Multiwavelet based moment method under discrete Sobolev-type norm

Multiwavelets are successfully applied to Galerkin's method for solving integral equations. High precision and fast convergence are demonstrated because of the desirable properties of multiwavelets, including compact support, symmetry and antisymmetry, regularity (continuity and smoothness), explicit expressions, and more importantly, the orthogonality under a Sobolev-type inner product. As a result, numerical integrations in the testing procedure are carried out explicitly. Numerical examples are conducted for electromagnetic waves scattering from smooth surfaces and surfaces with sharp edges, and propagating along microstrips with finite thickness. The new algorithm demonstrates significant improvement over the traditional MoM in terms of momery and CPU time up to two orders of magnitude. The new algorithm is easy to implement and program.