Patrícia C.T. Gonçalves^1,2, João Manuel R.S. Tavares^1,2, R.M. Natal Jorge^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.1, pp. 45-56, 2008, DOI:10.3970/cmes.2008.032.045

Abstract The main goals of the present work are to automatically extract the contour of an object and to simulate its deformation using a physical approach. In this work, to segment an object represented in an image, an initial contour is manually defined for it that will then automatically evolve until it reaches the border of the desired object. In this approach, the contour is modelled by a physical formulation using the finite element method, and its temporal evolution to the desired final contour is driven by internal and external forces. The internal forces are defined by the intrinsic characteristics of… More >

G.A. Gravvanis, K.M. Giannoutakis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.1, pp. 35-44, 2008, DOI:10.3970/cmes.2008.032.035

Abstract A new parallel normalized optimized approximate inverse algorithm, based on the concept of the ``fish bone'' computational approach with cyclic distribution of the processors satisfying an antidiagonal data dependency, for computing classes of explicit approximate inverses, is introduced for symmetric multiprocessor systems. The parallel normalized explicit approximate inverses are used in conjunction with parallel normalized explicit preconditioned conjugate gradient square schemes, for the efficient solution of finite element sparse linear systems. The parallel design and implementation issues of the new proposed algorithms are discussed and the parallel performance is presented, using OpenMP. More >

Hossein M. Shodja^1,2,3, Alireza Hashemian^1,4

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.1, pp. 17-34, 2008, DOI:10.3970/cmes.2008.032.017

Abstract Gradient reproducing kernel particle method (GRKPM) is a meshless technique which incorporates the first gradients of the function into the reproducing equation of RKPM. Therefore, in two-dimensional space GRKPM introduces three types of shape functions rather than one. The robustness of GRKPM's shape functions is established by reconstruction of a third-order polynomial. To enforce the essential boundary conditions (EBCs), GRKPM's shape functions are modified by transformation technique. By utilizing the modified shape functions, the weak form of the nonlinear evolutionary Buckley-Leverett (BL) equation is discretized in space, rendering a system of nonlinear ordinary differential equations (ODEs). Subsequently, Gear's method is… More >

Chein-Shan Liu¹, Chih-Wen Chang², Jiang-Ren Chang^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.1, pp. 1-16, 2008, DOI:10.3970/cmes.2008.032.001

Abstract In this paper, we propose a new method to tackle of two famous boundary layer equations in fluid mechanics, namely, the Falkner-Skan and the Blasius equations. We can employ this method to find unknown initial conditions. The pivotal point is based on the erection of a one-step Lie group element$\mathbf {G}(T)$ and the formation of a generalized mid-point Lie group element$\mathbf {G}(r)$. Then, by imposing$\mathbf {G}(T) = \mathbf {G}(r)$ we can seek the missing initial conditions through a minimum discrepancy from the target in terms of a weighting factor$r \in (0, 1)$. Numerical examples are worked out to persuade that… More >

Y.Y Zhang, L. Chen

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.3, pp. 189-200, 2008, DOI:10.3970/cmes.2008.031.189

Abstract A simplified meshless method for dynamic crack growth is presented. The method uses an extrinsic enrichment based on a local partition of unity concept. The crack is represented by a set of crack segments. The crack segments are required to pass through the entire domain of influence of node. They are introduced when the maximum principal stress exceeds the uniaxial tensile strength. The crack segments are allowed to rotate in order to avoid too stiff system responses. The major advantage of our method is that it does not require algorithms to track the crack path. More >

L. Mai-Cao¹, T. Tran-Cong²

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.3, pp. 157-188, 2008, DOI:10.3970/cmes.2008.031.157

Abstract This paper presents a new meshless numerical approach to solving a special class of moving interface problems known as the passive transport where an ambient flow characterized by its velocity field causes the interfaces to move and deform without any influences back on the flow. In the present approach, the moving interface is captured by the level set method at all time as the zero contour of a smooth function known as the level set function whereas one of the two new meshless schemes, namely the SL-IRBFN based on the semi-Lagrangian method and the Taylor-IRBFN scheme based on Taylor series… More >

Y. H. Liu^1,2, S. S. Chen¹, J. Li¹, Z. Z. Cen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.3, pp. 145-156, 2008, DOI:10.3970/cmes.2008.031.145

Abstract A novel meshless method for structural dynamic analysis is presented and discussed in this paper. It is called meshless local natural neighbour interpolation (MLNNI) method, which uses a meshless spatial approximation based only on nodes. The MLNNI is derived from the generalized meshless local Petrov-Galerkin (MLPG) method as a special case. Local weak forms are developed using weighted residual method locally from the dynamic partial differential equation. In the construction of trial functions, the natural neighbour interpolation (NNI) is employed to simplify the treatment of the essential boundary conditions. The domain integration is evaluated over included Delaunay triangles in each… More >

L. Codecasa¹, R. Specogna², F. Trevisan³

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.3, pp. 129-144, 2008, DOI:10.3970/cmes.2008.031.129

Abstract In the paper we introduce a methodology to construct discrete constitutive matrices relating magnetic fluxes with magneto motive forces (reluctance matrix) and electro motive forces with currents (conductance matrix) needed for discretizing eddy current problems over hexahedral primal grids by means of the Finite Integration Technique (FIT) and the Cell Method (CM). We prove that, unlike the mass matrices of Finite Elements, the proposed matrices ensure both the stability and the consistency of the discrete equations introduced in FIT and CM. More >

M. Steffen¹, P.C. Wallstedt², J.E. Guilkey^2,3, R.M. Kirby¹, M. Berzins¹

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.2, pp. 107-128, 2008, DOI:10.3970/cmes.2008.031.107

Abstract The Material Point Method (MPM) has shown itself to be a powerful tool in the simulation of large deformation problems, especially those involving complex geometries and contact where typical finite element type methods frequently fail. While these large complex problems lead to some impressive simulations and solutions, there has been a lack of basic analysis characterizing the errors present in the method, even on the simplest of problems. The large number of choices one has when implementing the method, such as the choice of basis functions and boundary treatments, further complicates this error analysis.\newline In this paper we explore some… More >

O. Buzzi¹, D. M. Pedroso², A. Giacomini¹

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.2, pp. 85-106, 2008, DOI:10.3970/cmes.2008.031.085

Abstract The material point method (MPM) is a numerical method for the solution of problems in continuum mechanics, including situations of large deformations. A generalization (GMPM) of this method was introduced by Bardenhagen and Kober (2004) in order to avoid some computational instabilities inherent to the original method (MPM). This generalization leads to a method more akin of the Petrov-Galerkin procedure. Although it is possible to find in the literature examples of the deduction and applications of the MPM/GMPM to specific problems, its detailed implementation is yet to be presented. Therefore, this paper attempts to describe all steps required for the… More >