Analysis of Three-Dimensional Dielectric Scatterer with Solenoidal Basis Functions and Iterative Solvers

The solenoidal basis functions proposed by Carvalho and Mendes, which are defined on tetrahedrons, are applied into multilevel fast multiple algorithm to analyze the electromagnetic scattering problem of the three-dimensional homogeneous or inhomogeneous dielectric objects. Necessary formulations for implementation are given in detail. Three popular Krylov subspace iterative methods, that is, conjugate gradient method (CG), bi-conjugate gradient method (BiCG), and general minimize residual (GMRES), are introduced to solve the resultant linear equations. We also introduce a novel iterative method-loose general minimize residual (LGMRES), which gives a little modification to GMRES, but promotes the convergence rate obviously. The results display that the LGMRES has a best performance, while CG is inefficient in the calculations for large electric-size using solenoidal basis functions method of moment