Donghong He¹, Hang Ma^{2, *}

CMES-Computer Modeling in Engineering & Sciences, Vol.118, No.1, pp. 15-40, 2019, DOI:10.31614/cmes.2019.04327

Abstract To deal with the problems encountered in the large scale numerical simulation of three dimensional (3D) elastic solids with fluid-filled pores, a novel computational model with the corresponding iterative solution procedure is developed, by introducing Eshelby’s idea of eigenstrain and equivalent inclusion into the boundary integral equations (BIE). Moreover, by partitioning all the fluid-filled pores in the computing domain into the near- and the far-field groups according to the distances to the current pore and constructing the local Eshelby matrix over the near-field group, the convergence of iterative procedure is guaranteed so that the problem… More >

Godwin Kakuba^1,∗, John M. Mango¹, Martijn J.H. Anthonissen²

CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 207-225, 2019, DOI:10.32604/cmes.2019.04269

Abstract Sometimes boundary value problems have isolated regions where the solution changes rapidly. Therefore, when solving numerically, one needs a fine grid to capture the high activity. The fine grid can be implemented as a composite coarse-fine grid or as a global fine grid. One cheaper way of obtaining the composite grid solution is the use of the local defect correction technique. The technique is an algorithm that combines a global coarse grid solution and a local fine grid solution in an iterative way to estimate the solution on the corresponding composite grid. The algorithm is… More >

Shenghu Ding^1,*, Qingnan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.114, No.3, pp. 335-349, 2018, DOI:10.3970/cmes.2018.114.335

Abstract A multi-layered model for heat conduction analysis of a thermoelectric material strip (TEMs) with a Griffith crack under the electric flux and energy flux load has been developed. The materials parameters of the TEMs vary continuously in an arbitrary manner. To derive the solution, the TEMs is divided into several sub-layers with different material properties. The mixed boundary problem is reduced to a system of singular integral equations, which are solved numerically. The effect of strip width on the electric flux intensity factor and thermal flux intensity factor are studied. More >

Jui-Hsiang Kao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.112, No.1, pp. 59-73, 2016, DOI:10.3970/cmes.2016.112.059

Abstract In this paper, a step approach method in the time domain is developed to calculate the radiated waves from an arbitrary obstacle pulsating with multiple frequencies. The computing scheme is based on the Boundary Integral Equation and derived in the time domain; thus, the time-harmonic Neumann boundary condition can be imposed. By the present method, the values of the initial conditions are set to zero, and the approach process is carried forward in a loop from the first time step to the last. At each time step, the radiated pressure on each element is updated. More >

H.-S. Wang^1,2, H. Jiang^3,4, B. Yang²

CMC-Computers, Materials & Continua, Vol.51, No.3, pp. 145-161, 2016, DOI:10.3970/cmc.2016.051.145

Abstract Potential field due to line sources residing on slender heterogeneities is involved in various areas, such as heat conduction, potential flow, and electrostatics. Often dipolar line sources are either prescribed or induced due to close interaction with other objects. Its calculation requires a higher-order scheme to take into account the dipolar effect as well as net source effect. In the present work, we apply such a higher-order line element method to analyze the potential field with cylindrical slender heterogeneities. In a benchmark example of two parallel rods, we compare the line element solution with the More >

K. N. Grivas¹, M. G. Vavva¹, E. J. Sellountos², D. I. Fotiadis³, D. Polyzos^1,4

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.2, pp. 87-122, 2015, DOI:10.3970/cmes.2015.105.087

Abstract A simple Local Boundary Integral Equation (LBIE) method for solving the Fisher nonlinear transient diffusion equation in two dimensions (2D) is reported. The method utilizes, for its meshless implementation, randomly distributed nodal points in the interior domain and nodal points corresponding to a Boundary Element Method (BEM) mesh, at the global boundary. The interpolation of the interior and boundary potentials is accomplished using a Local Radial Basis Functions (LRBF) scheme. At the nodes of global boundary the potentials and their fluxes are treated as independent variables. On the local boundaries, potential fluxes are avoided by More >

G. Kakuba¹, M. J. H. Anthonissen²

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.6, pp. 445-462, 2014, DOI:10.3970/cmes.2014.099.445

Abstract The aim in this paper is to develop a new local defect correction approach to gridding for problems with localised regions of high activity in the boundary element method. The technique of local defect correction has been studied for other methods as finite difference methods and finite volume methods. The initial attempts to developing such a technique by the authors for the boundary element method was based on block decomposition and manipulation of the coefficient matrix and right hand side of the system of equations in three dimension. It ignored the inherent global nature of… More >

Zichun Yang^1,2,3, Lei Zhang^1,4, Yueyun Cao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.2, pp. 101-130, 2014, DOI:10.3970/cmes.2014.097.101

Abstract Discretization of inverse problems often leads to systems of linear equations with a highly ill-conditioned coefficient matrix. To find meaningful solutions of such systems, one kind of prevailing and representative approaches is the so-called regularized total least squares (TLS) method when both the system matrix and the observation term are contaminated by some noises. We will survey two such regularization methods in the TLS setting. One is the iterative truncated TLS (TTLS) method which can solve a convergent sequence of projected linear systems generated by Lanczos bidiagonalization. The other one is to convert the Tikhonov… More >

Y.C. Shiah¹, C.L. Tan^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.6, pp. 425-447, 2014, DOI:10.3970/cmes.2014.102.425

Abstract Green’s functions, or fundamental solutions, are necessary items in the formulation of the boundary integral equation (BIE), the analytical basis of the boundary element method (BEM). In the formulation of the BEM for 3D general anisotropic elasticity, considerable attention has been devoted to developing efficient algorithms for computing these quantities over the years. The mathematical complexity of this Green’s function has also posed an obstacle in the development of this numerical method to treat problems of 3D anisotropic thermoelasticity. This is because thermal effects manifest themselves as an additional domain integral in the integral equation;… More >

Jizeng Wang^1,2, Lei Zhang¹, Youhe Zhou¹

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.2, pp. 127-148, 2014, DOI:10.3970/cmes.2014.102.127

Abstract In this paper, we propose an efficient wavelet method for numerical solution of nonlinear integral equations with singular kernels. The proposed method is established based on a function approximation algorithm in terms of Coiflet scaling expansion and a special treatment of boundary extension. The adopted Coiflet bases in this algorithm allow each expansion coefficient being explicitly expressed by a single-point sampling of the function, which is crucially important for dealing with nonlinear terms in the equations. In addition, we use the technique of integration by parts to transform the original integral equations with non-smooth or More >