The meshless analog equation method: I. Solution of elliptic partial differential equations

Katsikadelis, JT

dc.contributor.author	Katsikadelis, JT	en
dc.date.accessioned	2014-03-01T02:46:33Z
dc.date.available	2014-03-01T02:46:33Z
dc.date.issued	2009	en
dc.identifier.issn	0939-1533	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/32708
dc.subject	Analog equation method	en
dc.subject	Elliptic partial differential equations	en
dc.subject	Meshless method	en
dc.subject	Radial basis functions	en
dc.subject.classification	Mechanics	en
dc.subject.other	Analog equation	en
dc.subject.other	Analog equation method	en
dc.subject.other	Analog equation methods	en
dc.subject.other	Approximate solution	en
dc.subject.other	Coefficient matrix	en
dc.subject.other	Elliptic partial differential equation	en
dc.subject.other	Elliptic partial differential equations	en
dc.subject.other	Elliptic PDEs	en
dc.subject.other	Expansion coefficients	en
dc.subject.other	Fictitious sources	en
dc.subject.other	Integration constants	en
dc.subject.other	Mesh-less methods	en
dc.subject.other	Meshfree	en
dc.subject.other	Meshless	en
dc.subject.other	Meshless method	en
dc.subject.other	Multiquadric radial basis function	en
dc.subject.other	Multiquadrics	en
dc.subject.other	Nodal points	en
dc.subject.other	Optimal values	en
dc.subject.other	Radial basis functions	en
dc.subject.other	RBF collocation method	en
dc.subject.other	Second orders	en
dc.subject.other	Shape parameters	en
dc.subject.other	System of linear equations	en
dc.subject.other	Aircraft engines	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Computational fluid dynamics	en
dc.subject.other	Geometry	en
dc.subject.other	Image segmentation	en
dc.subject.other	Radial basis function networks	en
dc.subject.other	Three dimensional	en
dc.subject.other	Partial differential equations	en
dc.title	The meshless analog equation method: I. Solution of elliptic partial differential equations	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1007/s00419-008-0294-6	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00419-008-0294-6	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	A new purely meshless method for solving elliptic partial differential equations (PDEs) is presented. The method is based on the principle of the analog equation of Katsikadelis, hence its name meshless analog equation method (MAEM), which converts the original equation into a simple solvable substitute one of the same order under a fictitious source. The fictitious source is represented by multiquadric radial basis functions (MQ-RBFs). The integration of the analog equation yields new RBFs, which are used to approximate the sought solution. Then inserting the approximate solution into the PDE and boundary conditions (BCs) and collocating at the mesh-free nodal points results in a system of linear equations, which permit the evaluation of the expansion coefficients of the RBFs series. The method exhibits key advantages over other RBF collocation methods as it is highly accurate and the coefficient matrix of the resulting linear equations is always invertible. The accuracy is achieved using optimal values for the shape parameters and the centers of the multiquadrics as well as of the integration constants of the analog equation, which are obtained by minimizing the functional that produces the PDE. Without restricting its generality, the method is illustrated by applying it to the general second order 2D and 3D elliptic PDEs. The studied examples demonstrate the efficiency and high accuracy of the developed method. © 2008 Springer-Verlag.	en
heal.publisher	SPRINGER	en
heal.journalName	Archive of Applied Mechanics	en
dc.identifier.doi	10.1007/s00419-008-0294-6	en
dc.identifier.isi	ISI:000266260400008	en
dc.identifier.volume	79	en
dc.identifier.issue	6-7	en
dc.identifier.spage	557	en
dc.identifier.epage	578	en