Xinyuan Cao

Simpler generalized minimal residual (SGMRES) is a classic variant of the regular generalized minimal residual (GMRES) method that does not require upper Hessenberg factorization, which is applicable to solving matrix equations generated by the method of moments (MoMs). In this article, an accelerated technique by implementing the Gram–Schmidt process in a low-dimensional space is applied to improve the SGMRES algorithm, which can significantly reduce the elapsed CPU time. The analysis of the principle of the new algorithm is discussed in detail. Numerical experiments are reported to illustrate the performance and effectiveness of the proposed algorithm.

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.

The electromagnetic scattering problem over a wide incident angle can be rapidly solved by introducing the compressive sensing theory into the method of moments, whose main computational complexity is comprised of two parts: a few calculations of matrix equations and the recovery of original induced currents. To further improve the method, a novel construction scheme of measurement matrix is proposed in this paper. With the help of the measurement matrix, one can obtain a sparse sensing matrix, and consequently the computational cost for recovery can be reduced by at least half. The scheme is described in detail, and the analysis of computational complexity and numerical experiments are provided to demonstrate the effectiveness.

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.

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.

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.

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.

To avoid directly solving linear equations for major time marching in the finite element time-domain (FETD) method, the compressive sensing (CS) theory is introduced to construct an explicit iterative scheme instead of an implicit form. In this method, Whitney elements and a leapfrog model are applied to time-dependent Maxwell curl equations for space and time discretization. After a small number of iterations, steps for linear equations in the initial time, the electric field intensity and magnetic flux density are updated just by the linear combination of results of previous time steps. Furthermore, a restart mechanism is built to control the computational complexity and accuracy over a long simulation time. The effectiveness of the new algorithm is verified by analyzing 3-D resonant cavities.

To reduce the computing resource of full-scale impedance matrix and its high-order derivatives in traditional Asymptotic Waveform Evaluation (AWE), compressive sensing (CS) is applied to AWE for fast and accurate frequency-sweep analysis of electromagnetic scattering problems. In CS framework, some prior knowledge is extracted by constructing and solving undetermined equation of 0-order surface induced current, so that coefficients about high-order induced current can be accurately obtained by the prior knowledge, and finally the wide-band radar cross section (RCS) is calculated. Numerical results of two-dimensional objects and bodies of revolution (BOR) were presented to the show the efficiency of the proposed method.