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

被引：42
|
作者：
Fornberg, Bengt [2 ]
Flyer, Natasha [1 ]
机构：
[1] Natl Ctr Atmospher Res, Boulder, CO 80305 USA
[2] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA
来源：
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2011年 / 467卷 / 2134期
基金：
美国国家科学基金会;
关键词：
boundary integral method; global equations; Dirichlet-to-Neumann map; Laplace equation; Fokas transform method; polygonal domain; PARTIAL-DIFFERENTIAL-EQUATIONS; LINEAR ELLIPTIC PDES; TRANSFORM METHOD; SOLVING EVOLUTION; CONVEX POLYGON; ELEMENT-METHOD; SINGULARITIES; CORNER;
D O I：
10.1098/rspa.2011.0032
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
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.
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页码：2983 / 3003
页数：21
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