Geodesic
Quadrature of singular integrands over surfaces
Electronic transactions on numerical analysis, Tome 17 (2004), pp. 133-150
Consider integration over a simple closed smooth surface in , one that is homeomorphic to the $\textcent $###$\sterling $unit sphere, and suppose the integrand has a point singularity. We propose a numerical integration method based on using transformations that lead to an integration problem over the unit sphere with an integrand that is much smoother. At this point, the trapezoidal rule is applied to the spherical coordinate representation of the problem.
Classification : 65D32, 65B15
Keywords: spherical integration, singular integrand, boundary integral, trapezoidal rule 
@article{ETNA_2004__17__a6,
     author = {Atkinson,  Kendall},
     title = {Quadrature of singular integrands over surfaces},
     journal = {Electronic transactions on numerical analysis},
     pages = {133--150},
     year = {2004},
     volume = {17},
     zbl = {1065.65048},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2004__17__a6/}
}
TY  - JOUR
AU  - Atkinson,  Kendall
TI  - Quadrature of singular integrands over surfaces
JO  - Electronic transactions on numerical analysis
PY  - 2004
SP  - 133
EP  - 150
VL  - 17
UR  - http://geodesic.mathdoc.fr/item/ETNA_2004__17__a6/
LA  - en
ID  - ETNA_2004__17__a6
ER  - 
%0 Journal Article
%A Atkinson,  Kendall
%T Quadrature of singular integrands over surfaces
%J Electronic transactions on numerical analysis
%D 2004
%P 133-150
%V 17
%U http://geodesic.mathdoc.fr/item/ETNA_2004__17__a6/
%G en
%F ETNA_2004__17__a6
Atkinson,  Kendall. Quadrature of singular integrands over surfaces. Electronic transactions on numerical analysis, Tome 17 (2004), pp. 133-150. http://geodesic.mathdoc.fr/item/ETNA_2004__17__a6/