2012 Volume E95.C Issue 1 Pages 63-70
This paper presents the iterative progressive numerical methods (IPNMs) based on the induced dimension reduction (IDR) theorem. The IDR theorem is mainly utilized for the development of new nonstationary linear iterative solvers. On the other hand, the use of the IDR theorem enables to revise the classical linear iterative solvers like the Jacobi, the Gauss-Seidel (GS), the relaxed Jacobi, the successive overrelaxation (SOR), and the symmetric SOR (SSOR) methods. The new IPNMs are based on the revised solvers because the original one is similar to the Jacobi method. In the new IPNMs, namely the IDR-based IPNMs, we repeatedly solve linear systems of equations by using a nonstationary linear iterative solver. An initial guess and a stopping criterion are discussed in order to realize a fast computation. We treat electromagnetic wave scattering from 27 perfectly electric conducting spheres and reports comparatively the performance of the IDR-based IPNMs. However, the IDR-based SOR- and the IDR-based SSOR-type IPNMs are not subject to the above numerical test in this paper because of the problem with an optimal relaxation parameter. The performance evaluation reveals that the IDR-based IPNMs are better than the conventional ones in terms of the net computation time and the application range for the distance between objects. The IDR-based GS-type IPNM is the best among the conventional and the IDR-based IPNMs and converges 5 times faster than a standard computation by way of the boundary element method.
