Multiwavelets in solving integral equations of the 1st and 2nd kind

Multiwavelet based moment method (MMM) is employed to solve the integral equations of the 1st and 2nd kind in 3D cases. We implement partial derivative sampling along two orthogonal directions in order to keep tracking the directional derivative along arbitrary directions. This produces a nonsquare impedance matrix if the traditional Galerkin procedure is applied. We can obtain a square impedance matrix by reducing the number of observation points, but the solution is very sensitive to the distribution of the observation points. The least-mean-square (LMS) method is demonstrated to be very effective in solving nonsquare matrix equations. We conduct the LMS in our 3D MMM, thus the advantages of the MMM in 2D cases are preserved with a minor increase in the computational cost of the LMS.