Ilari Hanninen

SINGULARITY SUBTRACTION INTEGRAL FORMULAE FOR SURFACE INTEGRAL EQUATIONS WITH RWG, ROOFTOP AND HYBRID BASIS FUNCTIONS

Numerical solution of electromagnetic scattering problems by the surface integral methods leads to numerical integration of singular integrals in the Method of Moments. The heavy numerical cost of a straightforward numerical treatment of these integrals can be avoided by a more efficient and accurate approach based on the singularity subtraction method. In the literature the information of the closed form integral formulae required by the singularity subtraction method is quite fragmented. In this paper we give a uniform presentation of the singularity subtraction method for planar surface elements with RWG, ˆ n×RWG, rooftop, and ˆ n×rooftop basis functions, the latter three cases being novel applications. We also discuss the hybrid use of these functions. The singularity subtraction formulas are derived recursively and can be used to subtract more than one term in the Taylor series of the Greens function.

Polarizability analysis of cubical and square-shaped dielectric scatterers

The polarizability characteristics of nonspherical scatterers, especially cubes and squares, are studied. A surface integral equation for the electrostatic potential has been numerically solved for a cube and a square-shaped object. Nonuniform gridding of the dielectric object has been used to get a good accuracy in the solution. The results obtained for the polarizability of cubes using the surface integral equation are compared with those obtained from the volume integral equation and show a good agreement. We give simple approximation formulas for the polarizabilities as functions of the permittivity of the inclusions. The results give an improvement compared to earlier literature and also present a way to predict the effective properties of mixtures where cube-shaped inclusions are embedded in dielectric environment, which type of mixtures strongly generalize the effective-medium theories of the present literature.

REALIZATION OF GENERALIZED SOFT-AND-HARD BOUNDARY

The classical soft-and-hard surface boundary conditions have previously been gen- eralized to the form a ¢ E = 0 and b ¢ H = 0 where a and b are two complex vectors tangential to the boundary. A realization for such a boundary is studied in terms of a slab of special wave- guiding anisotropic material. It is shown that analytic expressions can be found for the material parameters and thickness of the slab as functions of the complex vectors a and b.

Implementation of Method of Moments for Numerical Analysis of Corrugated Surfaces With Impedance Boundary Condition

A method of moments formulation is developed to analyze the scattering of corrugated surfaces by using an impedance boundary condition. The numerical analysis of the impedance surface is done using closed-form formulae and accurate numerical integration. The studied formulation greatly decreases the computational resources required to study corrugated structures.

Method of moments analysis of the backscattering properties of a corrugated trihedral corner reflector

A method of moments (MoM) formulation is developed to analyze the backscattering properties of an anisotropic trihedral corner reflector, which is obtained by corrugating one or several of its interior faces. The proposed formulation treats the corrugated surface as ideally tuned to the incident wave frequency. The numerical analysis of the studied structures has been done using closed-form formulas and accurate numerical integration. The focus of the study reported in this paper has been the polarization responses of ideally tuned corrugated reflectors, which have interesting properties, particularly regarding elliptically or circularly polarized waves. We numerically verify that an appropriately corrugated reflector returns elliptically and circularly polarized waves with the same handedness as the incident wave. For a linearly polarized incident wave, the corner reflector is able to rotate them by 90/spl deg/. Also the effect of the direction of the corrugation to the backscattering properties is studied.

Efficient Evaluation of the Rokhlin Translator in Multilevel Fast Multipole Algorithm

In multilevel fast multipole algorithm (MLFMA) the direct evaluation of the Rokhlin translator is computationally expensive, and usually the cost is lowered by using local Lagrange interpolation in the evaluation, which requires oversampling of the translator. In this paper we improve the interpolation procedure by introducing a new, accurate, and fast oversampling technique based on the fast Fourier transform (FFT). In addition to speeding up the oversampling this also allows the use of lower number of points in the interpolation stencils improving the efficiency of the evaluation of the Rokhlin translator. We have optimized the interpolation parameters, i.e., the number of the stencil points and the oversampling factor, by using as the error criterion the accuracy in the translated (incoming) field rather than the usually used interpolation error. This choice leads to better optimized parameter pairs which further lowers the interpolation cost. We have computed and tabulated the optimized pairs for a wide range of target accuracies and the MLFMA division levels. These tables can be used for a good error control and maximal speed-up in practical computations.

Realization of perfectly anisotropic impedance boundary

The perfectly anisotropic boundary (PAB) is defined as one possessing no isotropic component in its surface impedance dyadic. It can be realized in terms of a slab of material called guiding-wave medium. PAB can serve as a polarization transformer transforming a linearly polarized field to a field with given elliptic polarization and handedness or conversely. Also, unlike an isotropic impedance boundary, PAB can simultaneously support two surface waves with orthogonal polarizations propagating within a certain sector along the boundary.

Modelling of dielectric materials with cubic inclusion shapes

The objective of this research is to calculate the polarizability of a cubical scatterer as accurately as possible and to develop an approximate formula for the polarizability. The problem of a dielectric cube in a uniform static electric field is solved numerically with a surface-integral-equation approach. The resulting dipole moment for this kind of scatterer is dependent on the dielectric contrast between the internal and external regions. The results give an improvement compared to earlier literature and also present a way to predict the effective properties of mixtures where cube-shaped inclusions are embedded in dielectric environment which type of mixtures strongly generalize the effective-medium theories of the present literature. Similar calculations are to be made also for other polyhedra.