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.<
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