Maxwellʹs Equations for Structures with Symmetries

Maxwellʹs equations for structures with arbitrary point symmetry groups are considered. It is shown that an initial boundary value problem for Maxwellʹs equations in a domain Ω can be reduced to ∼N independent problems in a 1/N part of the initial domain, where N is the order of the symmetry group of the domain Ω. This approach allows the developing of effective methods for the numerical solution of problems for structures with symmetries on the basis of any existing numerical algorithm. As virtually all numerical approaches have a more than linear dependence on the computational effort from the dimension of the problem, the approach of solving ∼N problems of size ∼1/N will result in more-efficient procedures.