This paper presents various Iterative Progressive Numerical Methods (IPNMs) for the computation of electromagnetic (EM) wave scattering from many objects. We previously modified the original IPNM from the standpoint of the classical and the IDR-based linear iterative solvers. We demonstrate the performance of the IDR(s)-based IPNMs through some numerical examples of EM wave scattering from regularly placed 27 perfectly electric conducting spheres.

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.

A major step in the numerical solution of electromagnetic scattering problems involves the computation of the convolution based reaction integrals. In this paper a procedure based on the analytical Fourier transform is introduced which allows us to calculate the convolution-based reaction integrals in the spectral domain without evaluating any convolution products directly. A numerical evaluation of the computational cost is presented to show the efficiency of the method when handling electrically large problems.

The comparative analysis of the well known Double Drift Region (DDR) IMPATT diode structure and the n+pvnp+ structure for the avalanche diode has been realized on the basis of the drift-diffusion nonlinear model. The last type of the diode was named as Double Avalanche Region (DAR) IMPATT diode. This structure includes two avalanche regions inside the diode. The phase delay which was produced by means of the two avalanche zones and the drift zone v is sufficient for the negative resistance obtained for the wide frequency region. The numerical model that is used for the analysis of the various diode structures includes all principal features of the physical phenomena inside the semiconductor structure. The admittance characteristics of both types of the diodes were analyzed in very wide frequency region.

A priori estimation is presented for a computational complexity of the homotopy method applying to a certain class of strongly monotone nonlinear equations. In the present papers, a condition is presented for a certain class of uniquely solvable equations, under which an upper bound of a computational complexity of the Newton type homotopy method can be a priori estimated. In this paper, a condition is considered in a case of linear homotopy equations including the Newton type homotopy equations. In the first place, the homotopy algorithm based on the simplified Newton method is introduced. Then by using Urabe type theorem, which gives a sufficient condition guaranteeing the convergence of the simplified Newton method, a condition is presented under which an upper bound of a computational complexity of the algorithm can be a priori estimated, when it is applied to a certain class of strongly monotone nonlinear equations. The presented condition is demonstrated by numerical experiments.