ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
A rigorous approach is discussed for solving the two-dimensional Helmholtz equation in a multiply-connected domain consisting of a ring of N circles distributed symmetrically within a closed space. The outer boundary has been taken to be such that the system as a whole has N-fold rotational symmetry. The Dirichlet boundary condition has been satisfied exactly at the outer as well as at each of the inner edges, using the addition theorems for the cylindrical Bessel functions in conjugation with the Fourier expansions. Numerical results, showing spatial configurational interference, are presented for the lowest cutoff value of the symmetric mode as a function of separation between centers of two inner circles, in the case N=2 with circular outer boundary. The application of the method to various problems of physics and engineering is enunciated.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.528405
