Fast Fourier Transform Multilevel Fast Multipole Algorithm in Rough Ocean Surface Scattering

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Abstract
In this article, the microwave backscattering from 3-D rough sea surfaces has been numerically studied. Due to the advantages of the memory and CPU savings of the rigorous multilevel fast multipole algorithm, it was employed to calculate the radar cross-section of the sea surface at large incident angles. Usually, the sea surface can be regarded as a planar scatterer comparing the roughness height with the domain; therefore, an algorithm, called the fast Fourier transform multilevel fast multipole algorithm, was applied in the calculation of this case for a nearly planar scatterer. The difference of the fast Fourier transform multilevel fast multipole algorithm is the use of fast Fourier transform for the translation operator, which can further reduce the computational memory and the CPU time compared with the common multilevel fast multipole algorithm. In the calculation, the Thorsos window and Gaussian window were used in the azimuthal and range direction, respectively, to suppress the edge effects. This fast Fourier transform multilevel fast multipole algorithm provides a useful tool to test the effectiveness of classic analytical methods in computing the backscattering of large sea surfaces at very large incident angles. Some numerical examples are presented to test the accuracy and efficiency of the fast Fourier transform multilevel fast multipole algorithm. It shows that the results of the small perturbation method agree very well with the fast Fourier transform multilevel fast multipole algorithm results at moderate incident angles.

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