Solving Electromagnetic Scattering Problems by Underdetermined Equations and Krylov Subspace

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.