On the convergence of an iterative formulation of the electromagnetic scattering from an infinite grating of thin wires
Abstract
Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or kspace) formulation is presented with an emphasis on application to periodic surfaces. The mathematical background for formulating an iterative equation is covered using straightforward single variable examples including an extension to vector spaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to onedimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.
 Publication:

Ph.D. Thesis
 Pub Date:
 1985
 Bibcode:
 1985PhDT........47B
 Keywords:

 Contraction;
 Convergence;
 Electromagnetic Scattering;
 Gratings (Spectra);
 Infinity;
 Iterative Solution;
 Periodic Functions;
 Vector Spaces;
 Analysis (Mathematics);
 Problem Solving;
 Communications and Radar