Nives Brajčić Kurbaša¹, Blaž Gotovac¹, Vedrana Kozulić¹

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.6, pp. 493-530, 2016, DOI:10.3970/cmes.2016.111.493

Abstract This paper presents exponential Atomic Basis Functions (ABF), which are called Eup(x,ω). These functions are infinitely differentiable finite functions that unlike algebraic up(x) basis functions, have an unspecified parameter - frequency w. Numerical experiments show that this class of atomic functions has good approximation properties, especially in the case of large gradients (Gibbs phenomenon). In this work, for the first time, the properties of exponential ABF are thoroughly investigated and the expression for calculating the value of the basis function at an arbitrary point of the domain is given in a form suitable for implementation in numerical analysis. Application of… More >

Chia-Cheng Tsai^1,2, D. L. Young³

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.2, pp. 175-205, 2013, DOI:10.3970/cmes.2013.094.175

Abstract It is well known that the method of fundamental solutions (MFS) is a numerical method of exponential convergence. In this study, the exponential convergence of the MFS is demonstrated by obtaining the eigensolutions of the Helmholtz equation. In the solution procedure, the sought solution is approximated by a superposition of the Helmholtz fundamental solutions and a system matrix is resulted after imposing the boundary condition. A golden section determinant search method is applied to the matrix for finding exponentially convergent eigenfrequencies. In addition, the least-squares method of fundamental solutions is applied for solving the corresponding eigenfunctions. In the solution procedure,… More >

Guizhong Xie¹, Jianming Zhang^1,2, Cheng Huang¹, Chenjun Lu¹, Guangyao Li¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.2, pp. 139-157, 2013, DOI:10.3970/cmes.2013.094.139

Abstract In this work, an improved exponential transformation is presented for nearly singular boundary element integrals in problems of thin structures. Accurate evaluation of nearly singular integrals is an important issue in the implementation of boundary element method (BEM) for thin structures. In this paper, the exponential transformation, which was firstly developed to evaluate nearly singular integrals arising in 2D BEM, is extended into 3D BEM to deal with nearly singular integrals. Firstly, a novel (α,β) coordinate system is introduced. Then, the conventional distance function is modified into a new form in (α,β) coordinate system. Based on the refined distance function,… More >

Cheng-Yu Ku^1,2,3,Weichung Yeih^1,2, Chein-Shan Liu⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.2, pp. 83-108, 2011, DOI:10.3970/cmes.2011.076.083

Abstract In this paper, a general dynamical method based on the construction of a scalar homotopy function to transform a vector function of Non-Linear Algebraic Equations (NAEs) into a time-dependent scalar function by introducing a fictitious time-like variable is proposed. With the introduction of a transformation matrix, the proposed general dynamical method can be transformed into several dynamical Newton-like methods including the Dynamical Newton Method (DNM), the Dynamical Jacobian-Inverse Free Method (DJIFM), and the Manifold-Based Exponentially Convergent Algorithm (MBECA). From the general dynamical method, we can also derive the conventional Newton method using a certain fictitious time-like function. The formulation presented… More >

K. Kakuda¹, A. Seki¹, Y. Yamauchi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.3, pp. 281-306, 2010, DOI:10.3970/cmes.2010.069.281

Abstract A finite element scheme based on the concept of TVD (total variation diminishing) with a flux-limiter for the hyperbolic systems of conservation laws is presented. The numerical flux is formulated effectively by the weighted integral form using exponential weighting functions. The TVD finite element scheme is applied to a Riemann problem, namely the shock-tube problem, for the Euler system of equations. Numerical results demonstrate the workability and the validity of the present approach through comparison with the exact solutions. More >

H. Zheng¹, X. Peng^1,2,3, N. Hu^1,4

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.6, pp. 505-532, 2012, DOI:10.3970/cmes.2012.086.505

Abstract The static and kinematic shakedown of a functionally graded plate (FGP) is analyzed. The FGP is subjected coupled constant mechanical load and cyclically varying temperature. The FGP is composed of elastoplastic matrix and elastic particles, with the particle volume fraction varying along its thickness. The thermal and mechanical properties and their distributions are evaluated with a mean filed approach, which is based on the Eshelby's inclusion theory and takes into account directly the interaction between particles. The FGP is assumed to be separated into a number of thin layers, the thermal and mechanical properties in the thickness direction of each… More >

R. Criado¹, J.E. Ortiz¹, V. Mantič¹, L.J. Gray^1,2, F. París¹

CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.2, pp. 151-164, 2007, DOI:10.3970/cmes.2007.022.151

Abstract A numerical implementation of the Somigliana identity in displacements for the solution of 3D elastic problems in exponentially graded isotropic solids is presented. An expression for the fundamental solution in displacements, U_jl, was deduced by Martin et al. (Proc. R. Soc. Lond. A, 458, pp. 1931--1947, 2002). This expression was recently corrected and implemented in a Galerkin indirect 3D BEM code by Criado et al. (Int. J. Numer. Meth. Engng., 2008). Starting from this expression of U_jl, a new expression for the fundamental solution in tractions T_jl has been deduced in the present work. These quite complex expressions of the… More >

Lan Sun¹, Chen Ge¹, Xin Huang¹, Yingjie Wu^1,*, Yan Gao²

CMC-Computers, Materials & Continua, Vol.58, No.1, pp. 61-78, 2019, DOI:10.32604/cmc.2019.03744

Abstract Continuous response of range query on steaming data provides useful information for many practical applications as well as the risk of privacy disclosure. The existing research on differential privacy streaming data publication mostly pay close attention to boosting query accuracy, but pay less attention to query efficiency, and ignore the effect of timeliness on data weight. In this paper, we propose an effective algorithm of differential privacy streaming data publication under exponential decay mode. Firstly, by introducing the Fenwick tree to divide and reorganize data items in the stream, we achieve a constant time complexity for inserting a new item… More >

S.D. Akbarov^1,2, M. Negin³

CMC-Computers, Materials & Continua, Vol.53, No.4, pp. 307-341, 2017, DOI:10.3970/cmc.2017.053.307

Abstract Dispersion of the generalized Rayleigh waves propagating in a covered half-space made of viscoelastic materials is investigated by utilizing the exact equations of the theory of linear viscoelasticity. The dispersion equation is obtained for an arbitrary type of hereditary operator of the materials of the constituents and a solution algorithm is developed for obtaining numerical results on the dispersion of the waves under consideration. Dispersion curves are presented for certain attenuation cases and the influence of the viscosity of the materials is studied through three rheological parameters of the viscoelastic materials which characterize the characteristic creep time, long-term values and… More >

Hsin-Fang Chan¹, Chia-Ming Fan^1,2, Weichung Yeih¹

CMC-Computers, Materials & Continua, Vol.24, No.2, pp. 125-142, 2011, DOI:10.3970/cmc.2011.024.125

Abstract The inverse boundary optimization problem, governed by the Helmholtz equation, is analyzed by the Trefftz method (TM) and the exponentially convergent scalar homotopy algorithm (ECSHA). In the inverse boundary optimization problem, the position for part of boundary with given boundary condition is unknown, and the position for the rest of boundary with additionally specified boundary conditions is given. Therefore, it is very difficult to handle the boundary optimization problem by any numerical scheme. In order to stably solve the boundary optimization problem, the TM, one kind of boundary-type meshless methods, is adopted in this study, since it can avoid the… More >