Fast algorithms for solving integral equations of electromagnetic wave scattering

Computational electromagnetics plays an important role in the study of wave scattering and radiation from large and complex objects. This dissertation develops fast numerical algorithms for solving two-dimensional and three-dimensional integral equations of electromagnetic wave scattering. They include: (1) The fast iterative method, which reduces the matrix-vector multiplication from {dollar}Nsp2{dollar} to {dollar}Nsp{lcub}1.5{rcub}{dollar} and to N (log(N) {dollar}sp2.{dollar} (2) A fast far-field approximation (FAFFA) method, which solves surface integral equations iteratively with computational complexity of O({dollar}Nsp{lcub}4/3{rcub}{dollar}) for one matrix vector multiplication. The FAFFA is applied to compute the RCSs of 2D and 3D objects with large electrical sizes. (3) The nested equivalence principle algorithm (NEPAL), which uses Huygens' equivalence principle to replace volume scatterers by surface scatterers, resulting in the reduction of the total number of unknowns. These algorithms have lower computational complexities compared to those for the classical low frequency methods and have the potential for solving larger electromagnetic scattering problems.