Wavelet-based preconditioner for three-dimensional electromagnetic integral equations

A wavelet-based method is proposed to effectively precondition 3D electromagnetic integral equations. The approximate-inverse preconditioner is constructed in the wavelet domain where both the moment matrix and its inverse exhibit sparse, multilevel finger structures. The inversion is carried out as a Frobenius-norm minimisation problem. Numerical results on a 3D cavity show that the iteration numbers are significantly reduced with the preconditioned system. The computational cost of the preconditioner is kept under O(NlogN)