Simulation of 3D EM fields by a weak-form biconjugate gradient FFT method

We develop two numerical schemes, the weak-form conjugate gradient-fast Fourier transform (CG-FFT) and biconjugate gradient-fast Fourier transform (BCG-FFT) methods, for the iterative solution of 3-D hypersingular integral equations in electromagnetics. The weak-form CG-FFT method is based on Zwamborn-van den Berg´s (1992) scheme, and excellent agreement has been shown for this method. The weak-form BCG-FFT method is a significant improvement over the weak-form CG-FFT method; for our examples it converges three to six times faster than the CG-FFT method with a comparable cost per iteration. Both the weak-form CG-FFT and BCG-FFT methods require O(Nlog /sub 2/N) CPU time, and O(N) computer memory. We have validated the numerical results by comparing with analytical solutions for high contrast multilayer spherical media.