M.A. Golberg¹, C.S. Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.1, pp. 87-96, 2001, DOI:10.3970/cmes.2001.002.087

Abstract The purpose of this paper is to develop a highly efficient mesh-free method for solving nonlinear diffusion-reaction equations in R^d, d=2, 3. Using various time difference schemes, a given time-dependent problem can be reduced to solving a series of inhomogeneous Helmholtz-type equations. The solution of these problems can then be further reduced to evaluating particular solutions and the solution of related homogeneous equations. Recently, radial basis functions have been successfully implemented to evaluate particular solutions for Possion-type equations. A more general approach has been developed in extending this capability to obtain particular solutions for Helmholtz-type equations by using polyharmonic spline… More >

J. Sladek¹, V. Sladek¹, V. Kompis², R. Van Keer³

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 1-8, 2000, DOI:10.3970/cmes.2000.001.453

Abstract This paper presents an application of a direct Trefftz method with domain decomposition to the two-dimensional elasticity problem. Trefftz functions are substituted into Betti's reciprocity theorem to derive the boundary integral equations for each subdomain. The values of displacements and tractions on subdomain interfaces are tailored by continuity and equilibrium conditions, respectively. Since Trefftz functions are regular, much less requirements are put on numerical integration than in the traditional boundary integral method. Then, the method can be utilized to analyse also very narrow domains. Linear elements are used for modelling of the boundary geometry and approximation of boundary quantities. Numerical… More >

S. Guimarães¹, J.C.F. Telles²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.3, pp. 131-139, 2000, DOI:10.3970/cmes.2000.001.433

Abstract The paper discusses further applications of the hyper-singular boundary integral equation to obtain the Green's function solution to general geometry fracture mechanics problems, such as curved multifracture crack simulation, static and transient dynamic in 2-D, 3-D and plate bending problems. This numerical Green's function (NGF) is implemented into alternative boundary element computer programs, as the fundamental solution, to enhance the scope of alternative applications of the NGF procedure.
The results to some typical linear fracture mechanics problems are presented. More >

V. Kozulić¹, H. Gotovac¹, B. Gotovac¹

CMC-Computers, Materials & Continua, Vol.6, No.2, pp. 51-70, 2007, DOI:10.3970/cmc.2007.006.051

Abstract In this paper, we present a multi-resolution adaptive algorithm for solving problems described by partial differential equations. The technique is based on the collocation method using Fup basis functions, which belong to a class of Rvachev's infinitely differentiable finite functions. As it is possible to calculate derivation values of Fup basis functions of high degree in a precise yet simple way, so it is possible to efficiently apply strong formulation procedures. The mesh free method developed in this work is named Adaptive Fup Collocation Method (AFCM). The distribution of collocation points within the observed area is changed adaptively, depending on… More >

Vladimir Sladek¹, Jan Sladek¹, Chuanzeng Zhang²

CMC-Computers, Materials & Continua, Vol.4, No.3, pp. 177-188, 2006, DOI:10.3970/cmc.2006.004.177

Abstract This paper concerns the stability, convergence of accuracy and cost efficiency of four various formulations for solution of boundary value problems in non-homogeneous elastic solids with functionally graded Young's modulus. The meshless point interpolation method is employed with using various basis functions. The interaction among the elastic continuum constituents is considered in the discretized formulation either by collocation of the governing equations or by integral satisfaction of the force equilibrium on local sub-domains. The exact benchmark solutions are used in numerical tests. More >

Lu Wang^1,2, Cuihhong Yang², Tong Liu³, Hongyan Wu^2,*

CMC-Computers, Materials & Continua, Vol.60, No.2, pp. 757-765, 2019, DOI:10.32604/cmc.2019.04499

Abstract Ab initio molecular-dynamics simulations have been used to investigate the liquid and amorphous Al94-xNi6Lax (x=3-9) alloys. Through calculating the pair distribution functions and partial coordination numbers, the structure and properties of these alloys are researched, which will help the design bulk metallic glass. The concentration of La atoms can affect the short-range order of Al94-xNi6Lax alloys, which is also studied in this calculation result. More >

Lin Chen^1,2, Chunfang Yang^1,2,*, Fenlin Liu^1,2, Daofu Gong^1,2, Shichang Ding³

CMC-Computers, Materials & Continua, Vol.56, No.2, pp. 199-210, 2018, DOI: 10.3970/cmc.2018.02574

Abstract When dealing with the large-scale program, many automatic vulnerability mining techniques encounter such problems as path explosion, state explosion, and low efficiency. Decomposition of large-scale programs based on safety-sensitive functions helps solve the above problems. And manual identification of security-sensitive functions is a tedious task, especially for the large-scale program. This study proposes a method to mine security-sensitive functions the arguments of which need to be checked before they are called. Two argument-checking identification algorithms are proposed based on the analysis of two implementations of argument checking. Based on these algorithms, security-sensitive functions are detected based on the ratio of… More >

V. G. Yakhno¹, B. Çiçek²

CMC-Computers, Materials & Continua, Vol.44, No.3, pp. 141-166, 2014, DOI:10.3970/cmc.2014.044.141

Abstract A method for an approximate computation of the electric and magnetic Green’s functions for the time-harmonic Maxwell’s equations in the general electrically gyrotropic materials is proposed. This method is based on the Fourier transform meta-approach: the equations for electric and magnetic fields are written in terms of images of the Fourier transform with respect to space variables and as a result of it the linear algebraic systems for finding Fourier images of the columns of the Green’s functions are obtained. The explicit formulas for the solutions of the obtained systems have been found. Finally, elements of the Green’s functions are… More >

B.A. Mamedov¹

CMC-Computers, Materials & Continua, Vol.43, No.2, pp. 87-96, 2014, DOI:10.3970/cmc.2014.043.087

Abstract In this paper, we propose an efficient method to calculate the isotropic and tetragonal lattice Green functions for the face-centered cubic (FCC), bodycentered cubic (BCC) and simple cubic (SC) lattices. The method is based on binomial expansion theorems, which provide us with analytical formulae through basic integrals. The resulting series present better convergence rates. Several acceleration techniques are combined to further improve the efficiency of the established formulas. The obtained results for the lattice Green functions are in good agreement with the known numerical calculation results. More >

L.H. Kuo¹, M.H. Gu², D.L. Young³, C.Y. Lin³

CMC-Computers, Materials & Continua, Vol.33, No.3, pp. 213-228, 2013, DOI:10.3970/cmc.2013.033.213

Abstract Coupled with the Houbolt method, a third order finite difference time marching scheme, the method of approximate particular solutions (MAPS) has been applied to solve wave equations. Radial basis function has played an important role in the solution process of the MAPS. To show the effectiveness of the MAPS, we compare the results with the well known Kansa's method, timemarching method of fundamental solutions (TMMFS), and traditional finite element methods. To validate the effectiveness and easiness of the MAPS, four numerical examples which including regular, smooth irregular, and non-smooth domains are given. More >