S.F. Moreira^∗, J. Belinha^{∗,† ,‡}, L.M.J.S. Dinis^∗,†, R.M. Natal Jorge^∗,†

Molecular & Cellular Biomechanics, Vol.11, No.3, pp. 151-184, 2014, DOI:10.3970/mcb.2014.011.151

Abstract In this work the maxillary central incisor is numerically analysed with an advance discretization technique – Natural Neighbour Radial Point Interpolation Method (NNRPIM). The NNRPIM permits to organically determine the nodal connectivity, which is essential to construct the interpolation functions. The NNRPIM procedure, based uniquely in the computational nodal mesh discretizing the problem domain, allows to obtain autonomously the required integration mesh, permitting to numerically integrate the differential equations ruling the studied physical phenomenon. A numerical analysis of a tooth structure using a meshless method is presented for the first time. A two-dimensional model of the maxillary central incisor, based… More >

B. Amaziane¹, A. Naji², D. Ouazar³

CMC-Computers, Materials & Continua, Vol.1, No.2, pp. 117-128, 2004, DOI:10.3970/cmc.2004.001.117

Abstract In this paper, a meshless method based on Radial Basis Functions (RBF) is coupled with genetic algorithms for parameter identification to some selected groundwater flow applications. The treated examples are generated by the diffusion equation with some specific boundary conditions describing the groundwater fluctuation in a leaky confined aquifer system near open tidal water. To select the best radial function interpolation and show the powerful of the method in comparison to domain based discretization methods, Multiquadric (MQ), Thin-Plate Spline (TPS) and Conical type functions are investigated and compared to finite difference results or analytical one. Through two sample problems in… More >

Q. Wang¹, Y. Miao^1,2, H.P. Zhu¹, C. Zhang³

CMC-Computers, Materials & Continua, Vol.28, No.1, pp. 1-26, 2012, DOI:10.3970/cmc.2012.028.001

Abstract The Hybrid boundary node method (Hybrid BNM) is a boundary type meshless method which based on the modified variational principle and the Moving Least Squares (MLS) approximation. Like the boundary element method (BEM), it has a dense and unsymmetrical system matrix and needs to be speeded up while solving large scale problems. This paper combines the fast multipole method (FMM) with Hybrid BNM for solving 3D elasticity problems. The formulations of the fast multipole Hybrid boundary node method (FM-HBNM) which based on spherical harmonic series are given. The computational cost is estimated and an O(N) algorithm is obtained. The algorithm… More >

G. Kosec¹, B. Šarler^1,2

CMC-Computers, Materials & Continua, Vol.26, No.3, pp. 227-254, 2011, DOI:10.3970/cmc.2011.026.227

Abstract This paper introduces an effective H-adaptive upgrade to solution of the transport phenomena by the novel Local Radial Basis Function Collocation Method (LRBFCM). The transport variable is represented on overlapping 5-noded influence-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the variable are calculated from the respective derivatives of the RBFs. The transport equation is solved through explicit time stepping. The H-adaptive upgrade includes refinement/derefinement of one to four nodes to/from the vicinity of the reference node. The number of the nodes added or removed depends on the topology of the reference… More >

Chihyu Liu¹, Chengyu Ku^1,2,*, Jingen Xiao¹, Weichung Yeih^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.118, No.1, pp. 229-252, 2019, DOI:10.31614/cmes.2019.04376

Abstract In this article, a meshless method using the spacetime collocation for solving the two-dimensional backward heat conduction problem (BHCP) is proposed. The spacetime collocation meshless method (SCMM) is to derive the general solutions as the basis functions for the two-dimensional transient heat equation using the separation of variables. Numerical solutions of the heat conduction problem are expressed as a series using the addition theorem. Because the basis functions are the general solutions of the governing equation, the boundary points may be collocated on the spacetime boundary of the domain. The proposed method is verified by conducting several heat conduction problems.… More >

S. Vahdati¹, D. Mirzaei²

CMES-Computer Modeling in Engineering & Sciences, Vol.109-110, No.3, pp. 247-262, 2015, DOI:10.3970/cmes.2015.109.247

Abstract In this paper we present a meshless collocation method based on the moving least squares (MLS) approximation for numerical solution of the multiasset (d-dimensional) American option in financial mathematics. This problem is modeled by the Black-Scholes equation with moving boundary conditions. A penalty approach is applied to convert the original problem to one in a fixed domain. In finite parts, boundary conditions satisfy in associated (d-1)-dimensional Black-Scholes equations while in infinity they approach to zero. All equations are treated by the proposed meshless approximation method where the method of lines is employed for handling the time variable. Numerical examples for… More >

Annamaria Mazzia¹, Giorgio Pini¹, Flavio Sartoretto²

CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.4, pp. 239-262, 2015, DOI:10.3970/cmes.2015.108.239

Abstract Meshless Local Petrov Galerkin (MLPG) methods are pure meshless techniques for solving Partial Differential Equations (PDE). MLPG techniques are nowadays used for solving a huge number of complex, real–life problems. While MLPG aims to approximate the solution of a given differential problem, its “dual” Direct MLPG (DMLPG) technique relies upon approximating linear functionals. Assume adaptive methods are to be implemented. When using a mesh–based method, inserting and/or deleting a node implies complex adjustment of connections. Meshless methods are more apt to implement adaptivity, since they does not require such adjustments. Nevertheless, ad–hoc insertion and/or deletion algorithms must be devised, in… More >

Isa Ahmadi¹, M.M. Aghdam²

CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.1, pp. 21-48, 2015, DOI:10.3970/cmes.2015.108.021

Abstract In this study, a truly meshless method based on the meshless local Petrov-Galerkin method is formulated for analysis of the elastic-plastic behavior of heterogeneous solid materials. The incremental theory of plasticity is employed for modeling the nonlinearity of the material behavior due to plastic strains. The well-known Prandtl-Reuss flow rule of plasticity is used as the constitutive equation of the material. In the presented method, the computational cost is reduced due to elimination of the domain integration from the formulation. As a practical example, the presented elastic-plastic meshless formulation is employed for micromechanical analysis of the unidirectional composite material. A… More >

Marjan Uddin^1,2, Hazrat Ali¹, Amjad Ali¹

CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.6, pp. 463-479, 2015, DOI:10.3970/cmes.2015.107.463

Abstract This work explores the application of kernel based local meshless method for solving multi-dimensional wave equations in irregular domain. The method is tested for various types of boundary conditions in irregular shaped domain. The method is capable of solving multi-dimension large scaled problems in complex shaped domain. More >

Taku Itoh¹, Susumu Nakata²

CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.3, pp. 187-199, 2015, DOI:10.3970/cmes.2015.107.187

Abstract To speed up generating a scalar field g(x) based on a piecewise polynomial, a new method for determining field values that are indispensable to generate g(x) has been proposed. In the proposed method, an intermediate for generating g(x) does not required, i.e., the field values can directly be determined from given point data. Numerical experiments show that the computation time for determining the field values by the proposed method is about 10.4–12.7 times less than that of the conventional method. In addition, on the given points, the accuracy of g(x) obtained by using the proposed method is almost the same… More >