In this work we are interested in constructing a uniformly convergent method to solve a 2d elliptic singularly perturbed weakly system of convection-diffusion type. We assume that small positive parameters appear at b...
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In this work we are interested in constructing a uniformly convergent method to solve a 2d elliptic singularly perturbed weakly system of convection-diffusion type. We assume that small positive parameters appear at both the diffusion and the convection terms of the partial differential equation. Moreover, we suppose that both the diffusion and the convection parameters can be distinct and also they can have a different order of magnitude. Then, the nature of the overlapping regular or parabolic boundary layers, which, in general, appear in the exact solution, is much more complicated. To solve the continuous problem, we use the classical upwind finite difference scheme, which is defined on piecewise uniform Shishkin meshes, which are given in a different way depending on the value and the ratio between the four singular perturbation parameters which appear in the continuous problem. So, the numerical algorithm is an almost first order uniformly convergent method. The numerical results obtained with our algorithm for a test problem are presented;these results corroborate in practice the good behavior and the uniform convergence of the algorithm, aligning with the theoretical results.
Surface impedance boundary condition (SIBC) is a potential way to improve the efficiency of the finite-difference time-domain (FdTd) method. However, it is still seldom used in FdTd simulations, especially for complic...
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Surface impedance boundary condition (SIBC) is a potential way to improve the efficiency of the finite-difference time-domain (FdTd) method. However, it is still seldom used in FdTd simulations, especially for complicatedproblems. In this study, the authors propose a novel SIBC, the perfect electric conductor (PEC) backed SIBC (PEC-SIBC). It is a combination of SIBC and PEC. This character makes it possible to integrate PEC-SIBC with the conventional FdTd method. The authors derive the updating equations of PEC-SIBC for a one-dimensional (1d), 2d and 3dproblems. Then, the authors verify the validity of PEC-SIBC with a 1d example and analyse the complexity with a 2d example. The comparison for a 1d configuration indicates that PEC-SIBC is a little more accurate than the traditional SIBC. For a 2d example, the SIBC is used to replace a lossy dielectric medium located in the middle of the problem domain. The complexity analysis indicates that PEC-SIBC is much easier and more practical to use than the traditional SIBC.
Two different types of 8-node cracked quadrilateral finite element are presented for fracture applications. The first element contains a central crack and the other one includes an edge crack. The introduced elements ...
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Two different types of 8-node cracked quadrilateral finite element are presented for fracture applications. The first element contains a central crack and the other one includes an edge crack. The introduced elements are applicable in 2d problems. The crack is not physically modeled within the element, but instead, its effects on the stiffness matrix are taken into account by utilizing linear fracture mechanics laws. Furthermore, a simple and practical procedure is proposed for calculation of stress intensity factor (SIF) by employing proposed cracked elements. Several numerical examples are presented to evaluate the capabilities of the proposed elements and procedure.
A meshless method based on the local Petrov-Galerkin approach is proposed, to solve initial-boundary value problems of magneto-electro-elastic solids with continuously varying material properties. Stationary and trans...
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A meshless method based on the local Petrov-Galerkin approach is proposed, to solve initial-boundary value problems of magneto-electro-elastic solids with continuously varying material properties. Stationary and transient thermal problems are considered in this paper. The mechanical 2-d fields are described by the equations of motion with an inertial term. Nodal points are spread on the analyzeddomain, and each node is surrounded by a small circle for simplicity. The spatial variation of displacements, electric and magnetic potentials is approximated by the moving least-squares (MLS) scheme. After performing the spatial integrations, one obtains a system of ordinary differential equations for certain nodal unknowns. That system is solved numerically by the Houbolt finite-difference scheme as a time stepping method. (C) 2010 Elsevier Ltd. All rights reserved.
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