CMES-Vol. 25, No. 1, 2008

Open Access

ARTICLE

Numerical Computation of Electromagnetic Fields by the Time-Domain Boundary Element Method and the Complex Variable Method
D. Soares Jr.¹, M. P. Vinagre²
CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.1, pp. 1-8, 2008, DOI:10.3970/cmes.2008.025.001
Abstract This work presents an alternative procedure to compute time-domain electromagnetic fields. The Boundary Element Method is here adopted to numerically analyze wave propagation problems, computing just a so-called primary field (either the electric or the magnetic field can be selected as primary field; the complementary field is here named secondary field). The secondary field is obtained following Maxwell's equations, i.e., considering space derivatives of the primary field (computed by the Complex Variable Method) and time integration procedures. This methodology is more efficient and flexible since fewer systems of equations must be solved at each time-step. At the end of the… More >

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ARTICLE

Meshless Local Petrov-Galerkin Method with Unity Test Function for Non-Isothermal Fluid Flow
A. Arefmanesh¹, M. Najaﬁ¹, H. Abdi¹
CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.1, pp. 9-22, 2008, DOI:10.3970/cmes.2008.025.009
Abstract The meshless local Petrov-Galerkin (MLPG) method with unity as the weighting function has been applied to the solution of the Navier-Stokes and energy equations. The Navier-Stokes equations in terms of the stream function and vorticity formulation together with the energy equation are solved for different test cases. This present study considers the implementation of the method on a non-isothermal lid-driven cavity flow, the lid-driven cavity flow with an inlet and outlet, and also on the non-isothermal flow over an obstacle. Nonuniform point distribution is employed for all the test cases for the numerical simulations. The flow streamlines for each test… More >

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Stable PDE Solution Methods for Large Multiquadric Shape Parameters
Arezoo Emdadi¹, Edward J. Kansa², Nicolas Ali Libre^1,3, 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 >

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A Meshless Modeling of Dynamic Strain Localization in Quasi-Brittle Materials Using Radial Basis Function Networks
P. Le¹, N. Mai-Duy², T. Tran-Cong³, G. Baker⁴
CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.1, pp. 43-68, 2008, DOI:10.3970/cmes.2008.025.043
Abstract This paper describes an integrated radial basis function network (IRBFN) method for the numerical modelling of the dynamics of strain localization due to strain softening in quasi-brittle materials. The IRBFN method is a truly meshless method that is based on an unstructured point collocation procedure. We introduce a new and effective regularization method to enhance the performance of the IRBFN method and alleviate the numerical oscillations associated with weak discontinuity at the elastic wave front. The dynamic response of a one dimensional bar is investigated using both local and non-local continuum models. Numerical results, which compare favourably with those obtained… More >

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