Comments on “On solving first-kind integral equation usingwavelets on a bounded interval” [and reply]

摘要

The author comments that the paper of Goswami, Chan and Chui (see ibid., vol.43, no.6, p.614, 1995) presented an interesting application of semi-orthogonal wavelets on a bounded interval to a numerical solution of first-kind integral equations. The major merit of the wavelet-based methods is to reduce an integral operator into a sparse matrix which is extremely valuable for large-scale problems. Compared with the discussion in the theoretical portion of the paper, the explanation of the numerical results is somewhat short and insufficient. In particular, examples for the demonstration of the sparse matrix lack insight and conviction. Goswami et al. reply that apparently Dr. Wang has not understood the main objective of their paper. The contribution of the paper should be seen not through one specific example, but rather in its totality. The method of moments (MoM) is well known and so is the fact that for a specific example discussed in our paper, namely TM scattering from an infinitely long PEC circular cylinder with small radius, 11 (or even less) basis functions will be sufficient for an accurate representation of the current distribution. The main purpose of our paper is to present wavelet MoM to the electromagnetic community in a simplified way so that readers can apply this technique to their problems which may be more interesting and challenging than the one we discussed. For this purpose, we provided explicit closed-form expressions for scaling functions and wavelets which, to the best of our knowledge, have not appeared anywhere in the literature