CMES-Vol. 50, No. 2, 2009

Open Access

ARTICLE

Numerical Modelling of Electromagnetic Wave Propagation by Meshless Local Petrov-Galerkin Formulations
Delﬁm Soares Jr. ¹
CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.2, pp. 97-114, 2009, DOI:10.3970/cmes.2009.050.097
Abstract In this work, meshless methods based on the local Petrov-Galerkin (MLPG) approach are presented to analyse electromagnetic wave propagation problems. Formulations adopting the Heaviside step function and the Gaussian weight function as the test functions in the local weak form are considered. The moving least square (MLS) method is used to approximate the physical quantities in the local integral equations. After spatial discretization is carried out, a system of ordinary differential equations of second order is obtained. This system is solved in the time-domain by the Houbolt's method, allowing the computation of the so-called primary fields (either the electric or… More >

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Dynamic Analysis by Meshless Local Petrov-Galerkin Formulations Considering a Time-Marching Scheme Based on Implicit Green's Functions
D. Soares Jr.¹, J. Sladek², V. Sladek²
CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.2, pp. 115-140, 2009, DOI:10.3970/cmes.2009.050.115
Abstract In recent years the idea of using mesh-free or mesh-less methods for numerical solution of partial differential equations has received much attention, due to their potential advantage in eliminating the costly effort of mesh generation and re-meshing. A variety of meshless methods has been proposed so far. Many of them are derived from a weak-form formulation on global domain or a set of local subdomains. In the global formulation background cells are required for the integration of the weak form. In methods based on local weak-form formulation no cells are required and therefore they are often referred to as truly… More >

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Free Vibration Analysis of a Circular Plate with Multiple Circular Holes by Using the Multipole Trefftz Method
Wei-Ming Lee¹, Jeng-Tzong Chen²
CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.2, pp. 141-160, 2009, DOI:10.3970/cmes.2009.050.141
Abstract This paper presents the multipole Trefftz method to derive an analytical model describing the free vibration of a circular plate with multiple circular holes. Based on the addition theorem, the solution of multipoles centered at each circle can be expressed in terms of multipoles centered at one circle, where boundary conditions are specified. In this way, a coupled infinite system of simultaneous linear algebraic equations is derived for the circular plate with multiple holes. The direct searching approach is employed in the truncated finite system to determine the natural frequencies by using the singular value decomposition (SVD). After determining the… More >

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ARTICLE

Wavelet Based Adaptive RBF Method for Nearly Singular Poisson-Type Problems on Irregular Domains
Nicolas Ali Libre^1,2, Arezoo Emdadi², Edward J. Kansa^3,4, Mohammad Shekarchi², Mohammad Rahimian²
CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.2, pp. 161-190, 2009, DOI:10.3970/cmes.2009.050.161
Abstract We present a wavelet based adaptive scheme and investigate the efficiency of this scheme for solving nearly singular potential PDEs over irregularly shaped domains. For a problem defined over Ω∈ℜ^d, the boundary of an irregularly shaped domain, Γ, is defined as a boundary curve that is a product of a Heaviside function along the normal direction and a piecewise continuous tangential curve. The link between the original wavelet based adaptive method presented in Libre, Emdadi, Kansa, Shekarchi, and Rahimian (2008, 2009) or LEKSR method and the generalized one is given through the use of simple Heaviside masking procedure. In addition… More >

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