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Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods
dc.contributor.author | Arroyo Balaguer, Marino |
dc.contributor.author | Ortiz, Michael |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III |
dc.date.accessioned | 2010-07-16T10:49:34Z |
dc.date.available | 2010-07-16T10:49:34Z |
dc.date.created | 2006-03 |
dc.date.issued | 2006-03 |
dc.identifier.citation | Arroyo, M.; Ortiz, M. Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods. "International journal for numerical methods in engineering", Març 2006, vol. 65, núm. 13, p. 2167-2202. |
dc.identifier.issn | 0029-5981 |
dc.identifier.uri | http://hdl.handle.net/2117/8208 |
dc.description | This is the pre-peer reviewed version of the following article: Arroyo, M.; Ortiz, M. Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods. "International journal for numerical methods in engineering", Març 2006, vol. 65, núm. 13, p. 2167-2202, which has been published in final form at http://www3.interscience.wiley.com/journal/112159842/abstract |
dc.description.abstract | We present a one-parameter family of approximation schemes, which we refer to as local maximum-entropy approximation schemes, that bridges continuously two important limits: Delaunay triangulation and maximum-entropy (max-ent) statistical inference. Local max-ent approximation schemes represent a compromise - in the sense of Pareto optimality - between the competing objectives of unbiased statistical inference from the nodal data and the definition of local shape functions of least width. Local max-ent approximation schemes are entirely defined by the node set and the domain of analysis, and the shape functions are positive, interpolate affine functions exactly, and have a weak Kronecker-delta property at the boundary. Local max-ent approximation may be regarded as a regularization, or thermalization, of Delaunay triangulation which effectively resolves the degenerate cases resulting from the lack or uniqueness of the triangulation. Local max-ent approximation schemes can be taken as a convenient basis for the numerical solution of PDEs in the style of meshfree Galerkin methods. In test cases characterized by smooth solutions we find that the accuracy of local max-ent approximation schemes is vastly superior to that of finite elements. |
dc.format.extent | 36 p. |
dc.language.iso | eng |
dc.publisher | Wiley and Sons |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits |
dc.subject.lcsh | Maximum entropy method |
dc.subject.other | Maximum entropy |
dc.subject.other | Information theory |
dc.subject.other | Approximation theory |
dc.subject.other | Meshfree methods |
dc.subject.other | Delaunay triangulation |
dc.title | Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods |
dc.type | Article |
dc.subject.lemac | Entropia |
dc.contributor.group | Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1534 |
dc.rights.access | Open Access |
local.identifier.drac | 799396 |
dc.description.version | Postprint (author’s final draft) |
local.citation.author | Arroyo, M.; Ortiz, M. |
local.citation.publicationName | International journal for numerical methods in engineering |
local.citation.volume | 65 |
local.citation.number | 13 |
local.citation.startingPage | 2167 |
local.citation.endingPage | 2202 |
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