Meshless Methods and Partition of Unity Finite Elements
نویسندگان
چکیده
منابع مشابه
Meshless Methods and Partition of Unity Finite Elements
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 de...
متن کاملThe 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,...
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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 کاملParticle–partition of Unity Methods in Elasticity
The particle–partition of unity method (PUM) [1, 2, 3, 4, 5, 8] is a meshfree Galerkin method for the numerical treatment of partial differential equations (PDE). In essence, it is a generalized finite element method (GFEM) which employs piecewise rational shape functions rather than piecewise polynomial functions. The PUM shape functions, however, make up a basis of the discrete function space...
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ژورنال
عنوان ژورنال: International Journal of Forming Processes
سال: 2005
ISSN: 1292-7775
DOI: 10.3166/ijfp.8.409-427