Matrix thinning with reduced field testing (RFT)

A number of methods have been proposed recently for the generation of sparse, rather than dense matrices in the context of integral equations. Most notably, we refer to Canning's impedance matrix localization (IML), the wavelet expansion, the fast multipole method (FMM), and the use of uni-directional basis functions, including a dual source representation and the complex multipole beam approach. A good approximation for a sparse matrix is obtained by the reduced field testing (RFT) method, presented here. The method is a spatial domain alternative to the spectral domain FMM, based on the distinction between near field and far field interactions, and providing a single, explicit sparse matrix invertible by either direct or iterative methods. The procedure does not change essentially the way by which MoM matrix elements are computed, hence it can be incorporated into existing MoM codes. Accuracy has been demonstrated by a number of examples.