An efficient linear-precision partition of unity basis for unstructured meshless methods
نویسندگان
چکیده
منابع مشابه
An 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...
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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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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...
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Meshfree radial basis function (RBF) methods are of interest for solving partial differential equations due to attractive convergence properties, flexibility with respect to geometry, and ease of implementation. For global RBF methods, the computational cost grows rapidly with dimension and problem size, so localised approaches, such as partition of unity or stencil based RBF methods, are curre...
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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: Communications in Numerical Methods in Engineering
سال: 2000
ISSN: 1069-8299,1099-0887
DOI: 10.1002/(sici)1099-0887(200004)16:4<239::aid-cnm322>3.0.co;2-w