Electromagnetic Scattering From a Rough Layer: Propagation-Inside-Layer Expansion Method Combined to the Forward-Backward Novel Spectral Acceleration

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, an efficient method is developed to calculate the bistatic cross section (BSC) from a stack of two one-dimensional rough interfaces separating homogeneous media. The PILE (propagation-inside-layer expansion) method recently developed by DÉchamps <etal/> was efficient with a complexity <formula formulatype="inline"><tex>${\cal O}(N^2)$</tex></formula> (<formula formulatype="inline"> <tex>$N$</tex></formula> being the number of samples per interface). To reduce this complexity, a fast method valid for a single rough surface, the forward-backward with novel spectral acceleration (FBNSA) is combined to the PILE method. Furthermore, the calculation of the coupling interactions between both interfaces are also accelerated using the NSA. The PILE-FBNSA method reaches then a complexity of only <formula formulatype="inline"><tex>${\cal O}(N)$</tex></formula>. A study of the convergence of the PILE is done and compared to the FBNSA of Moss <etal/> </para>