Computation of 2.5-dimensional static fields in uniaxial anisotropic media

We apply the reduced-order modeling technique to so-called 2.5-dimensional static field problems. The configuration in such a problem consists of media that are two-dimensional, while the sources that generate the field are three-dimensional. Starting with a second-order differential equation for the potential, Allers et al., (1994), have shown that 2.5-dimensional problems are efficiently solved by the spectral Lanczos decomposition method. We propose to work with the full first-order system of equations and we consider uniaxial anisotropic media as well. The main reason for including this type of anisotropy is that for a specific choice of the diagonal elements of the resistivity tensor we can properly simulate regions of unbounded extent. We give a simple numerical example that illustrates this point.