New wavelet based approach for time domain simulations

A new numerical method for the time domain solution of Maxwell's equations in linear media is proposed in this paper. The field quantities derived from the spatial discretization of Maxwell's equations are expanded in the time domain by wavelets on the interval. This choice yields a new arrangement of the unknowns into a matrix (instead of the usual vector) and transforms the differential equations in time in a Sylvester matrix equation. The memory requirements are proportional to the number of spatial unknowns and the time evolution of the space quantities is obtained with better accuracy than in conventional marching-on-time techniques.