Geodesic
Boundary element collocation method for solving the exterior Neumann problem for Helmholtz's equation in three dimensions
Electronic transactions on numerical analysis, Tome 39 (2012), pp. 113-143
We describe a boundary integral equation that solves the exterior Neumann problem for the Helmholtz equation in three dimensions. The unique solution is found by approximating a Fredholm integral equation of the second kind with the boundary element collocation method. We prove superconvergence at the collocation points, distinguishing the cases of even and odd interpolation. Numerical examples demonstrate the performance of the method solving the integral equation and confirm the superconvergence.
Classification : 35J05, 45B05, 65N35, 65N38
Keywords: Fredholm integral equation of the second kind, Helmholtz's equation, exterior Neumann problem, boundary element collocation method, superconvergence 
@article{ETNA_2012__39__a18,
     author = {Kleefeld,  Andreas and Lin,  Tzu-Chu},
     title = {Boundary element collocation method for solving the exterior {Neumann} problem for {Helmholtz's} equation in three dimensions},
     journal = {Electronic transactions on numerical analysis},
     pages = {113--143},
     year = {2012},
     volume = {39},
     zbl = {1288.35205},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2012__39__a18/}
}
TY  - JOUR
AU  - Kleefeld,  Andreas
AU  - Lin,  Tzu-Chu
TI  - Boundary element collocation method for solving the exterior Neumann problem for Helmholtz's equation in three dimensions
JO  - Electronic transactions on numerical analysis
PY  - 2012
SP  - 113
EP  - 143
VL  - 39
UR  - http://geodesic.mathdoc.fr/item/ETNA_2012__39__a18/
LA  - en
ID  - ETNA_2012__39__a18
ER  - 
%0 Journal Article
%A Kleefeld,  Andreas
%A Lin,  Tzu-Chu
%T Boundary element collocation method for solving the exterior Neumann problem for Helmholtz's equation in three dimensions
%J Electronic transactions on numerical analysis
%D 2012
%P 113-143
%V 39
%U http://geodesic.mathdoc.fr/item/ETNA_2012__39__a18/
%G en
%F ETNA_2012__39__a18
Kleefeld,  Andreas; Lin,  Tzu-Chu. Boundary element collocation method for solving the exterior Neumann problem for Helmholtz's equation in three dimensions. Electronic transactions on numerical analysis, Tome 39 (2012), pp. 113-143. http://geodesic.mathdoc.fr/item/ETNA_2012__39__a18/