Solution of electromagnetic transients by wavelet expansion in the time domain

This paper presents a new numerical method far the solution of linear Maxwell's equations in the time domain avoiding the conventional time stepping techniques. The spatial unknowns derived from a conventional spatial discretization, ie, FEM (finite element method) or FD (finite difference), 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 an algebraic system of Lyapunov type for which memory requirements are nearly the same as that of the spatial unknowns and that gives the time evolution of the space quantities with better accuracy and lower CPU time resources than conventional stepping techniques.