A modified Lanczos reduction method for the computation of transient wavefields

A standard method for computing a transient wavefield in an inhomogeneous medium is the finite difference time domain (FDTD) method. Because of stability reasons, the time step in this method can not be chosen too large and as a consequence the FDTD method is a very time consuming process. Druskin and Knizhnerman (see Radio Science, vol.29, p.937-53, 1994) have shown that for electromagnetic diffusion problems (neglecting the displacement current) a much more efficient approach is possible by employing the method of Lanczos. This so-called SLDM method constructs a reduced-model that approximates the diffusive field problem very accurately within a given bounded time interval. Their approach is based on a second-order differential equation for either the electric or magnetic field strength. We present a method based on the full Maxwell wave equations as a system of first-order partial differential equations. By exploiting the specific structure of these equations, we are able to devise a Lanczos type algorithm, yielding a very efficient solution method for transient wavefields.