A. Vukovic¹, P. Sewell¹, T. M. Benson¹

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 171-190, 2010, DOI:10.3970/cmes.2010.055.171

Abstract A fast and accurate method is developed for the analysis of a class of metal three-dimensional resonators with rotational symmetry. The analysis is formulated using the Body of Revolution approach and the Method of Analytical Regularization. This development is motivated by the need for three-dimensional analytical solvers that could enable fast and accurate analysis of photonic resonant structures which support very high Q whispering gallery modes and which are computationally challenging for numerical simulations. The paper outlines the formulation of the method and demonstrates the stability and the source of computation errors of the method. More >

J. Trevelyan¹and G. Coates¹

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 147-170, 2010, DOI:10.3970/cmes.2010.055.147

Abstract The terminology "wave boundary elements" relates to boundary elements enriched in the Partition of Unity sense by a multiple plane wave basis for the analysis of the propagation of short wavelength waves. This paper presents a variant of this approach in which the plane wave basis is selected adaptively according to an error indicator. The error indicator is residual based, and exhibits useful local and global properties. Model improvement in each adaptive iteration is carried out by the addition of new plane waves with no h-refinement. The convergence properties of the scheme are demonstrated. More >

Chih-Wen Chang¹, Chein-Shan Liu²

CMC-Computers, Materials & Continua, Vol.17, No.1, pp. 19-40, 2010, DOI:10.3970/cmc.2010.017.019

Abstract In this study, we employ a semi-analytical approach to solve a two-dimensional advection-dispersion equation (ADE) for identifying the contamination problems. First, the Fourier series expansion technique is used to calculate the concentration field C(x, y, t) at any time t < T. Then, we ponder a direct regularization by adding an extra termaC(x, y, 0) on the final time data C(x, y, T), to reach a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us obtaining a closed-form solution of the Fourier coefficients. A strategy to choose the regularization parameter is More >

Chih-Wen Chang¹, Chein-Shan Liu², Jiang-Ren Chang³

CMC-Computers, Materials & Continua, Vol.15, No.1, pp. 45-66, 2010, DOI:10.3970/cmc.2010.015.045

Abstract In this article, we propose a semi-analytical method to tackle the two-dimensional backward heat conduction problem (BHCP) by using a quasi-boundary idea. First, the Fourier series expansion technique is employed to calculate the temperature field u(x, y, t) at any time t < T. Second, we consider a direct regularization by adding an extra termau(x, y, 0) to reach a second-kind Fredholm integral equation for u(x, y, 0). The termwise separable property of the kernel function permits us to obtain a closed-form regularized solution. Besides, a strategy to choose the regularization parameter is suggested. When several numerical examples were More >

J. Sladek¹, V. Sladek¹, P. Stanak¹, Ch. Zhang²

CMC-Computers, Materials & Continua, Vol.15, No.1, pp. 1-26, 2010, DOI:10.3970/cmc.2010.015.001

Abstract A meshless local Petrov-Galerkin (MLPG) method is applied to solve laminate plate problems described by the Reissner-Mindlin theory. Both stationary and transient dynamic loads are analyzed here. The bending moment and the shear force expressions are obtained by integration through the laminated plate for the considered constitutive equations in each lamina. The Reissner-Mindlin theory reduces the original three-dimensional (3-D) thick plate problem to a two-dimensional (2-D) problem. Nodal points are randomly distributed over the mean surface of the considered plate. Each node is the center of a circle surrounding this node. The weak-form on small More >

P.R. Venkatesh¹, B.Chandrasekhar² , M.M.Benal³

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.1, pp. 83-104, 2009, DOI:10.3970/cmes.2009.052.083

Abstract In this work, node based basis functions are used to solve the acoustic scattering from plain thin bodies like plates, discs; and intersecting thin bodies like fins on a cylinder. Node based basis functions are defined on the vertices of triangles generated by triangular patch modeling, and these functions are used to define the unknown source distribution. Also the same functions are used as testing functions in the method of moment's solution. Three kinds of nodes were treated for defining the basis functions, namely, boundary node, non-boundary node and non boundary intersecting node. Also, three More >

Z.H.Yao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.1, pp. 21-46, 2009, DOI:10.3970/cmes.2009.050.021

Abstract The traditional time domain boundary integral equation (TDBIE) of elastodynamics is formulated based on the time dependent fundamental solution and the reciprocal theorem of elastodynamics. The time dependent fundamental solution of the elastodynamics is the response of the infinite elastic medium under a unit concentrate impulsive force subjected at a point and at an instant, including not only the pressure wave and shear wave, but also the Laplace wave with speed between that of P and S waves. In this paper, a new TDBIE is derived directly from the initial boundary value problem of the… More >

M.V. Menshykova¹, O.V. Menshykov, I.A. Guz

CMES-Computer Modeling in Engineering & Sciences, Vol.48, No.2, pp. 107-120, 2009, DOI:10.3970/cmes.2009.048.107

Abstract The study is devoted to the problem for a linear crack located between two dissimilar elastic half-spaces under normally incident time-harmonic plane shear wave. The system of boundary integral equations for displacements and tractions is derived from the dynamic Somigliana identity. The distributions of the displacements and tractions at the bonding interface and the surface of the crack are analysed. The dynamic stress intensity factors (the opening and the transverse shear modes) are computed as functions of the frequency of the incident wave for different material properties. More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.1, pp. 1-22, 2009, DOI:10.3970/cmes.2009.047.001

Abstract In this paper an analytical method for approximating the solution of backward heat conduction problem is presented. The Fourier series expansion technique is used to formulate a first-kind Fredholm integral equation for the temperature field u(x,t) at any time t < T, when the data are specified at a final time T. Then we consider a direct regularization, instead of the Tikhonov regularization, by adding the term αu(x,t) to obtain a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us by transforming it to a two-point boundary value problem, and thus a closed-form solution More >

Xiaolin Li¹, Jialin Zhu²

CMES-Computer Modeling in Engineering & Sciences, Vol.45, No.1, pp. 1-30, 2009, DOI:10.3970/cmes.2009.045.001

Abstract In this paper, a Galerkin boundary node method (GBNM) is developed for boundary-only analysis of 2D problems in linear elasticity. The GBNM combines the variational form of a boundary integral formulation for the elastic equations with the moving least-squares approximations for generating the trial and test functions. Unlike the boundary node method, the main idea here is to use the Galerkin scheme for numerical analysis, thus boundary conditions in the GBNM can be satisfied easily and directly in the weak formulation of the boundary integral equation. Another advantage with the Galerkin scheme is that the More >