W. Chen^1,2, C. J. Liu¹, Y. Gu^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.4, pp. 251-270, 2015, DOI:10.3970/cmes.2015.105.251

Abstract The singular boundary method (SBM) is a recently-developed meshless boundary collocation method. This method overcomes the well-known fictitious boundary issue associated with the method of fundamental solutions (MFS) while remaining the merits of the later of being truly meshless, integral-free, and easy-to-program. Similar to the MFS, this method, however, produces dense and unsymmetrical coefficient matrix, which although much smaller in size compared with domain discretization methods, requires O(N²) operations in the iterative solution of the resulting algebraic system of equations. To remedy this bottleneck problem for its application to large-scale problems, this paper makes the first More >

A.H. Bhrawy^1,2, E.H. Doha³, S.S. Ezz-Eldien⁴, M.A. Abdelkawy²

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.3, pp. 185-209, 2015, DOI:10.3970/cmes.2015.104.185

Abstract In this paper, a high accurate numerical approach is investigated for solving the time-fractional linear and nonlinear Korteweg-de Vries (KdV) equations. These equations are the most appropriate and desirable definition for physical modeling. The spectral collocation method and the operational matrix of fractional derivatives are used together with the help of the Gauss-quadrature formula in order to reduce such problem into a problem consists of solving a system of algebraic equations which greatly simplifying the problem. Our approach is based on the shifted Jacobi polynomials and the fractional derivative is described in the sense of More >

Costas D. Lallas¹, Yomi Fashola¹, Robert B. Den², Francisco Gelpi-Hammerschmidt¹, Anne E. Calvaresi¹, Peter McCue³, Ruth Birbe³, Leonard G. Gomella¹, Edouard J. Trabulsi¹

Canadian Journal of Urology, Vol.21, No.5, pp. 7479-7486, 2014

Abstract Introduction: To identify and assess predictive factors for positive surgical margins (PSM) in patients undergoing radical prostatectomy (RP).
Materials and methods: An Institution Review Board (IRB) approved retrospective review of 1751 patients that underwent RP from March 2000 to June 2013 was performed. Identified were 1740 patients whom had not received neoadjuvant therapy; these were used for the purpose of this analysis. Univariate and multivariate analysis were performed to determine factors associated with and predictive of PSMs, divided into preoperative and pathological. Variables analyzed include age, body mass index (BMI), race, surgeon, surgical modality, pathologic T-stage and… More >

Li^1,2 YY, X-T Lü¹, Z-W Wang¹, C Zhou^3,4, X-G Han¹

Phyton-International Journal of Experimental Botany, Vol.83, pp. 283-289, 2014, DOI:10.32604/phyton.2014.83.283

Abstract Relative growth rate (RGR) of plants is a key component of fitness. Theoretically, the RGR of plants would be closely related with biomass allocation. Our mechanistic understanding of the relationship between RGR and biomass allocation under global change scenarios is still limited. We examined the responses of RGR and biomass allocation of Leymus chinensis, a dominant grass in the temperate steppe of northern China, to a wide range of N addition. We found that N addition increased RGR of L. chinensis up to a threshold of 10 g N/m². While leaf and stem weight ratios were positively correlated… More >

Zhuo-Jia Fu¹, Wen Chen^1,2, Jeng-Tzong Chen³, Wen-Zhen Qu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.5, pp. 417-443, 2014, DOI:10.3970/cmes.2014.099.417

Abstract This study investigates the singular boundary method (SBM) with three regularization approaches for solving 2D and 3D exterior wave problems. The singular boundary method is a recent meshless boundary collocation method, which introduces the concept of source intensity factors to eliminate the singularity of the fundamental solutions. Recently, three approaches, the inverse interpolation technique (IIT), the semi-analytical technique with boundary IIT (SAT1) and the semi-analytical technique with integral mean value (SAT2), have been proposed to determine the source intensity factors for removing the singularities of Helmholtz fundamental solutions at origin. This study compares numerical accuracy… More >

K.P. Baxevanakis¹, A.E. Giannakopoulos²

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.6, pp. 535-544, 2014, DOI:10.3970/cmes.2014.097.535

Abstract This article has no abstract. More >

Tao Zhang^1,2, Yiqian He³, Leiting Dong⁴, Shu Li¹, Abdullah Alotaibi⁵, Satya N. Atluri^2,5

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.6, pp. 509-533, 2014, DOI:10.3970/cmes.2014.097.509

Abstract In this article, the Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method is developed to solve the Cauchy inverse problems of Steady- State Heat Transfer In the MLPG mixed collocation method, the mixed scheme is applied to independently interpolate temperature as well as heat flux using the same meshless basis functions The balance and compatibility equations are satisfied at each node in a strong sense using the collocation method. The boundary conditions are also enforced using the collocation method, allowing temperature and heat flux to be over-specified at the same portion of the boundary. For the… More >

S. Saha Ray¹, A. K. Gupta²

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.5, pp. 315-341, 2014, DOI:10.3970/cmes.2014.103.315

Abstract In this paper, an efficient numerical schemes based on the Haar wavelet method are applied for finding numerical solution of nonlinear third-order modified Korteweg-de Vries (mKdV) equation as well as modified Burgers' equations. The numerical results are then compared with the exact solutions. The accuracy of the obtained solutions is quite high even if the number of calculation points is small. More >

V. C. Loukopoulos¹, G. C. Bourantas²

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.1, pp. 49-70, 2014, DOI:10.3970/cmes.2014.103.049

Abstract A numerical solution of the linear and nonlinear time-dependent Schrödinger equation is obtained, using the strong form MLPG Collocation method. Schrödinger equation is replaced by a system of coupled partial differential equations in terms of particle density and velocity potential, by separating the real and imaginary parts of a general solution, called a quantum hydrodynamic (QHD) equation, which is formally analogous to the equations of irrotational motion in a classical fluid. The approximation of the field variables is obtained with the Moving Least Squares (MLS) approximation and the implicit Crank-Nicolson scheme is used for time More >

Jin Li^1,2, De-hao Yu^3,4

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.2, pp. 103-126, 2014, DOI:10.3970/cmes.2014.102.103

Abstract The generalized composite middle rectangle rule for the computation of Hilbert integral is discussed. The pointwise superconvergence phenomenon is presented, i.e., when the singular point coincides with some a priori known point, the convergence rate of the rectangle rule is higher than what is global possible. We proved that the superconvergence rate of the composite middle rectangle rule occurs at certain local coordinate of each subinterval and the corresponding superconvergence error estimate is obtained. By choosing the superconvergence point as the collocation points, a collocation scheme for solving the relevant Hilbert integral equation is presented More >