Meshless Methods and Partition of Unity Finite Elements
نویسنده
چکیده
In this paper, meshless methods and partition of unity based finite element methods are reviewed. In meshless methods, the approximation is built without the explicit connectivity information between the nodes; moving-least squares approximants and natural neighbor-based interpolants are discussed. The enrichment of the finite element approximation through the partition of unity framework is described, and recent advances in crack modeling are summarized.
منابع مشابه
The generalized product partition of unity for the meshless methods
The partition of unity is an essential ingredient for meshless methods named by GFEM, PUFEM (partition of unity FEM), XFEM(extended FEM), RKPM(reproducing kernel particle method), RPPM(reproducing polynomial particle method), the method of clouds in the literature. There are two popular choices for partition of unity: a piecewise linear FEM mesh and the Shepard-type partition of unity. However,...
متن کاملThe Partition of Unity Finite Element Approach to the Stationary Fokker-Planck Equation
The stationary Fokker-Planck Equation (FPE) is solved for nonlinear dynamic systems using a local numerical technique based on the meshless Partition of Unity Finite Element Method (PUFEM). The method is applied to the FPE for two-dimensional dynamical systems, and argued to be an excellent candidate for higher dimensional systems and the transient problem. Variations of the conventional PUFEM ...
متن کاملThe Generalized Finite Element Method - Improving Finite Elements Through Meshless Technology
The Generalized Finite Element Method (GFEM) presented in this paper combines and extends the best features of the finite element method with the help of meshless formulations based on the Partition of Unity Method. Although an input finite element mesh is used by the proposed method, the requirements on the quality of this mesh are significantly relaxed. The main technique presented in this pa...
متن کاملProposing the Frequency Dependent Shape Functions for Meshless Method in Electromagnetics
The root of this study, comes from the lack of regularity where exists in shape function selection in direct meshless methods. In this work, we are going to establish a technique which is based on both analytical and simulated results; helps select a well-behaved shape function for which the shape parameters have been predetermined. This work has been focused on wave equation as the most import...
متن کاملAn efficient linear-precision partition of unity basis for unstructured meshless methods
We describe an approach to construct approximation basis functions for meshless methods, which is based on the concept of a partition of unity. The approach has the following properties: (i) the grid consists of scattered nodes, (ii) the basis reproduces exactly complete linear polynomials, (iii) only the values of the approximated function at the nodes are used as unknowns, (iv) the constructi...
متن کامل