Adaptive Wavelet Collocation Method for Simulation of Time Dependent   Maxwell's Equations
  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. 
Haojun Li, Kirankumar R. Hiremath, Andreas Rieder, and Wolfgang Freude
math.NA math-ph math.MP physics.comp-ph physics.optics