The asymptotic waveform evaluation (AWE) technique is proposed with a preprocessing technique which is achieved by the arbitrarily dimensional fast lifting wavelet-like transform. With the new preprocessing technique, the sparse matrix equation in wavelet-domain is formed firstly. The wide band solution of this sparse linear system is obtained by application of AWE technique, and the actual induced surface current is computed by an inverse wavelet transform.Numerical simulation for differently shaped three dimensional objects has shown the efficiency of the present method.Keywords-Asymptotic waveform evaluation, sparse matrix, method of moments, arbitrarily dimensional wavelet matrix transform.

A direct rational approximation method based on Thiele interpolating continued fractions theory is proposed for fast frequency sweep analysis of electromagnetic problems. And an adaptive algorithm is also formed. Compared with the conventional rational approximation method, the proposed method can get a rational approximation directly without a great number of matrix inverse computations and doesn't need to allocate much memory for high derivatives of the dense impedance matrix. Meanwhile, the computation of surface currents by continued fractions can be sped up as compared with the traditional rational approximation. Numerical simulations for broad band scattering analysis of different shaped objects are discussed to shown the effectiveness of the present method. Index Terms -Computational Electromagnetics, Thiele interpolating continued fractions, method of moments, fast frequency sweep analysis.