Adaptive wavelet collocation method for simulation of a 2D micro-ring resonator

In this paper, we use adaptive wavelet collocation method (AWCM) to solve the 2D time domain Maxwell's equations. Our motivation of choosing AWCM is because it effectively adapts numerical grid points along moving signals according to the requirements of resolution levels of them. In the region where moving signals are intensive, there will be assigned more grid points; and in the region where signals are sparse, there will be arranged less grid points. Since signals are moving during time stepping, the grid changes dynamically at each time step. We verified that AWCM is an efficient method especially for problems in which signals are highly concentrated inside and guided through optical waveguides such as micro-ring resonators.