A Direct Solution Scheme for Wide-Angle Electromagnetic Scattering Problems Using Compressive Sensing-Based Method of Moments

One application of the compressive sensing (CS) technique in the method of moments involves restructuring matrix equations into a CS model to enhance computational efficiency. However, this compressive sensing-based method of moments (CS-MoM) model that has been reported is restricted to single excitation electromagnetic scattering contributions, as its iterative solver does not facilitate multiple excitation problems. In this paper, a direct solution scheme for CS-MoM is proposed to address wide-angle electromagnetic scattering challenges. The method is developed on overdetermined equation-based CS-MoM and utilizes the characteristic modes to construct the sparse transformation matrix. By converting the overdetermined equation into a normal matrix equation, the CS-MoM model is transformed into a reduced matrix equation with a smaller size, thus facilitating the solution using a direct solver such as lower-upper (LU) decomposition. For right-hand sides with varying incident angles, the reduced impedance matrix is LU-decomposed once in advance, and the decomposition factors are repeatedly used to derive the current coefficients. Moreover, the proposed method introduces the adaptive cross-approximation algorithm for filling mutual impedance. It not only enhances time performance but also significantly reduces memory consumption. Compared with the traditional characteristic mode basis function method, the proposed method exhibits superior time and memory performance, with the total time reduced by 71%, 51% and 35%, respectively, and the memory consumption reduced by about 85% in the given simulation results.