B.I. Yun¹, W.T. Ang^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.3, pp. 217-244, 2010, DOI:10.3970/cmes.2010.065.217

Abstract A dual-reciprocity boundary element method is proposed for simulating numerically axisymmetric dual-phase-lag heat conduction in nonhomogeneous thermally isotropic media. The properties of the media, such as thermal conductivity and specific heat, are assumed to vary continuously in space. To check its validity and assess its accuracy, the proposed method is first applied to solve some specific test problems with known solutions. It is then used to simulate the axisymmetric dual-phase-lag heat conduction in a particular nonhomogeneous medium subject to a concentrated surface heating. The effects of the dual phase lags and the spatial variations of the thermal properties of the… More >

J. Tausch¹, J. Xiao²

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.3, pp. 221-246, 2010, DOI:10.3970/cmes.2010.058.221

Abstract A fast method for the computation of layer potentials that arise in acoustic scattering is introduced. The principal idea is to split the singular kernel into a smooth and a local part. The potential due to the smooth part is discretized by a Nyström method and is evaluated efficiently using a sequence of FFTs. The potential due to the local part is approximated by a truncated series in the mollification parameter. The smooth approximation of the kernel is obtained by multiplication of its Fourier transform with a filter. We will show that for a rational filter the smooth part and… More >

Y.C. Chen¹, Chyanbin Hwu²

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.1, pp. 31-50, 2010, DOI:10.3970/cmes.2010.057.031

Abstract The Green's function for anisotropic bimaterials has been investigated around three decades ago. Since the mathematical formulation of piezoelectric elasticity can be organized into the same form as that of anisotropic elasticity by just expanding the dimension of the corresponding matrix to include the piezoelectric effects, the extension of the Green's function to piezoelectric bimaterials can be obtained immediately through the associated anisotropic bimaterials. In this paper, the Green's function for the bimaterials bonded together with one anisotropic material and one piezoelectric material is derived by applying Stroh's complex variable formalism with the aid of analytical continuation method. For this… More >

B. Chandrasekhar¹

CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.3, pp. 211-230, 2010, DOI:10.3970/cmes.2010.056.211

Abstract In this work, various basis functions used in the Method of Moments or Boundary Element (MoM/BEM) solution of acoustic scattering problems are compared with each other for their performance. Single layer formulation of the rigid bodies is considered in comparison of the solutions. Geometry of a scatterer is descritized using triangular patch modeling and basis functions are defined on triangular patches, edges and nodes for three different solutions. Far field scattering cross sections for different frequencies of incident acoustic wave are compared with the closed form solutions. Also, the errors of the solutions using these three types of basis functions… More >

Z. Y. Yan^1,2, J. Zhang¹, W. Ye¹, T.X. Yu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.1, pp. 33-60, 2010, DOI:10.3970/cmes.2010.055.033

Abstract An 3-D precorrected-FFT accelerated BEM approach for the linear elastic analysis of porous solids with randomly distributed pores of arbitrary shape and size is described in this paper. Both the upper bound and the lower bound of elastic properties of solids with spherical pores are obtained using the developed fast BEM code. Effects of porosity and pore shape on the elastic properties are investigated. The performance of several theoretical models is evaluated by comparing the theoretical predictions with the numerical results. It is found that for porous solids with spherical pores, the performances of the generalized self-consistent method and Mori-Tanaka… More >

Chih-Chang Chi¹, Weichung Yeih^1,2, Chein-Shan Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.2, pp. 167-190, 2009, DOI:10.3970/cmes.2009.047.167

Abstract In this study, a novel method for solving the Cauchy problem of Laplace equation is developed. Through the fictitious time integration method (FTIM), the finding of the root of the resulting linear equations can be transformed into for finding the fixed point of a system of first order ordinary differential equations, in which a fictitious time variable is introduced. In such a sense, the inverse of ill-posed leading matrix is not necessary for the FTIM. This method uses the residual of each equation to control the evolution of unknowns in the fictitious time, and it is different from the conventional… More >

T.N. Killian¹, S.M. Rao¹ and M.E. Baginski¹

CMES-Computer Modeling in Engineering & Sciences, Vol.46, No.3, pp. 255-270, 2009, DOI:10.3970/cmes.2009.046.255

Abstract In this work, we present a new method of moments solution procedure for calculating acoustic/electromagnetic scattering and radiation by a metallic body whose physical dimension is very large with respect to wavelength. The specially computed basis functions and the testing procedure results in a block-diagonally-dominant moment matrix where each block along the diagonal corresponds to a portion of the structure. The new solution procedure results in considerable savings in terms of computer storage and processing times. Although the procedure is outlined in general mathematical terms, the numerical results are presented only for electromagnetic scattering from two-dimensional bodies and compared with… More >

A. Brancati¹, M. H. Aliabadi¹, I. Benedetti^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.2, pp. 149-172, 2009, DOI:10.3970/cmes.2009.043.149

Abstract In this paper a new Rapid Acoustic Boundary Element Method (RABEM) is presented using a Hierarchical GMRES solver for 3D acoustic problems. The Adaptive Cross Approximation is used to generate both the system matrix and the right hand side vector. The ACA is also used to evaluate the potential and the particle velocity values at selected internal points. Two different GMRES solution strategies (without preconditioner and with a block diagonal preconditioner) are developed and tested for low and high frequency problems. Implementation of different boundary conditions (i.e. Dirichlet, Neumann and mixed Robin) is also described. The applications presented include the… More >

Jin Li¹, Ji-ming Wu², De-hao Yu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.2, pp. 151-176, 2009, DOI:10.3970/cmes.2009.042.151

Abstract The trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods is discussed, and the asymptotic expansion of error function is obtained. A series to approach the singular point is constructed and the convergence rate is proved. Based on the asymptotic expansion of the error functional, algorithm with theoretical analysis of the generalized extrapolation are given. Some examples show that the numerical results coincide with the theoretic analysis very well. More >

C. L. Tan¹, Y.C. Shiah², C.W. Lin²

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.3, pp. 195-214, 2009, DOI:10.3970/cmes.2009.041.195

Abstract The explicit, closed-form expressions of the Green's functions for generally anisotropic elastic solids in three-dimensions that have been derived using Stroh's formalism are employed in a formulation of the boundary element method (BEM). Unlike several other existing schemes, the evaluation of these fundamental solutions does not require further numerical integration in the BEM algorithm; they have surprisingly not been implemented previously. Three numerical examples are presented to demonstrate the veracity of the implementation and the general applicability of the BEM for the 3D elastic stress analysis of generally anisotropic solids. The results are compared with known solutions in the literature… More >