A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain

A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain

A recently discovered transform approach allows a large class of PDEs to be solved in terms of boundary and/or contour integrals. We introduce here a spectrally accurate numerical discretization of this approach for the case of Laplace's equation on a polygonal domain, and compare it against an...

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Veröffentlicht in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2011-10, Vol.467 (2134), p.2983-3003
Hauptverfasser: Fornberg, Bengt, Flyer, Natasha
Format: Artikel
Sprache:eng
Schlagworte:
Boundary Integral Method
Boundary value problems
Coefficients
Dirichlet-To-Neumann Map
Error rates
Fokas Transform Method
Global Equations
Laplace Equation
Linear systems
Mathematical functions
Mathematical integrals
Polygonal Domain
Textual collocation
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Beschreibung
Zusammenfassung:A recently discovered transform approach allows a large class of PDEs to be solved in terms of boundary and/or contour integrals. We introduce here a spectrally accurate numerical discretization of this approach for the case of Laplace's equation on a polygonal domain, and compare it against an also spectrally accurate implementation of the traditional boundary integral formulation.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2011.0032