An implicit meshless scheme for the solution of transient non-linear Poisson-type equations

Handle URI:
http://hdl.handle.net/10754/562834
Title:
An implicit meshless scheme for the solution of transient non-linear Poisson-type equations
Authors:
Bourantas, Georgios; Burganos, Vasilis N.
Abstract:
A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.
KAUST Department:
Applied Mathematics and Computational Science Program; Biological and Environmental Sciences and Engineering (BESE) Division; Physical Sciences and Engineering (PSE) Division
Publisher:
Elsevier BV
Journal:
Engineering Analysis with Boundary Elements
Issue Date:
Jul-2013
DOI:
10.1016/j.enganabound.2013.04.003
Type:
Article
ISSN:
09557997
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division; Biological and Environmental Sciences and Engineering (BESE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBourantas, Georgiosen
dc.contributor.authorBurganos, Vasilis N.en
dc.date.accessioned2015-08-03T11:12:01Zen
dc.date.available2015-08-03T11:12:01Zen
dc.date.issued2013-07en
dc.identifier.issn09557997en
dc.identifier.doi10.1016/j.enganabound.2013.04.003en
dc.identifier.urihttp://hdl.handle.net/10754/562834en
dc.description.abstractA meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.en
dc.publisherElsevier BVen
dc.subjectKeywords Meshfree point collocation method MLS Nonlinear Poisson equation Linearization method Lagging coefficientsen
dc.titleAn implicit meshless scheme for the solution of transient non-linear Poisson-type equationsen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentBiological and Environmental Sciences and Engineering (BESE) Divisionen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalEngineering Analysis with Boundary Elementsen
dc.contributor.institutionInstitute of Chemical Engineering Sciences - Foundation for Research and Technology, Stadiou, Platani, Patras 26504, Greeceen
kaust.authorBourantas, Georgiosen
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