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The three dimensional weak form of the conjugate gradient FFT method for solving scattering problems

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2 Author(s)
Zwamborn, P. ; Dept. of Electr. Eng., Delft Univ. of Technol., Netherlands ; Van den Berg, P.M.

The problem of electromagnetic scattering by a three-dimensional dielectric object can be formulated in terms of a hypersingular integral equation, in which a grad-div operator acts on a vector potential. The vector potential is a spatial convolution of the free space Green's function and the contrast source over the domain of interest. A weak form of the integral equation for the relevant unknown quantity is obtained by testing it with appropriate testing functions. The vector potential is then expanded in a sequence of the appropriate expansion functions and the grad-div operator is integrated analytically over the scattering object domain only. A weak form of the singular Green's function has been used by introducing its spherical mean. As a result, the spatial convolution can be carried out numerically using a trapezoidal integration rule. This method shows excellent numerical performance

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Microwave Theory and Techniques, IEEE Transactions on  (Volume:40 ,  Issue: 9 )