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  • Open Access

    ARTICLE

    Topological Shape Optimization of Electromagnetic Problems using Level Set Method and Radial Basis Function

    Hokyung Shim1, Vinh Thuy Tran Ho1,,Semyung Wang1,2, Daniel A. Tortorelli3

    CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.2, pp. 175-202, 2008, DOI:10.3970/cmes.2008.037.175

    Abstract This paper presents a topological shape optimization technique for electromagnetic problems using a level set method and radial basis functions. The proposed technique is a level set (LS) based optimization dealing with geometrical shape derivatives and topological design. The shape derivative is computed by an adjoint variable method to avoid numerous sensitivity evaluations. A level set model embedded into the scalar function of higher dimensions is propagated to represent the design boundary of a domain. The level set function interpolated into a fixed initial domain is evolved by using the Hamilton-Jacobi equation. The moving free… More >

  • Open Access

    ARTICLE

    The Shape Identification Problem in Estimating the Geometry of A Three-Dimensional Irregular Internal Cavity

    Cheng-Hung Huang1, Chi-An Chen1

    CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.1, pp. 1-22, 2008, DOI:10.3970/cmes.2008.036.001

    Abstract A three-dimensional shape identification problem (or inverse geometry problem) in estimating the unknown irregular shape of internal cavity by using the steepest descent method (SDM) and a general purpose commercial code CFD-RC is examined in this study based on the simulated measured temperature distributions on the outer surface by infrared thermography. The advantage of calling CFD-RC as a subroutine in the present shape identification problem lies in its characteristics of easily-handling the problem considered here since the auto mesh function of CFD-RC enables the handling of this moving boundary problem. \newline Three test cases are More >

  • Open Access

    ARTICLE

    Continuation Schemes for Shape Detection in Inverse Acoustic Scattering Problems

    S.-W. Na1, L.F. Kallivokas2

    CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.1, pp. 73-90, 2008, DOI:10.3970/cmes.2008.035.073

    Abstract We discuss simple numerical schemes, termed continuation schemes, for detecting the location and shape of a scatterer embedded in a host acoustic medium, when considering scant measurements of the scattered acoustic pressure in the vicinity (near- or far-field) of the obstacle. The detection is based on incomplete information, i.e., the measurement stations are distributed in the backscatter region and do not circumscribe the sought scatterer. We consider sound-hard scatterers, and use boundary integral equations for the underlying numerical scheme. We favor amplitude-based misfit functionals, and use frequency- and directionality-continuation schemes to resolve the scatterer's location More >

  • Open Access

    ARTICLE

    Multi-material Eulerian Formulations and Hydrocode for the Simulation of Explosions

    Ma Tianbao1, Wang Cheng, Ning Jianguo

    CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.2, pp. 155-178, 2008, DOI:10.3970/cmes.2008.033.155

    Abstract A multi-material Eulerian hydrodynamic numerical method and hydrocode that can effectively simulate explosion problems in engineering practice were developed in this study. A modified Youngs' interface reconstruction algorithm was proposed for mixed cells, in which the material's volume fractions of the surrounding cells are not only used to reconstruct the material interface but also adopted to determine the transport order of the material. The algorithm developed herein was validated by the modeling of several tests, such as objects with different shapes moving in translational, rotating and shear flow field in two dimensional Descartes coordinates and More >

  • Open Access

    ARTICLE

    Estimation of Deformed Shapes of Beam Structures using 3D Coordinate Information from Terrestrial Laser Scanning

    H.M. Lee1, H.S. Park1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.29, No.1, pp. 29-44, 2008, DOI:10.3970/cmes.2008.029.029

    Abstract This paper presents a computational model to estimate deformed shapes of beam structures using 3D coordinate information from terrestrial laser scanning (TLS). The model is composed of five components: 1) formulation of polynomial shape function, 2) application of boundary condition, 3) inducement of compatibility condition, 4) application of the least square method and 5) evaluation of error vector and determination of reasonable polynomial shape function. In the proposed model, the optimal degree of polynomial function is selected based on the complexity of beam structures, instead of using a specific degree of polynomial function. The chosen More >

  • Open Access

    ARTICLE

    Sensitivity of the Acoustic Scattering Problem in Prolate Spheroidal Geometry with Respect to Wavenumber and Shape

    D. Kourounis1, L.N. Gergidis1, A. Charalambopoulos1

    CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.3, pp. 185-202, 2008, DOI:10.3970/cmes.2008.028.185

    Abstract The sensitivity of analytical solutions of the direct acoustic scattering problem in prolate spheroidal geometry on the wavenumber and shape, is extensively investigated in this work. Using the well known Vekua transformation and the complete set of radiating "outwards'' eigensolutions of the Helmholtz equation, introduced in our previous work ([Charalambopoulos and Dassios(2002)], [Gergidis, Kourounis, Mavratzas, and Charalambopoulos (2007)]), the scattered field is expanded in terms of it, detouring so the standard spheroidal wave functions along with their inherent numerical deficiencies. An approach is employed for the determination of the expansion coefficients, which is optimal in… More >

  • Open Access

    ARTICLE

    Natural neighbour Petrov-Galerkin Method for Shape Design Sensitivity Analysis

    Kai Wang1, Shenjie Zhou1,2, Zhifeng Nie1, Shengli Kong1

    CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.2, pp. 107-122, 2008, DOI:10.3970/cmes.2008.026.107

    Abstract The natural neighbour Petrov-Galerkin method (NNPG) is one of the special cases of the generalized meshless local Petrov-Galerkin method (MLPG). This paper demonstrates the NNPG can be successfully used in design sensitivity analysis in 2D elasticity. The design sensitivity analysis method based on the local weak form (DSA-LWF) in the NNPG context is proposed. In the DSA-LWF, the local weak form of governing equation is directly differentiated with respect to design variables and discretized with NNPG to obtain the sensitivities of structural responds. The calculation of derivatives of shape functions with respect to design variables More >

  • Open Access

    ARTICLE

    Stable PDE Solution Methods for Large Multiquadric Shape Parameters

    Arezoo Emdadi1, Edward J. Kansa2, Nicolas Ali Libre1,3, Mohammad Rahimian1, Mohammad Shekarchi1

    CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.1, pp. 23-42, 2008, DOI:10.3970/cmes.2008.025.023

    Abstract We present a new method based upon the paper of Volokh and Vilney (2000) that produces highly accurate and stable solutions to very ill-conditioned multiquadric (MQ) radial basis function (RBF) asymmetric collocation methods for partial differential equations (PDEs). We demonstrate that the modified Volokh-Vilney algorithm that we name the improved truncated singular value decomposition (IT-SVD) produces highly accurate and stable numerical solutions for large values of a constant MQ shape parameter, c, that exceeds the critical value of c based upon Gaussian elimination. More >

  • Open Access

    ARTICLE

    Strain Energy on the Surface of an Anisotropic Half-Space Substrate: Effect of Quantum-Dot Shape and Depth

    E. Pan1,2, Y. Zhang2, P. W. Chung3, M. Denda4

    CMES-Computer Modeling in Engineering & Sciences, Vol.24, No.2&3, pp. 157-168, 2008, DOI:10.3970/cmes.2008.024.157

    Abstract Quantum-dot (QD) semiconductor synthesis is one of the most actively investigated fields in strain energy band engineering. The induced strain fields influence ordering and alignment, and the subsequent surface formations determine the energy bandgap of the device. The effect of the strains on the surface formations is computationally expensive to simulate, thus analytical solutions to the QD-induced strain fields are very appealing and useful. In this paper we present an analytical method for calculating the QD-induced elastic field in anisotropic half-space semiconductor substrates. The QD is assumed to be of any polyhedral shape, and its… More >

  • Open Access

    ARTICLE

    Computer Simulation of Random Sphere Packing in an Arbitrarily Shaped Container

    S.X. Li1, L. Zhao1, Y.W. Liu2

    CMC-Computers, Materials & Continua, Vol.7, No.2, pp. 109-118, 2008, DOI:10.3970/cmc.2008.007.109

    Abstract Most simulations of random sphere packing concern a cubic or cylindric container with periodic boundary, containers of other shapes are rarely studied. In this paper, a new relaxation algorithm with pre-expanding procedure for random sphere packing in an arbitrarily shaped container is presented. Boundaries of the container are simulated by overlapping spheres which covers the boundary surface of the container. We find 0.4~0.6 of the overlap rate is a proper value for boundary spheres. The algorithm begins with a random distribution of small internal spheres. Then the expansion and relaxation procedures are performed alternately to… More >

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