Hongfen Gao¹, Gaofeng Wei^2,3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.3, pp. 1793-1814, 2022, DOI:10.32604/cmes.2022.019687

Abstract By introducing the radial basis functions (RBFs) into the reproducing kernel particle method (RKPM), the calculating accuracy and stability of the RKPM can be improved, and a novel meshfree method of the radial basis RKPM (meshfree RRKPM) is proposed. Meanwhile, the meshfree RRKPM is applied to transient heat conduction problems (THCP), and the corresponding equations of the meshfree RRKPM for the THCP are derived. The two-point time difference scheme is selected to discretize the time of the THCP. Finally, the numerical results illustrate the effectiveness of the meshfree RRKPM for the THCP. More >

M. R. Hematiyan^1,*, B. Jamshidi¹, M. Mohammadi²

CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.3, pp. 1349-1369, 2022, DOI:10.32604/cmes.2022.018235

Abstract The method of fundamental solutions (MFS) is a boundary-type and truly meshfree method, which is recognized as an efficient numerical tool for solving boundary value problems. The geometrical shape, boundary conditions, and applied loads can be easily modeled in the MFS. This capability makes the MFS particularly suitable for shape optimization, moving load, and inverse problems. However, it is observed that the standard MFS lead to inaccurate solutions for some elastostatic problems with stress concentration and/or highly anisotropic materials. In this work, by a numerical study, the important parameters, which have significant influence on the accuracy of the MFS for… More >

Hau Nguyen-Ngoc^1,2, H. Nguyen-Xuan³, Magd Abdel-Wahab^4,5,*

CMC-Computers, Materials & Continua, Vol.66, No.1, pp. 165-178, 2021, DOI:10.32604/cmc.2020.012948

Abstract This study adapts the flexible characteristic of meshfree method in analyzing three-dimensional (3D) complex geometry structures, which are the interlocking concrete blocks of step seawall. The elastostatic behavior of the block is analysed by solving the Galerkin weak form formulation over local support domain. The 3D moving least square (MLS) approximation is applied to build the interpolation functions of unknowns. The pre-defined number of nodes in an integration domain ranging from 10 to 60 nodes is also investigated for their effect on the studied results. The accuracy and efficiency of the studied method on 3D elastostatic responses are validated through… More >

Jie Bai^1,#, Liqiang Lin^1,#, Xiaowei Zeng ^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.121, No.3, pp. 787-800, 2019, DOI:10.32604/cmes.2019.07159

Abstract The collective cell migration behavior on a substrate was studied using RKPM meshfree method. The cells were modeled as nematic liquid crystal with hyperelastic cell nucleus. The cell-substrate and cell-cell interactions were modeled by coarse-grained potential forces. Through this study, the pulling and pushing phenomenon during collective cell migration process was observed and it was found that the individual cell mobility significantly influenced the collective cell migratory behavior. More self-propelled cells are in the system along the same direction, the faster the collective group migrates toward coordinated direction. The parametric study on cell-cell adhesion strength indicated that as the adhesion… More >

Dongdong Wang, Zhuoya Li, Youcai Wu

The International Conference on Computational & Experimental Engineering and Sciences, Vol.17, No.4, pp. 107-108, 2011, DOI:10.3970/icces.2011.017.107

Abstract Meshfree methods have experienced substantially fundamental development and various applications. One distinguished advantage for meshfree methods is that they can relieve the mesh tangling burden of FEM and are more suitable for finite deformation analysis. In this work a three dimensional updated Lagrangian Galerkin meshfree formulation with improved computational efficiency is presented to analyze the failure of soil slopes. This nonlinear meshfree formulation is featured by the Lagrangian stabilized conforming nodal integration method where the low cost nature of nodal integration approach is kept and at the same time the numerical stability is obtained as is not the case for… More >

G. R. Liu^{1, 2}

The International Conference on Computational & Experimental Engineering and Sciences, Vol.12, No.4, pp. 113-114, 2009, DOI:10.3970/icces.2009.012.113

Abstract This paper introduces first a weakened weakform (W2) using a generalized gradient smoothing technique for an unified formulation of a wide class of compatible and incompatible displacement methods including settings of the finite element methods (FEM) and meshfree methods of special properties including the upper bound properties. A G space is first defined to include discontinuous functions allowing the use of much more types of methods/techniques to create shape functions for numerical models; Properties and a set of important inequalities for G spaces are then proven in theory and analyzed in detail. We prove that the numerical methods developed based… More >

Suely Oliveira², Fang Yang²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 113-120, 2007, DOI:10.3970/icces.2007.003.113

Abstract In this paper we describe and compare preconditioners for saddle-point systems obtained from meshfree discretizations, using the concepts of hierarchical (or H-)matrices. Previous work by the authors using this approach did not use H-matrix techniques throughout, as is done here. Comparison shows the method described here to be better than the author's previous method, an AMG method adapted to saddle point systems, and conventional iterative methods such as JOR. More >

Armin Iske¹, Martin Käser²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 133-148, 2005, DOI:10.3970/cmes.2005.007.133

Abstract Petroleum reservoir modelling requires effective multiscale methods for the numerical simulation of two-phase flow in porous media. This paper proposes the application of a novel meshfree particle method to the Buckley-Leverett model. The utilized meshfree advection scheme, called AMMoC, is essentially a method of characteristics, which combines an adaptive semi-Lagrangian method with local meshfree interpolation by polyharmonic splines. The method AMMoC is applied to the five-spot problem, a well-established model problem in petroleum reservoir simulation. The numerical results and subsequent numerical comparisons with two leading commercial reservoir simulators, ECLIPSE and FrontSim, show the good performance of our meshfree advection scheme… More >

Y. Wang¹, E. Lü^1,2, J. Zhao¹, J. Guo¹

CMES-Computer Modeling in Engineering & Sciences, Vol.109-110, No.1, pp. 35-53, 2015, DOI:10.3970/cmes.2015.109.035

Abstract Meshfree methods have found good applications in many new researches, which show very good potential to be powerful numerical tools. As an alternative to the mesh based methods, meshfree methods have the advantage of not using a predefined mesh for the domain discretization. In this study, a mesh free scheme based on the radial point interpolation method was used to solve the topological design of microstructures for composite materials. The explicit form of the radial point interpolation method (RPIM) interpolation augmented with polynomials is presented, which satisfies range-restricted properties and is applicable to integrate a physically meaningful density interpolation. Meanwhile… More >

J.B. Alford¹, D.C. Simkins¹, R.A. Rembert¹, L. Hoyte, MD²

CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.2, pp. 129-149, 2014, DOI:10.3970/cmes.2014.098.129

Abstract Mechanical deformation of tissues in the female pelvic floor is believed to be central to understanding a number of important aspects of women’s health, particularly pelvic floor dysfunction. A 2008 study of US women reported the prevalence of pelvic floor disorders in the 20 and 39 years range as 9.7% with the prevalence increasing with age until it reaches roughly 50% in the 80 and older age group [Nygaard, Barber, Burgio, and et al (2008)]. Clinical observation indicates a strong correlation between problems such as pelvic organ prolapse/urinary incontinence and vaginal childbirth. It is thought that childbirth parameters like fetal… More >