Chih-Ping Wu^*, Ruei-Syuan Chang

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.1, pp. 917-949, 2024, DOI:10.32604/cmes.2024.052307 - 20 August 2024

Abstract This work develops a Hermitian C differential reproducing kernel interpolation meshless (DRKIM) method within the consistent couple stress theory (CCST) framework to study the three-dimensional (3D) microstructure-dependent static flexural behavior of a functionally graded (FG) microplate subjected to mechanical loads and placed under full simple supports. In the formulation, we select the transverse stress and displacement components and their first- and second-order derivatives as primary variables. Then, we set up the differential reproducing conditions (DRCs) to obtain the shape functions of the Hermitian C differential reproducing kernel (DRK) interpolant’s derivatives without using direct differentiation. The interpolant’s… More >

Weiwu Jiang¹, Xiaowei Gao^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.1, pp. 41-76, 2024, DOI:10.32604/cmes.2024.048313 - 16 April 2024

Abstract The collocation method is a widely used numerical method for science and engineering problems governed by partial differential equations. This paper provides a comprehensive review of collocation methods and their applications, focused on elasticity, heat conduction, electromagnetic field analysis, and fluid dynamics. The merits of the collocation method can be attributed to the need for element mesh, simple implementation, high computational efficiency, and ease in handling irregular domain problems since the collocation method is a type of node-based numerical method. Beginning with the fundamental principles of the collocation method, the discretization process in the continuous… More >

Zhuojia Fu^1,*, Qiang Xi², Wenzhi Xu¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.1, pp. 1-1, 2023, DOI:10.32604/icces.2023.09393

Abstract In the past few decades, although traditional computational methods such as finite element have been successfully used in many scientific and engineering fields, they still face several challenging problems such as expensive computational cost, low computational efficiency, and difficulty in mesh generation in the numerical simulation of wave propagation under infinite domain, large-scale-ratio structures, engineering inverse problems and moving boundary problems. This paper introduces a class of collocation discretization techniques based on physical-informed kernel function (PIKF) to efficiently solve the above-mentioned problems. The key issue in the physical-informed kernel function collocation methods (PIKFCMs) is to… More >

Jingwen Ren¹, Hongwei Lin^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 2957-2984, 2023, DOI:10.32604/cmes.2023.025983 - 09 March 2023

Abstract Isogeometric analysis (IGA) is introduced to establish the direct link between computer-aided design and analysis. It is commonly implemented by Galerkin formulations (isogeometric Galerkin, IGA-G) through the use of nonuniform rational B-splines (NURBS) basis functions for geometric design and analysis. Another promising approach, isogeometric collocation (IGA-C), working directly with the strong form of the partial differential equation (PDE) over the physical domain defined by NURBS geometry, calculates the derivatives of the numerical solution at the chosen collocation points. In a typical IGA, the knot vector of the NURBS numerical solution is only determined by the… More > Graphic Abstract

A.Wakif^a,* , Z. Boulahia^a, A. Amine^b , I.L. Animasaun^c , M. I. Afridi^d, M. Qasim^d , R. Sehaqui^a

Frontiers in Heat and Mass Transfer, Vol.12, pp. 1-15, 2019, DOI:10.5098/hmt.12.3

Abstract The significance of an externally applied magnetic field and an imposed negative temperature gradient on the onset of natural convection in a thin horizontal layer of alumina-water nanofluid for various sizes of spherical alumina nanoparticles (e.g., 30 More >

M. Dehghan¹, M. Abbaszadeh², A. Mohebbi³

CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.6, pp. 481-516, 2015, DOI:10.3970/cmes.2015.107.481

Abstract In the current paper the two-dimensional time fractional Klein-Kramers equation which describes the subdiffusion in the presence of an external force field in phase space has been considered. The numerical solution of fractional Klein-Kramers equation is investigated. The proposed method is based on using finite difference scheme in time variable for obtaining a semi-discrete scheme. Also, to achieve a full discretization scheme, the Kansa's approach and meshless local Petrov-Galerkin technique are used to approximate the spatial derivatives. The meshless method has already proved successful in solving classic and fractional differential equations as well as for… 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 >

D. Ho-Minh¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.70, No.3, pp. 217-252, 2010, DOI:10.3970/cmes.2010.070.217

Abstract In this paper, one-dimensional integrated radial-basis-function networks (1D-IRBFNs) are introduced into the Galerkin and point-collocation formulations to simulate viscoelastic flows. The computational domain is represented by a Cartesian grid and IRBFNs, which are constructed through integration, are employed on each grid line to approximate the field variables including stresses in the streamfunction-vorticity formulation. Two types of fluid, namely Oldroyd-B and CEF models, are considered. The proposed methods are validated through the numerical simulation of several benchmark test problems including flows in a rectangular duct and in a corrugated tube. Numerical results show that accurate results More >

Shih-Wei Yang¹, Yung-Ming Wang¹, Chih-Ping Wu^1,2, Hsuan-Teh Hu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.1, pp. 1-40, 2010, DOI:10.3970/cmes.2010.060.001

Abstract A differential reproducing kernel (DRK) approximation-based collocation method is developed for solving ordinary and partial differential equations governing the one- and two-dimensional problems of elastic bodies, respectively. In the conventional reproducing kernel (RK) approximation, the shape functions for the derivatives of RK approximants are determined by directly differentiating the RK approximants, and this is very time-consuming, especially for the calculations of their higher-order derivatives. Contrary to the previous differentiation manipulation, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of RK approximants. A meshless collocation method based on More >

Chih-Ping Wu^1,2, Jian-Sin Wang², Yung-Ming Wang²

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.1, pp. 1-38, 2009, DOI:10.3970/cmes.2009.052.001

Abstract A meshless collocation method based on the differential reproducing kernel (DRK) interpolation is developed for the three-dimensional (3D) coupled analysis of simply-supported, functionally graded (FG) piezoelectric hollow cylinders. The material properties of FG hollow cylinders are regarded as heterogeneous through the thickness coordinate, and then specified to obey an exponent-law dependent on this. In the present formulation, the shape function for the reproducing kernel (RK) interpolation function at each sampling node is separated into a primitive function possessing Kronecker delta properties and an enrichment function constituting reproducing conditions. By means of this DRK interpolation, the… More >