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.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {39},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2012__39__a18/}
}
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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/