The hybrid extended Born approximation and CG-FFT method for electromagnetic induction problems

The authors propose the hybridization of the extended Born approximation (EBA) with the conjugate-gradient fast Fourier transform (CG-FFT) method to improve the efficiency of numerical solution of electromagnetic induction problems. This combination improves the solution efficiency in two ways. First, using the FFT in the extended Born approximation decreases the computational cost of the conventional EBA method from O(N²) to O(N log₂ N) arithmetic operations, where N is the number of unknowns in the problem. This approach, referred to as the FFT-EBA method, applies to problems with a fairly large contrast. Secondly, using the EBA as a partial preconditioner for the CG-FFT method increases the convergence speed of the conventional CG-FFT method. This second approach, referred to as the EBA-CGFFT method, is in principle applicable to all problems with a homogeneous background, but is particularly efficient for problems with a higher contrast. Numerical experiments suggest that the combination of these two methods is more accurate and more efficient for electromagnetic induction problems