Electron. J. Diff. Eqns., Vol. 2002(2002), No. 01, pp. 1-20.

Solutions of boundary-value problems in discretized volumes

Mihaly Makai & Yuri Orechwa

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.

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
H-1525 Budapest 114, POB 49
e-mail: makai@sunserv.kfki.hu
  Yuri Orechwa
United States Nuclear Regulatory Commission
Washington DC, USA
e-mail: yxo@nrc.gov

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