An analysis of two-dimensional scattering by metallic cylinders using wavelets on a bounded interval

Summary form only given. The method of moments (MOM) when applied to integral equations results into a fully-populated matrix which is often ill-conditioned, causing numerical instability and poor convergence in the case of iterative techniques. The condition number increases with the decrease in the step-size of the discretisation. It is now well known that multigrid methods offer a solution to such difficulties. Wavelets, because of their multiresolution properties, are naturally suited for multigrid methods. Their applications to integral equations lead to a well-conditioned matrix. Furthermore, the resultant matrix is sparse because of the local supports and the vanishing moment property of wavelets. The purpose of the paper is to demonstrate the application of semi-orthogonal compactly supported spline-wavelets on a bounded interval to resolve integral equations encountered in the two-dimensional electromagnetic scattering by metallic cylinders. In order to achieve a higher degree of sparsity, one must use higher order spline wavelets. However, higher order wavelets have higher spatial supports. The authors restrict themselves to the use of linear and cubic spline wavelets. The results obtained using the wavelet approach and the conventional MOM approach are presented.<>