A time-domain differential solver for electromagnetic scattering problems

The authors´ objective is to extend computational fluid dynamics (CFD) based upwind schemes to solve numerically the Maxwell equations for scattering from objects with layered non-metallic sections. After a discussion on the character of the Maxwell equations it is shown that they represent a linearly degenerate set of hyperbolic equations. To show the feasibility of applying CFD-based algorithms, first the transverse magnetic (TM) and the transverse electric (TE) waveforms of the Maxwell equations are considered. A finite-volume scheme is developed with appropriate representations for the electric and magnetic fluxes at a cell interface, accounting for variations in material properties in both space and time. This process involves a characteristic subpath integration known as the `Riemann solver´. An explicit-Lax-Wendroff upwind scheme, which is second-order accurate in both space and time, is employed to solve the TM and TE equations. A body-fitted coordinate transformation is introduced to treat arbitrary cross-sectioned bodies with computational grids generated using an elliptic grid solver procedure. For treatment of layered media, a multizonal representation is employed satisfying appropriate zonal boundary conditions in terms of flux conservation. The computational solution extending from the object to a far-field boundary located a few wavelengths away constitutes the near-field solution. A Green´s function based near-field-to-far-field transformation is employed to obtain the bistatic radar cross section (RCS) information