Finite Element-boundary Integral Technique Research Articles

Excitation of Complex Modes of Periodic Structures Using Inhomogeneous Plane Wave Scattering in Fast and Slow Wave Regions

Periodic metamaterial unit cells are analyzed by using inhomogeneous plane wave scattering. The complex modes of the unit cell are derived using either the poles or the zeroes of the complex reflection coefficient of the fundamental Floquet mode. The required reflection coefficients are computed by a doubly periodic finite element boundary integral technique. The search for the eigenvalues is accelerated by the nonlinear Nelder-Mead method. Usually, pairs of eigenvalues are observed, which can be both, real or conjugate complex. Also, the eigenvalues correspond either to proper or improper modes. By selecting the proper or the improper modes during field computation, the other type of modes is removed from the observed response and, instead, zeroes are found in the reflection coefficient. This can explain the absorption behavior of single-sided open periodic leaky structures by investigating their reflection coefficient with the proposed inhomogeneous plane wave excitation approach. The obtained results for various single-sided open periodic unit cells are in good agreement with the results of other methods, where in the presented excitation based method there is no need to solve any dispersion equation in the complex plane.

Dispersion Analysis of Periodic Structures by Solving Corresponding Excitation Problems

Eigenproblems of periodic structures with complicated material distribution are solved efficiently by solving corresponding excitation problems. A unit cell with periodic boundary conditions is discretised and handled by a doubly periodic hybrid finite element boundary integral technique, which even considers complex propagation constants. Instead of solving algebraic eigenproblems, the analogy to resonance problems is exploited which gives improved physical insight into the problem. Moreover, open problem types can be handled. Numerical results for composite right/left-handed waveguides in one and three dimensions confirm the presented approach.

Ray Optical Electromagnetic Far-Field Scattering Computations Using Planar Near-Field Scanning Techniques

For accurate scattering computations in the far-field of flat finite objects, field based ray optical methods cannot be used directly, since the finiteness of the objects is not considered in the formulations. In this paper, planar near-field scanning techniques are used to overcome this problem. In particular, scattered ray optical fields are first computed in a scanning plane in the near-field region of the involved objects and are transformed into the far-field afterwards using field expansions in terms of spectrum density functions of outgoing waves. Since evanescent waves are avoided in the scanning plane, sampling rates less than lambda <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> /2 can be used for restricted angle range around the normal direction to the scanning plane. Reduced accuracy at grazing directions of observation is overcome by combining solutions provided by several scanning planes. The proposed approach is applied in the postprocessing stage of the recently developed hybrid method combining the uniform geometrical theory of diffraction with the finite element boundary integral technique and with the multilevel fast multipole method.

Application of the Fast Multipole Method to the FE-BI Analysis of Cavity Backed Structures with Comprehensive FMM Error Control

Starting with the Finite Element-Boundary Integral technique for the electromagnetic analysis of cavity backed structures, it is shown how the Fast Multipole Method can be applied to the BI component of this formulation. A new scheme is presented for controlling the error incurred by FMM that affords greater freedom when using the threedimensional FMM by allowing independent specification of the desired error level and the group far-interaction criterion. This scheme is also valid when FMM is applied to general, free-space, three-dimensional Method of Moments implementations.

Hybrid/sup 2/: combining the three-dimensional hybrid finite element-boundary integral technique for planar multilayered media with the uniform geometrical theory of diffraction

The fully three-dimensional (3-D) hybrid finite element (FE)-boundary integral (BI) technique is extended by further hybridization with the uniform geometrical theory of diffraction (UTD) resulting in a so-called hybrid/sup 2/ FE-BI-UTD approach. The formulation is capable of modeling arbitrarily shaped strongly inhomogeneous objects together with electrically large obstacles of relatively simple shape within the common environment of a planar-multilayered medium. The arbitrarily shaped inhomogeneous objects are discretized by finite elements, whereas, the electrically-large obstacles are described by the UTD and both of these models are included into an integral equation derived from the equivalence principle for planar-multilayered media. Thus, full-electromagnetic coupling is realized between all parts of the formulation. The integral equation is implemented using mixed potentials with appropriate Green's functions derived from Sommerfeld integral representations for planar-multilayered media. The UTD contributions are accounted for by corresponding modifications of the Green's functions and the FE technique is coupled to the integral equation via introduction of equivalent surface current densities in the bounding surfaces of the discretized objects. After presenting the formulation of this novel fully 3-D hybrid/sup 2/ technique, the implemented computer code is validated against conventional hybrid FE-BI computations and a wireless base station antenna is analyzed in several situations of complex real world, microcell environments.