This paper investigates an adaptive wavelet collocation time domain method
for the numerical solution of Maxwell's equations. In this method a
computational grid is dynamically adapted at each time step by using the
wavelet decomposition of the field at that time instant. In the regions where
the fields are highly localized, the method assigns more grid points; and in
the regions where the fields are sparse, there will be less grid points. On the
adapted grid, update schemes with high spatial order and explicit time stepping
are formulated. The method has high compression rate, which substantially
reduces the computational cost allowing efficient use of computational
resources. This adaptive wavelet collocation method is especially suitable for
simulation of guided-wave optical devices
