Fokas Method and Kelvin transformation applied to potential problems in non convex unbounded domains

Show simple item record Hadjinicolaou, Maria 2014-10-11T08:57:49Z 2014-10-11T08:57:49Z 2014-09-02
dc.identifier.isbn 978-960-8475-22-9
dc.description The author gratefully acknowledges the contribution of the “ARISTEIA” Action of the “OPERATIONAL PROGRAMME EDUCATION AND LIFELONG LEARNING”, co-funded by the European Social Fund (ESF) and National Resources Resources. en_US
dc.description.abstract Fokas integral method combined with Kelvin transformation develop/acquire a new method for solving Dirichlet or Neumann problems in non-convex unbounded domains. On the one hand, a key aspect in Fokas method is the coupling of all boundary values in one equation, called “global relation”. Through this, the missing type of data on a boundary value problem can be derived, as Dassios and Fokas have shown. On the other hand, Kelvin transformation preserves har- monicity, and thus, its application to an interior potential problem, provides the solution of the equivalent exterior one, in the domain which is the Kelvin image of the original interior one and vice versa. These two methods have been employed by Baganis and Hadjinicolaou in order to derive integral representations for the Dirichlet and the Neumann problem respectively, in a non-convex domain which is the Kelvin image of an equilateral triangle. The outline of the proposed methodology and the derivation of the corresponding analytical results is the subject of this presentation. Discussion for the generalization of the method is also included. en_US
dc.description.sponsorship ESF - ARISTEIA en_US
dc.language.iso en en_US
dc.publisher AMCL/TUC en_US
dc.subject Fokas Method en_US
dc.subject Kelvin inversion en_US
dc.subject potential probles en_US
dc.subject equilateral triangle en_US
dc.subject non covex domain en_US
dc.title Fokas Method and Kelvin transformation applied to potential problems in non convex unbounded domains en_US
dc.type Article en_US

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  • NumAn2014 Proceedings
    Proceedings of the 6th International Conference on Numerical Analysis (NumAn2014)

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