As compressed sensing theory was introduced into the method of moments, an underdetermined system calculation model has been recently proposed to accelerate the solution of electromagnetic (EM) scattering problems. In this method, the measurement matrix is generated by extracting several rows from the impedance matrix, and the unknown current coefficient vector can be reconstructed from a sparse transform domain. In the actual application of this method, the selection of the sparse transform is the key difficult point, which greatly determines the final efficiency. Up until now, with some commonly used sparse transform bases (e.g., Fourier basis and wavelet basis), the solution can only be applied to 2-D and 2.5-D EM scattering problems. In order to extend its application and further reduce the number of measurements, this letter employs the Krylov subspace to replace the sparse transform in the underdetermined system calculation model. Benefiting from the exploitation of the Krylov subspace, the underdetermined equations will no longer be solved as a sparse reconstruction but rather as a standard least-squares solution. Numerical results have shown that the proposed method, compared to the original method, can not only reduce the number of measurements for the EM scattering problems of 2-D and 2.5-D objects but can also be applied to 3-D objects.

For electromagnetic scattering analysis of inhomogeneous dielectric objects over a wide incident angle, method of moments is used to solve volume integral equation (VIE), and a special excitation source with multiple incident angles information based on compressive sensing is introduced into the VIE so as to construct a fast solving model to reduce the number of repeated calculations of the matrix equation. By the analysis of computational complexity, the computational cost of the proposed method is significantly lower than that of the traditional method, and the effectiveness of the proposed method is verified by the simulation experiments of the inhomogeneous dielectric objects with different structures.

Rapid and accurate calculation of electromagnetic scattering problems over a wide incident angle range is a difficult but valuable subject in computational electromagnetics (CEM). Traditional methods need to calculate repeatedly at each finer angle step, which lead to low efficiency. Based on the recently proposed compressed sensing (CS) method in CEM, a new scheme is proposed to further improve the computation efficiency, in which CS is used two times to form an undetermined equation model and incident sources including much information of incident angles simultaneously. Theoretical frame and specific formulas are derived in detail, and numerical results verified that it provided an efficient technical route for solving electromagnetic scattering problems.

To improve computational efficiency of obtaining local induced current distribution under multiple incidents angles when electromagnetic scattering problems of electrically large objects are considered, a novel method is proposed to form small-scale impedance matrix and reduce number of repeated calculation for different incident angles, which is implemented by following three steps. Firstly, an undetermined matrix equation including multiple incident angles is constructed by interrelating part field nodes and all source nodes on object surface. Secondly, the undetermined matrix equation is transformed into a form that conforms to the compressive sensing (CS) framework, which is solved by reconstructed algorithm to obtain approximate induced currents of all source nodes under a wide incident angle range. Finally, exact wide-angle currents of a given node are obtained by calculating total magnetic field, and neighborhood wide-angle currents of the given node can be expanded by choosing appropriate technology in different boundary conditions. Numerical results of electrically large objects shown the efficiency of the proposed method.

Method of moments (MoM) is a classical numerical method for analyzing electromagnetic (EM) scattering from various objects. Generalized minimal residual (GMRES) is a kind of widely used solver for linear systems of equations generated by MoM, whose calculation complexity mainly includes two parts, matrix-vector multiplications and the orthogonalization procedure. In order to accelerate the solution of matrix equations arising in MoM, an efficient strategy for constructing non-orthonormal Krylov bases is proposed in this paper, which can be introduced into standard GMRES and its variants (e.g., GMRES(m) and quasi-GMRES) and can be easily combined with the fast approaches for MOM (e.g., FMM and ACA). The principle of the method is described in detail, and the effectiveness is verified by numerical results.

To further accelerate the analysis of monostatic electromagnetic (EM) scattering problems of objects, an improved compressive sensing (CS)-based model is proposed. First, an orthogonal subspace spanned by the wide-angle induced currents is identified by means of the wide-angle incident sources. Then, the sparse transform of the induced currents is replaced by the subspace projection. In addition, an optimal number of measurements is determined, only slightly larger than the dimension of the subspace. Finally, the recovery algorithm is simplified to the least-squares method to solve the resulting overdetermined system. Compared with the traditional CS-based model, the proposed model significantly improves the efficiency of the recovery step and optimizes both the requirement for and the way of determining the number of measurements.