Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 01, pp. 1-20.

Title: Solutions of boundary-value problems in discretized volumes
   
Authors: Mihaly Makai (Atomic Energy Research Inst., Budapest, Hungary)
         Yuri Orechwa (Nuclear Regulatory Commission, Washington, USA )

Abstract:  
  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