An interesting stabilizing variant of the biconjugate A-orthogonal residual (BiCOR) method is investigated for solving dense complex non-Hermitian systems of linear equations arising from the Galerlcin discretization of surface integral equations in electromagnetics. The novel variant is naturally based on and inspired by the composite step strategy employed for the composite step biconjugate gradient method from the point of view of pivot-breakdown treatment when the BiCOR method has erratic convergence behaviors. Besides reducing the number of spikes in the convergence history of the norm of the residuals to the greatest extent, the present composite step BiCOR method can provide some further practically desired smoothing behavior towards stabilizing the numerical performance of the BiCOR method in the case of irregular convergence.

Investigating the Composite Step Biconjugate A-Orthogonal Residual Method for Non-Hermitian Dense Linear Systems in Electromagnetics

─ The bistatic electromagnetic scattering from the composite model of a three-dimensional (3-D) arbitrarily shaped object located above a two -dimensional (2-D) Gaussian rough surface is analyzed in this work. The object suited above is assumed to be a perfect electric conductor (PEC) while the rough surface is dielectric. Firstly, the Poggio, Miller, Chang, Harrington, Wu and Tsai (PMCHWT) integral equations, electric field integral equation (EFIE) are implemented and extended on the rough surface and on the surface of the object respectively. Then, the method of moments (MoM) combined with Galerkin method is introduced to discretize the integral equations to the matrix form using RWG basis function. Due to the memory requirement and computational complexity of traditional MOM are 2 ( ) O N ( N is the number of unknowns), the rank based 3-D Multilevel UV method (3DMLUV) is employed to reduce memory and CPU time overhead. The 3DMLUV has been successfully applied in the scattering of PEC targets, however, when the object or rough surface become dielectric, the fast fill-in method proposed in Reference [19] often breaks down due to the oscillatory nature of the gradient of Green’s function. Therefore, the ACA is applied to speed up the filling of the impedance entries required in 3DMLUV because of its algebraic nature. The efficiency and accuracy of the proposed method are demonstrated in a variety of scattering problems. Index Terms Composite model, bistatic scattering, PMCHWT, 3DMLUV, ACA

A Hybrid 3DMLUV-ACA Method for Scattering from a 3-D PEC Object above a 2-D Gaussian Dielectric Rough Surface

An efficient electromagnetic (EM) scattering solution of iterative bidirectionally ray tracing method has been proved to analyze the scattering from electrically large bodies with multiple reflection structures. The algorithm starts by building a bidirectionally ray tracing in both incident and backward observed directions. More specifically, both the multiple geometric optical reflections and physical optical scatterings are taken into consideration during the process of ray tracing. Meanwhile, the selected current interactions are iterative accounted so as to obtain the reradiation effect for the multiple reflections. On this bases, the reradiation effect supplements the mechanism of the nonspecular scattering obtained on side lobe directions and achieves higher accuracy than the ray tracing-based method. After that, the target-coupled edge diffraction theory is used to modify the target scattering field to obtain valuable RCS results. The EM scatterings from complex structures are simulated to verify the performance of the proposed method.

RCS Calculation of Electrically Large Targets by Iterative Bidirectionally Ray Tracing Method

─ An improved MM-PO-UV hybrid method is developed to calculate the bistatic scattering from the two-dimensional (2-D) composite model of an electrically large ship (ELS) on a one-dimensional (1-D) rough sea surface at a low grazing angle (LGA). The subdivision of the MM and PO region is performed flexibly according to the physical considerations. The MM region contains not only the ship but also a small portion of the neighboring sea region where the surface currents need to be modeled accurately. An iterative solution BiCGSTAB is adopted to solve the final matrix equation of a large dimension caused by the ELS. Then, a UV matrix decomposition technique is applied as the fast algorithm to accelerate the matrix-vector productions and the matrix elements filling in. The improved method makes it possible for the Monte-Carlo simulation of large-scale complex target/rough surface problems under an LGA. The accuracy is validated in comparison with the traditional MOM method. Index Terms ─ LGA, MM-PO hybrid method, target/rough surface scattering, UV.

J. L. Volakis

Papers

An Improved MM-PO Method with UV Technique for Scattering from an Electrically Large Ship on a Rough Sea Surface at Low Grazing Angle