Application of the Fast Fourier Transform and the Conjugate Gradient Method for Efficient Solution of Electromagnetic Scattering from Both Electrically Large and Small Conducting Bodies

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Abstract
This paper presents a combination of the conjugate gradient method with the fast Fourier Transform technique. With this combination, the computational time required to solve large scatterer problems is much less than the time required by the ordinary conjugage gradient method and the method of moments. Also, the advantages of the conjugate gradient method over the conventional matrix methods is also outlined. In this novel approach, since the spatial derivatives are replaced by simple multiplications in the transformed domain, some of the computational difficulties present in the ordinary conjugate gradient method and the method of moments do not exist here. Therefore, both electrically large and small structures can be handled easily. Finally, since the method is iterative, it is possible to know with what accuracy is the problem solved. Computational results are presented for electromagnetic scattering from square plates (very large and small). Also, the method of conjugate gradient can be applied directly to solve singular operator equations, yielding the minimum norm solution.