Geodesic
Solutions of boundary-value problems in discretized volumes
Electronic Journal of Differential Equations, Tome 2002 (2002).

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

Summary: The solution of a boundary-value problem in a volume discretized by finitely many copies of a tile is obtained via a Green's function. The algorithm for constructing the solution exploits results from graph and group theory. This technique produces integral equations on the internal and external boundaries of the volume and demonstrates that two permutation matrices characterize the symmetries of the volume. We determine the number of linearly independent solutions required over the tile and the conditions needed for two boundary-value problems to be isospectral. Our method applies group theoretical considerations to asymmetric volumes.
Classification : 35B99, 20F29
Keywords: boundary value problem, covering group 
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     author = {Makai, Mih\'aly and Orechwa, Yuri},
     title = {Solutions of boundary-value problems in discretized volumes},
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     volume = {2002},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a74/}
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Makai, Mihály; Orechwa, Yuri. Solutions of boundary-value problems in discretized volumes. Electronic Journal of Differential Equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a74/