부산대학교 도서관

We present computational techniques based on the class of preconditioned Krylov subspace methods that enable to carry out large-scale simulations of Computational Electromagnetics problems modeled via integral equations. This analysis requires the solution of very large, typically dense, linear systems that cannot be afforded by conventional direct methods. For example, accurate modeling of a perfectly conducting sphere of diameter of 1,800 wavelengths yields systems with more than 3 billion equations. For many integral formulations of practical interest, the convergence of Krylov subspace methods is often slow and needs to be accelerated by a technique called preconditioning, which transforms the initial system into an equivalent one that has more favorable eigenvalues distribution, i.e., most of the eigenvalues are grouped close to point one of the spectra. An effective preconditioner should be cheap to compute, easy to combine with the data structure of fast integral equations solvers, so that it can maintain an overall O(n log n) complexity in both time and space, and scale satisfactorily with the frequency of the problem and the number of processors, delivering fast convergence on a wide range of geometries and physical parameters. These requirements are often in contradiction with each other.