The meshless analog equation method: A new highly accurate truly mesh-free method for solving partial differential equations

Katsikadelis, JT

dc.contributor.author	Katsikadelis, JT	en
dc.date.accessioned	2014-03-01T02:50:54Z
dc.date.available	2014-03-01T02:50:54Z
dc.date.issued	2006	en
dc.identifier.issn	1743355X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/35199
dc.subject.other	Integration	en
dc.subject.other	Linear equations	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Mesh generation	en
dc.subject.other	Optimal systems	en
dc.subject.other	Problem solving	en
dc.subject.other	Analog equation	en
dc.subject.other	Expansion coefficients	en
dc.subject.other	Meshless analog equation method (MAEM)	en
dc.subject.other	Nodal points	en
dc.subject.other	Partial differential equations	en
dc.title	The meshless analog equation method: A new highly accurate truly mesh-free method for solving partial differential equations	en
heal.type	conferenceItem	en
heal.identifier.primary	10.2495/BE06002	en
heal.identifier.secondary	http://dx.doi.org/10.2495/BE06002	en
heal.publicationDate	2006	en
heal.abstract	A new purely meshless method to solve PDEs is presented. The method is based on the concept 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 MQ-RBFS. Integration of the analog equation allows the approximation of the sought solution by new RBFs. Then inserting the solution into the PDE and BCs and collocating at the mesh-free nodal points yields a system of linear equations, which permit the evaluation of the expansion coefficients. The method exhibits key advantages of over other RBF collocation methods as it is highly accurate and the matrix of the resulting linear equations is always invertible. The accuracy is increased using optimal values of the shape parameters of the multiquadrics by minimizing the potential that produces the PDE. Without restricting its generality, the method is illustrated by applying it to the general second order elliptic PDE. The studied examples demonstrate the efficiency and high accuracy of the developed method.	en
heal.journalName	WIT Transactions on Modelling and Simulation	en
dc.identifier.doi	10.2495/BE06002	en
dc.identifier.volume	42	en
dc.identifier.spage	13	en
dc.identifier.epage	22	en