Y.C. Cai¹ and H.H. Zhu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.2, pp. 179-204, 2008, DOI:10.3970/cmes.2008.034.179

Abstract The popular Shepard PU approximations are easy to construct and have many advantages, but they have several limitations, such as the difficulties in handling essential boundary conditions and the known problem of linear dependence regarding PU-based methods, and they are not the good choice for MLPG method. With the objective of alleviating the drawbacks of Shepared PU approximations, a new meshless PU-based Shepard and Least Square (SLS) interpolation is employed here to develop a new type of MLPG method, which is named as Local Meshless Shepard and Least Square (LMSLS) method. The SLS interpolation possesses the much desired Kronecker-delta property,… More >

D. Ngo-Cong^1,2, N. Mai-Duy¹, W. Karunasena², T. Tran-Cong^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.3, pp. 275-310, 2012, DOI:10.3970/cmes.2012.083.275

Abstract In this paper, natural convection flows in concentric and eccentric annuli are studied using a new numerical method, namely local moving least square - one dimensional integrated radial basis function networks (LMLS-1D-IRBFN). The partition of unity method is used to incorporate the moving least square (MLS) and one dimensional-integrated radial basis function (1D-IRBFN) techniques in an approach that leads to sparse system matrices and offers a high level of accuracy as in the case of 1D-IRBFN method. The present method possesses a Kronecker-Delta function property which helps impose the essential boundary condition in an exact manner. The method is first… More >

K. Wang¹, S.J. Zhou^2,3, Z.F. Nie⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.1, pp. 77-102, 2011, DOI:10.3970/cmes.2011.073.077

Abstract The natural neighbour Galerkin method is tailored to solve boundary value problems of the couple-stress elasticity to model the size dependent behaviour of materials. This method is based on the displacement-based Galerkin approach, and the calculation of the global stiffness matrix is performed using gradient smoothing technique combined with the non-Sibsonian partition of unity approximation scheme. This method possesses the following properties: the complex C1-continuous approximation scheme is avoided without using either Lagrange multipliers or penalty parameters; no domain integrals involved in the assembly of the global stiffness matrix; and the imposition of essential boundary conditions is straightforward. The validity… More >

Phong B.H. Le¹, Timon Rabczuk², Nam Mai-Duy¹, Thanh Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.1, pp. 25-52, 2010, DOI:10.3970/cmes.2010.066.025

Abstract A novel meshless method based on Radial Basis Function networks (RBFN) and variational principle (global weak form) is presented in this paper. In this method, the global integrated RBFN is localized and coupled with the moving least square method via the partition of unity concept. As a result, the system matrix is symmetric, sparse and banded. The trial and test functions satisfy the Kronecker-delta property, i.e. Φ_i(x_j) = δ_ij. Therefore, the essential boundary conditions are imposed in strong form as in the FEMs. Moreover, the proposed method is applicable to scattered nodes and arbitrary domains. The method is examined with… More >

Raju Sethuraman¹, N.R.Rajesh²

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.1, pp. 67-100, 2009, DOI:10.3970/cmes.2009.039.067

Abstract This paper presents a methodology based on Partition of Unity Finite Element Method (PUFEM) and Pseudo Elastic Analysis for solving material non-linear fracture problems within the scope of total deformation theory of plasticity. Local enrichment base functions are used to represent the asymptotic field near the crack tip and discontinuous field across the crack faces. An iterative linear elastic analysis using PUFEM is carried out for the determination of elastic-plastic crack tip stress fields by treating effective material properties as spatial field variables. The effective material parameters are defined using deformation theory and are updated in an iterative manner based… More >

A. Arefmanesh¹, M. Najafi¹, H. Abdi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.1, pp. 9-22, 2008, DOI:10.3970/cmes.2008.025.009

Abstract The meshless local Petrov-Galerkin (MLPG) method with unity as the weighting function has been applied to the solution of the Navier-Stokes and energy equations. The Navier-Stokes equations in terms of the stream function and vorticity formulation together with the energy equation are solved for different test cases. This present study considers the implementation of the method on a non-isothermal lid-driven cavity flow, the lid-driven cavity flow with an inlet and outlet, and also on the non-isothermal flow over an obstacle. Nonuniform point distribution is employed for all the test cases for the numerical simulations. The flow streamlines for each test… More >

Di Shang^1,*, Mohammed Ghriga¹

CMC-Computers, Materials & Continua, Vol.61, No.1, pp. 1-10, 2019, DOI:10.32604/cmc.2019.08217

Abstract In this research, we aim to identify and investigate the impacts of key influencers on community formations and developments. We assess the impacts of key influencers by analyzing the activities and structure of the social media presence of a local community. Results of our analysis show that key influencers play important roles in connecting the community, transferring information, and improving overall sentiment of the community members. Our findings suggest that community practitioners can apply social network analysis to identify value-added influencers and discover strategies for improving the community and keeping leadership roles. More >