M. Rajendran2, S. N. Atluri3

    CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.2, pp. 119-128, 2006, DOI:10.3970/cmes.2006.014.119

    Abstract This paper presents the implementation of a three-dimensional dynamic code, for contact, impact, and penetration mechanics, based on the Meshless Local Petrov-Galerkin (MLPG) approach. In the current implementation, both velocities and velocity-gradients are interpolated independently, and their compatibility is enforced only at nodal points. As a result, the time consuming differentiations of the shape functions at all integration points is avoided, and therefore, the numerical process becomes more stable and efficient. The ability of the MLPG code for solving high-speed contact, impact and penetration problems with large deformations and rotations is demonstrated through several computational More >

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