Construction of polygonal interpolants: a maximum entropy approach

By Natarajan Sukumar. 2004

307 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e89780b2512c6b64817c7fd797fa7b44e214e9ed

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In Civil and Structural Engineering

In Statistical and Nonlinear Physics

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Citations in the corpus

Polygon scaled boundary finite elements for crack propagation modelling (2012, methodology): “This method retains the attractive feature of the SBFEM in that it does not require any nodal enrichment or special integration techniques such as in [13–19, 21–25] and yet, still captures the singular stress field at the crack tip Compared with the polygon elements developed in [1–3, 21, 22], class”
A scaled boundary polygon formulation for elasto-plastic analyses (2014, methodology): “The shape functions of the polygon elements reported in [1, 2, 3, 4, 11, 12] are rational polynomials and require special integration techniques e.”
Consistent element‐free Galerkin method (2014, background): “Sukumar N. Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons.”
Meshfree Methods: Progress Made after 20 Years (2017, unknown): “…local radial point interpolation method (Liu and Gu 2001); (cid:129) LS: least squares; (cid:129) MaxEnt: maximum entropy (Arroyo and Ortiz 2006; Sukumar 2004); (cid:129) MFEM: meshless finite element method (Idelsohn et al. 2003f); (cid:129) MFS: method of finite spheres (De and Bathe 2000);…”
Meshless methods: A review and computer implementation aspects (2008, methodology): “The recent inception of the smoothed finite element method (SFEM) [108,110–112,125,126], regained interest in polygonal interpolation [127] and, in particular, the recent discovery of maximum entropy approximations [123,124] may help bringing some more flexibility to the XFEM.”
Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks (2021, methodology): “A related approach is the local maximum-entropy (max-ent) meshfree method [48] that yield compactly-supported basis functions of exponential form that constitute a partition-ofunity [49], possess linear completeness, and provide a smooth transition from Delaunay basis functions [50] to global maximu”
On the optimum support size in meshfree methods: A variational adaptivity approach with maximum‐entropy approximants (2010, background): “Recently, the informationtheoretic concept of maximum-entropy (max-ent) has been put forth to develop meshfree first-order and second-order approximants [6, 7], and polygonal approximants [8].”
An n-sided polygonal smoothed finite element method (nSFEM) for solid mechanics (2007, unknown): “[12–15], or the”
A displacement smoothing induced strain gradient stabilization for the meshfree Galerkin nodal integration method (2015, methodology): “Alternatively, several convex approximations were introduced [1,31] to simplify the essential boundary condition treatment in meshfree methods.”
Local maximum‐entropy approximation schemes: a seamless bridge between finite elements and meshfree methods (2006, methodology): “In recent independent work, maximum entropy methods have been used to construct barycentric co-ordinates for convex polyhedra, thus defining C0 approximants on polygonal tesselations [22].”