Electron. J. Diff. Eqns.,
Vol. 2002(2002), No. 01, pp. 120.
Solutions of boundaryvalue problems in discretized volumes
Mihaly Makai & Yuri Orechwa
Abstract:
The solution of a boundaryvalue 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 boundaryvalue problems to be isospectral.
Our method applies group theoretical considerations to asymmetric volumes.
Submitted June 1, 2001. Published January 2, 2002.
Math Subject Classifications: 35B99, 20F29
Key Words: boundary value problem, covering group, equispectral volumes
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Mihaly Makai
KFKI Atomic Energy Research Institute
H1525 Budapest 114, POB 49
Hungary
email: makai@sunserv.kfki.hu 

Yuri Orechwa
United States Nuclear Regulatory Commission
Washington DC, USA
email: yxo@nrc.gov 
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