Solution And Application Of The Method Of Moments On The Multiscale Problems

The meshing of multiscale problem is very inhomogeneous, giving rise to anill-conditioned impedance matrix in the method of moments (MOM). The iterative solutionof the resultant matrix system always converges slowly or even fails to converge. In thisthesis, the SAI preconditioner is used to accelerate the convergence of multiscale MoMsystems. Improvements on the SAI preconditioner has been developed to alleviate thedifficulties caused by the inhomogeneous meshing in multiscale problems. The problem ofantenna radiation, a typical multiscale application, is employed to verify the efficiency ofthe improved SAI preconditioner. The numerical experiments show that the improvementsmake the SAI more efficient than the traditional one. With the nice preconditioner, werealize a simplification of a multiscale model to reduce the computational cost where thecomputation would be repeated many times for an optimized design. The model issimplified by focusing on the tiny structures, while suppressing the interferences fromuninterested parts to the negligible level.