In this study, a cellular automaton (CA) is developed o combine the advantages of finite element method (FEM) and meshless method to analyze two-dimensional elastic problems. By the CA, a two-dimensional domain is discretized into a grid of nodes which are distributed randomly in the domain. For convenience, the nodes are classified into the FEM group and the meshless group. In the FEM zone tha...

The Natural Element Method (NEM) is a meshless Galerkin method which has shown promise in the area of computational mechanics. In earlier applications of NEM [1–3], natural neighbor (Sibson) coordinates [4] were used to construct the trial and test functions. Recently, Belikov and co-workers [5] proposed a new interpolation scheme (non-Sibsonian interpolation) based on natural neighbors. In thi...

in this paper, we propose a new numerical method for solution of urysohn two dimensional mixed volterra-fredholm integral equations of the second kind on a non-rectangular domain. the method approximates the solution by the discrete collocation method based on inverse multiquadric radialbasis functions (rbfs) constructed on a set of disordered data. the method is a meshless method, because it i...

In this paper, the meshless local Petrov-Galerkin (MLPG) method is applied for solving a generalized Black-Scholes equation in financial problems. This equation is a PDE governing the price evolution of a European call or a European put under the Black-Scholes model. The θ-weighted method and MLPG are used for discretizing the governing equation in time variable and option pricing, respectively...

In the theoretical part of this paper, we introduce a simplified proof technique for error bounds and convergence of a variation of E. Kansa’s well-known unsymmetric meshless collocation method. For a numerical implementation of the convergent variation, a previously proposed greedy technique is coupled with linear optimization. This algorithm allows a fully adaptive on-the-fly data-dependent m...

The optimal incremental function approximation method is implemented for the adaptive and meshless solution of differential equations. The basis functions and associated coefficients of a series expansion representing the solution are selected optimally at each step of the algorithm according to appropriate error minimization criteria. Thus, the solution is built incrementally. In this manner, ...

A meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n, and the condition that the shape functions depend only on the node positions. Furthermore, the method proposed also shares several of the advantages of the Finite Element Method such as: (a) the simplicity of the shape functi...

In this paper, we articulate a meshless computational paradigm for the effective modeling, accurate physical simulation, and real-time animation of point-sampled solid objects. Both the interior and the boundary geometry of our volumetric object representation only consist of points, further extending the powerful and popular method of point-sampled surfaces to the volumetric setting. We build ...

A local symmetric weak form (LSWF) for linear potential problems is developed, and a truly meshless method, based on the LSWF and the moving least squares approximation, is presented for solving potential problems with high accuracy. The essential boundary conditions in the present formulation are imposed by a penalty method. The present method does not need a ``®nite element mesh'', either for...