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  • Open Access

    ARTICLE

    Sound Propagation Analysis on Sonic Crystal Elastic Structures using the Method of Fundamental Solutions (MFS)

    P.G. Santos1, J. Carbajo2, L. Godinho3, J. Ramis2

    CMC-Computers, Materials & Continua, Vol.43, No.2, pp. 109-136, 2014, DOI:10.3970/cmc.2014.043.109

    Abstract The study of periodic structures, namely sonic crystals, for sound attenuation purposes has been a topic of intense research in the last years. Some efficient methods are available in literature to solve the problem of sound propagation in the presence of this kind of structures such as those based in the Multiple Scattering Theory (MST) or the Finite Element Method (FEM). In this paper a solution based on the Method of Fundamental Solutions (MFS) which presents advantages, namely in computational discretization and calculation costs, is presented. The proposed formulation considers the presence of elastic ring More >

  • Open Access

    ARTICLE

    A Novel Metamaterial FSS-based Structure for Wideband Radome Applications

    Shiv Narayan1, R M Jha1

    CMC-Computers, Materials & Continua, Vol.37, No.2, pp. 97-108, 2013, DOI:10.3970/cmc.2013.037.097

    Abstract A novel metamaterial based FSS (frequency selective surfaces) structure is presented in this paper for wideband airborne radome applications. The proposed metamaterial-FSS structure consists of three layers, where a DPS (double positive sign) layer is sandwiched between a MNG (μ-negative) and ENG (ε- negative) layer, exhibits very good bandpass characteristics inside the operational band along with excellent roll-off characteristics outside the band. The EM performance analysis of the proposed structure has been carried out using transmission line transfer matrix (TLTM) method, which shows excellent bandpass characteristics over a wide frequency range. The transmission efficiency is More >

  • Open Access

    ARTICLE

    Stable Boundary and Internal Data Reconstruction in Two-Dimensional Anisotropic Heat Conduction Cauchy Problems Using Relaxation Procedures for an Iterative MFS Algorithm

    Liviu Marin1

    CMC-Computers, Materials & Continua, Vol.17, No.3, pp. 233-274, 2010, DOI:10.3970/cmc.2010.017.233

    Abstract We investigate two algorithms involving the relaxation of either the given boundary temperatures (Dirichlet data) or the prescribed normal heat fluxes (Neumann data) on the over-specified boundary in the case of the iterative algorithm of Kozlov91 applied to Cauchy problems for two-dimensional steady-state anisotropic heat conduction (the Laplace-Beltrami equation). The two mixed, well-posed and direct problems corresponding to every iteration of the numerical procedure are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according More >

  • Open Access

    ARTICLE

    An Alternating Iterative MFS Algorithm for the Cauchy Problem in Two-Dimensional Anisotropic Heat Conduction

    LiviuMarin 1

    CMC-Computers, Materials & Continua, Vol.12, No.1, pp. 71-100, 2009, DOI:10.3970/cmc.2009.012.071

    Abstract In this paper, the alternating iterative algorithm originally proposed by Kozlov, Maz'ya and Fomin (1991) is numerically implemented for the Cauchy problem in anisotropic heat conduction using a meshless method. Every iteration of the numerical procedure consists of two mixed, well-posed and direct problems which are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point More >

  • Open Access

    ARTICLE

    Regularized MFS-Based Boundary Identification in Two-Dimensional Helmholtz-Type Equations

    Liviu Marin1, Andreas Karageorghis2

    CMC-Computers, Materials & Continua, Vol.10, No.3, pp. 259-294, 2009, DOI:10.3970/cmc.2009.010.259

    Abstract We study the stable numerical identification of an unknown portion of the boundary on which a given boundary condition is provided and additional Cauchy data are given on the remaining known portion of the boundary of a two-dimensional domain for problems governed by either the Helmholtz or the modified Helmholtz equation. This inverse geometric problem is solved using the method of fundamental solutions (MFS) in conjunction with the Tikhonov regularization method. The optimal value for the regularization parameter is chosen according to Hansen's L-curve criterion. The stability, convergence, accuracy and efficiency of the proposed method More >

  • Open Access

    ARTICLE

    A Matrix Decomposition MFS Algorithm for Biharmonic Problems in Annular Domains

    T. Tsangaris1, Y.–S. Smyrlis1, 2, A. Karageorghis1, 2

    CMC-Computers, Materials & Continua, Vol.1, No.3, pp. 245-258, 2004, DOI:10.3970/cmc.2004.001.245

    Abstract The Method of Fundamental Solutions (MFS) is a boundary-type method for the solution of certain elliptic boundary value problems. In this work, we develop an efficient matrix decomposition MFS algorithm for the solution of biharmonic problems in annular domains. The circulant structure of the matrices involved in the MFS discretization is exploited by using Fast Fourier Transforms. The algorithm is tested numerically on several examples. More >

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