The authors discuss in this chapter approaches that can significantly reduce the memory storage associated with the AVM method. We show that the methods of spatial and spectral sampling can be applied to make the AVM approach more efficient. The authors also discuss how the AVM approach can be implemented using numerical techniques other than the FDTD method. The authors discuss how the approach applies to the transmission line modeling (TLM) method. The TLM method is another time domain technique that can be shown to be related to the FDTD. The authors also briefly discuss how the AVM technique can be applied using frequency domain solvers such as the finite element method (FEM) and the method of moments (MoM). The authors conclude this chapter by briefly illustrating some applications of adjoint sensitivity analysis.