An improved conjugate gradient FFT method

A number of electromagnetic field problems can be formulated in terms of a hypersingular integral equation, in which a grad-div operator acts on a vector potential. A weak form of this integral equation is obtained by testing it with subdomain basis functions. As the next step, the vector potential is expanded in a sequence of subdomain basis functions and the grad-div operator is integrated analytically. It is shown that a well-behaved operator is obtained which can properly be solved numerically by a conjugate gradient FFT (fast Fourier transform) iterative method. For the problem of electromagnetic scattering by a plate, the present method shows excellent numerical performance. The numerical difficulties encountered in the previous CGFFT methods have been eliminated.<>