Fast construction of wavelet-based moment matrices in solving thin-wire electric field integral equations

Efficient numerical solution of the thin-wire electric field integral equation (EFIE) by the multiresolution wavelet expansion method involves a time-consuming double numerical integration for each nonzero element of the resulting moment matrix which in turn can outweigh the advantages of achieving a sparse matrix in the wavelet approach. To reduce the tedious numerical efforts in construction of the moment matrix, this paper introduce the near-zone radiated electromagnetic fields of piecewise linear wavelet basis functions. In this regard, each subsection of the semi-orthogonal linear spline wavelet bases is replaced by a convenient sinusoidal electric monopole for which closed-form expressions are available. Numerical results on a linear antenna demonstrate that excluding even one of numerical integrations in evaluation of each matrix entry reduces computational costs of matrix fill process and thus the overall solution time significantly.