A generalized Ritz method for partial differential equations in domains of arbitrary geometry using global shape functions

Katsikadelis, JT

dc.contributor.author	Katsikadelis, JT	en
dc.date.accessioned	2014-03-01T01:27:41Z
dc.date.available	2014-03-01T01:27:41Z
dc.date.issued	2008	en
dc.identifier.issn	0955-7997	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18536
dc.subject	boundary element method	en
dc.subject	partial differential equations	en
dc.subject	meshless	en
dc.subject	analog equation	en
dc.subject	Ritz method	en
dc.subject	variational	en
dc.subject	optimal rnultiquadrics	en
dc.subject	global shape functions	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.title	A generalized Ritz method for partial differential equations in domains of arbitrary geometry using global shape functions	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.enganabound.2007.09.001	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.enganabound.2007.09.001	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	A boundary element method (BEM)-based variational method is presented for the solution of elliptic PDEs describing the mechanical response of general inhomogeneous anisotropic bodies of arbitrary geometry. The equations, which in general have variable coefficients, may be linear or nonlinear. Using the concept of the analog equation of Katsikadelis the original equation is converted into a linear membrane (Poisson) or a linear plate (biharmonic) equation, depending on the order of the PDE under a fictitious load, which is approximated with radial basis function series of multiquadric (MQ) type. The integral representation of the solution of the substitute equation yields shape functions, which are global and satisfy both essential and natural boundary conditions, hence the name generalized Ritz method. The minimization of the functional that produces the PDE as the associated Euler-Lagrange equation yields not only the Ritz coefficients but also permits the evaluation of optimal values for the shape parameters of the MQs as well as optimal position of their centers, minimizing thus the error. If a functional does not exists or cannot be constructed as it is the usual case of nonlinear PDEs, the Galerkin principle can be applied. Since the arising domain integrals are converted into boundary line integrals, the method is boundary-only and, therefore, it maintains all the advantages of the pure BEM. Example problems are studied, which illustrate the method and demonstrate its efficiency and great accuracy. (C) 2007 Elsevier Ltd. All rights reserved.	en
heal.publisher	ELSEVIER SCI LTD	en
heal.journalName	ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS	en
dc.identifier.doi	10.1016/j.enganabound.2007.09.001	en
dc.identifier.isi	ISI:000256536000001	en
dc.identifier.volume	32	en
dc.identifier.issue	5	en
dc.identifier.spage	353	en
dc.identifier.epage	367	en