dc.contributor |
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III |
dc.contributor |
Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
dc.contributor.author |
Arroyo Balaguer, Marino |
dc.contributor.author |
Ortiz, Michael |
dc.date |
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.citation |
0029-5981 |
dc.identifier.uri |
http://hdl.handle.net/2117/8208 |
dc.language.iso |
eng |
dc.publisher |
Wiley and Sons |
dc.rights |
info:eu-repo/semantics/openAccess |
dc.subject |
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits |
dc.subject |
Maximum entropy method |
dc.subject |
Maximum entropy |
dc.subject |
Information theory |
dc.subject |
Approximation theory |
dc.subject |
Meshfree methods |
dc.subject |
Delaunay triangulation |
dc.subject |
Entropia |
dc.title |
Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods |
dc.type |
info:eu-repo/semantics/submittedVersion |
dc.type |
info:eu-repo/semantics/article |
dc.description.abstract |
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.description.abstract |
Peer Reviewed |