Entire Domain Galerkin Research Articles

On an electrostatic micropump with a rigorous mathematical model

The novel electrostatic micropump model for applications such as in biomedical drug delivery is presented. The geometrical arrangement of the coupling rigid electrodes lets us exploit our mathematically rigorous boundary integral equation formulation and its solution. Thus, the charge densities involving the fringe effects on the plates are obtained by means of analytical regularization method (ARM) constructed for annular strips earlier. The efficiency of the constructed method is demonstrated with respect to the direct integral equation solvers implemented via the entire domain Galerkin method and point matching. The main physical characteristics of the suggested system and their deviation from that of infinitely large plane approximation are discussed.

Superalgebraically Converging Galerkin Method for Electromagnetic Scattering by Dielectric Cylinders

AbstractThe high‐order solutions of the well‐known Green's formulation of the boundary value problems to determine the scattering monochromatic electromagnetic waves by dielectric cylinders are presented. The boundaries are given via infinitely smooth closed contours. That is why the solutions to the transverse electric/transverse magnetic wave scattering problems are obtained by solving the matrix equations, entries of which are Fourier coefficients of the electric field integral equations/magnetic field integral equations kernels obtained via the Fourier transform over the periodic domain on the boundary. This procedure is equivalent to an entire domain Galerkin formulation of the considered problems, with their unknown functions expanded into series with complex exponentials as bases. The algebraic system is solved by truncation, and the superalgebraic convergence of the unknowns is achieved by the suggested algorithm. The numerical results are validated by that of circular cylinders' obtained via a well‐conditioned algorithm based on separation of variables method. Numerical results demonstrate the superalgebraic convergence, owing to the suggested nonsaturated algorithm.

Efficient integral equation modeling of scattering by a gradient dielectric metasurface

Plane-wave scattering by a gradient dielectric metasurface, composed of a dielectric slab on which has been etched an infinitely periodic grating, is analyzed by means of rigorous semi-analytical integral equation techniques based on the Method of Moments with entire domain basis functions. The electric field integral equation is considered with unknown function the electric field on the grating and is then solved by applying an entire domain Galerkin’s technique. The proposed methodology is characterized by high numerical stability and controllable accuracy; the obtained solution is analytic with the sole approximation of the final truncation of the expansion functions sets. The operation of the metasurface as a narrow-band reflection frequency filter is investigated. Moreover, it is also shown that under certain conditions anomalous reflection and transmission can be generated even for a metasurface composed of conventional materials. The numerical results obtained provide design guidelines, which may pave the way for more systematic investigations of gradient dielectric metasurfaces assisting the control and manipulation of electromagnetic waves.

Magnetic field integral equation analysis of surface plasmon scattering by rectangular dielectric channel discontinuities

The scattering of a surface plasmon polariton (SPP) by a rectangular dielectric channel discontinuity is analyzed through a rigorous magnetic field integral equation method. The scattering phenomenon is formulated by means of the magnetic-type scalar integral equation, which is subsequently treated through an entire-domain Galerkin method of moments (MoM), based on a Fourier-series plane wave expansion of the magnetic field inside the discontinuity. The use of Green's function Fourier transform allows all integrations over the area and along the boundary of the discontinuity to be performed analytically, resulting in a MoM matrix with entries that are expressed as spectral integrals of closed-form expressions. Complex analysis techniques, such as Cauchy's residue theorem and the saddle-point method, are applied to obtain the amplitudes of the transmitted and reflected SPP modes and the radiated field pattern. Through numerical results, we examine the wavelength selectivity of transmission and reflection against the channel dimensions as well as the sensitivity to changes in the refractive index of the discontinuity, which is useful for sensing applications.

Diffraction of plane waves incident on a grated dielectric slab: An entire domain integral equation analysis

Diffraction of electromagnetic waves by periodic grating waveguides is investigated by using a rigorous integral equation method, which combines semianalytical techniques and the Method of Moments with entire domain basis functions. The electric field integral equation is employed with unknown function the electric field on the grooves. This equation is subsequently solved by applying an entire domain Galerkin's technique. The proposed analysis provides high numerical stability and controllable accuracy. All the involved computations are analytically carried out, leading to an analytic solution with the sole approximation of the final truncation of the expansion functions sets. The computed results exhibit superior accuracy and numerical efficiency compared with those already derived by applying different methods. The effect of the incident field's and grating's characteristics on the diffraction process as well as the grating structure's efficient operation as a narrow band reflection filter are thoroughly investigated. The numerical results obtained provide design guidelines, which may be exploited appropriately in the development of millimeter and optical waveguide structures.

Rigorous integral equation analysis of nonsymmetric coupled grating slab waveguides

A rigorous integral equation formulation in conjunction with Green's function theory is used to analyze the waveguiding and coupling phenomena in nonsymmetric (composed of dissimilar slabs) optical couplers with gratings etched on both slabs. The resulting integral equation is solved by applying an entire-domain Galerkin technique based on a Fourier series expansion of the unknown electric field on the grating regions. The proposed analysis actually constitutes a special type of the method of moments and provides high numerical stability and controllable accuracy. The singular points of the system's matrix accurately determine the complex propagation constants of the guided waves. The results obtained improve on those derived by coupled-mode methods in the cases of large grating perturbations and highly dissimilar slabs. Numerical results referring to the evolution of the propagation constants as a function of the grating's characteristics are presented. Optimal grating parameters with respect to minimum coupling length and maximum coupling efficiency are reported. The coupler's efficient operation as an optical bandpass filter is thoroughly investigated.

Rigorous analysis of the coupling between two nonparallel optical fibers

The rigorous electromagnetic analysis of the coupling between two nonparallel optical-fiber waveguides is developed for the first time. Green's theorem, involving the dyadic Green's function of the fiber guiding the incident mode, is used to formulate the electric-field integral equation inside the second fiber. By applying the entire-domain Galerkin technique and by utilizing the generalized addition theorem for cylindrical waves for nonparallel axis translation, which is derived by the authors, this equation is analytically transformed into a system of coupled integral equations for the spectral weights of the field on the basis of TE and TM cylindrical vector wave functions. The Neumann-series iterative procedure is adopted to solve this system and obtain analytical expressions for the field scattering coefficients, which are sufficiently accurate for weakly coupled fibers

Integral equation analysis of coupling in symmetric grating-assisted optical waveguides

The propagation and coupling phenomena in grating-assisted optical couplers are analyzed by using an integral equation formulation and applying an entire-domain Galerkin technique. The proposed method constitutes a special type of the method of moments and provides high numerical stability and controllable accuracy. The electric field in the grating region is the unknown quantity and the resulting integral equation is subsequently solved by using Galerkin's method. The propagation constants of the guided waves are computed accurately by determining the singular points of the corresponding system's matrix. Numerical results regarding the propagation constants are presented for various coupler parameters, and the effect of the grating's physical and geometric characteristics on the coupling process is investigated.

Integral equation analysis of scattering by a spherical microparticle coupled to a subwavelength-diameter wire waveguide

A rigorous integral equation analysis of the coupling between a fiber waveguide and an adjacent spherical particle is developed. The solution is obtained by applying the entire-domain Galerkin technique, based on Mie-type spherical wave expansion of the field in the sphere and the use of dyadic Green's function of the fiber waveguide. The conversion between cylindrical and spherical wave functions is done through classic analytical formulas. The analysis is applied to numerically investigate transmission through silica wires of subwavelength diameter in the presence of particles of comparable size. The results show the possibility of sensing microparticles through the reduction of transmitted power, which is maximum for certain critical values of the fiber diameter.

Convergent Galerkin MoM Solver for the EFIE in Two Dimensions

The convergence of the entire domain Galerkin MoM solution to the electric field integral equation (EFIE) is provided in the Hilbert space of square integrable functions (L 2 ) for the nonresonant case. To this end, the traditional MoM equation is transformed into a Fredholm second-kind equation in the space of sequences for a smooth closed boundary of a scatterer. A rigorous relation between actual and residual errors is also obtained that permits one to compute the both errors in L 2 . Advantages of the new MoM equation are demonstrated in terms of accuracy and efficiency compared to the traditional MoM equation.

Transmission and radiation in a slab waveguide coupled to a whispering-gallery resonator: volume-integral-equation analysis.

The excitation of a whispering gallery resonator by a surface wave guided in a dielectric slab is analyzed with a rigorous volume-integral-equation approach. The analysis is based on the Green's function concept and the application of the entire-domain Galerkin technique through expansion of the electric field in the resonator in terms of cylindrical wave functions. The algorithm developed yields highly accurate results for the transmission and reflection coefficients in the waveguide. The radiated far field is computed, and the effect of the excitation of a whispering gallery mode on the radiation pattern is studied.

Analysis of coupling between two slab waveguides in the presence of ring resonators.

The coupling phenomena between two slab waveguides in the presence of ring resonators are investigated through a rigorous integral equation analysis. A Green's-function-theory approach is utilized to develop the integral equation formulation. The solution is obtained by applying an entire-domain Galerkin technique, using the orthogonality properties of involved wave functions in the ring resonators. The field's transmission and reflection coefficients are accurately computed and a practical directional-coupler approach is discussed. The presented results reveal strong resonant coupling phenomena between the two waveguides and the resonators.

Moment‐method analysis of a slot‐coupled circular waveguide orthomode transducer

AbstractAn analysis of a slot‐coupled circular to rectangular waveguide orthomode transducer (OMT) is presented. A set of four coupled integrodifferential equations are obtained from the enforcement of the continuity conditions of tangential magnetic fields at the slot–aperture interfaces. The method of moments, with entire‐domain sinusoidal basis functions and Galerkin testing, is used to solve the coupled‐integral equations, with finite wall thickness taken into account. Mutual coupling between the two aperture slots, which plays a major role in isolating the orthogonal ports, is properly accounted for. Resonant length of the slots and reflection coefficient and coupling between ports are computed. A comparison between the experimental and computed data by the present method as well as HFSS is presented. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 285–289, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10439

Accurate Analysis of a Cylindrical Dielectric Resonator Mounted On a Grounded Dielectric Substrate - Abstract

The resonance properties of a finite height cylindrical resonator of high permittivity value, placed on a dielectric grounded substrate are analyzed, using a volume integral equation formulation in conjunction with a Method of Moments technique. The Green's function of the microstrip-grounded dielectric substrate is employed and an integral equation is derived in terms of the electric field inside the finite cylinder, which is solved via an entire domain Galerkin technique. Superposition of plane waves, satisfying individually the wave equations are employed and the complex resonance frequencies are determined by computing the stored average electric and magnetic energies. Detailed convergence checks and comparisons with previously published data prove the proposed technique to be numerically stable and accurate.

Full-Wave Analysis of a Fabry-Perot Type Resonator - Abstract *

A Fabry-Perot type resonator consisting of a system of two parallel finite size orthogonal conducting plates is examined, employing an integral equation formulation in conjunction with a Method of Moments. The system of coupled integral equations in terms of the conductivity currents induced on the resonator surface is solved via an entire domain Galerkin technique with Chebyshev type basis functions incorporating the current edge behaviour. Numerical results are computed for several resonator sizes and operation frequencies and the resonance behavior of the examined structure is investigated.

Using Parallel Processing as a Computational Tool to Solve Multi-Plate Electromagnetic Scattering Problems

The Parallel Method of Moments (PMoM) technique is used to solve electrically large multi-plate scattering problems. After introducing the PMoM, an integral equation formulation in conjunction with an entire domain Galerkin technique is employed to analyse the multi-plate scattering problem. The resulting algorithm parallelisation enables for the proposed approach to be applied above the resonance region. Numerical results and computational times concerning a specific worked example are presented, using High Performance Computing purely as a computational tool.

General entire-domain Galerkin method for analysis of wire antennas in the presence of dielectric bodies

A novel, entire-domain moment-method is proposed for the analysis of wire antennas and scatterers in the presence of lossy inhomogeneous dielectric bodies of finite extent. The wire part of the structure is approximated by arbitrarily positioned and interconnected straight-wire segments of lengths which can exceed one wavelength. The dielectric bodies are approximated by a system of trilinear hexahedrons, which can be electrically large (can also exceed one wavelength inside the dielectric, in any direction). The current along wires and inside dielectric bodies is approximated by one- and three-dimensional polynomials, respectively. The unknown current-distribution coefficients are obtained by a Galerkin-type solution of the system of coupled two-potential integral equations. The method is accurate, efficient and reliable. Its fundamental advantage over the (only existing) subdomain methods for the analysis of the same type of structures is a significantly reduced number of unknowns and, consequently, greatly reduced computing time. The proposed method enables rapid analysis of wire/dielectric structures exceeding moderate electrical size with even standard personal computers.

Mode transitions between bound and leaky regimes in lossy dielectric waveguides: a numerical investigation

The authors present a novel numerical study of mode transitions between bound and leaky regimes in a lossy-substrate dielectric rib waveguide. An entire-domain basis Galerkin's method is employed to determine the wavenumbers of the transmission line modes. The obtained results show that as the loss tangent gradually increases from zero to infinity, the plots of the attenuation constants alter between regions of constant and linear variation. In the progress of this behavior the modes evolve from leaky to bound state, or the inverse, and their corresponding poles in the spectral plane cross the real axis.

Analysis of dielectrically loaded radiators using entire-domain Galerkin technique

The response of various types of dielectrically loaded radiators to a time-harmonic excitation is analyzed, by employing an integral-equation formulation in conjunction with an entire-domain Galerkin technique. Coupled integral equations are derived in the frequency domain. These are written in terms of the conductivity currents or/and the electric fields developed on the conducting surfaces or/and inside the dielectric materials, respectively. They are solved via the method-of-moments technique. In particular, an entire-domain Galerkin technique is employed, and proves very efficient, when rather specific geometries are considered and appropriate "intelligent" basis-function sets are chosen, accelerating the convergence of the method. To prove this claim, three representative antenna structures, of significant practical use, corresponding to the three types of geometries (cylindrical, spherical, and planar), are solved in the resonance region. Parallelization of the developed sequential code is employed, in order to extend the use of Galerkin technique to electrically large structures. The validity of the proposed method is checked, and numerical results are presented for several cases.

Benchmarking high‐performance computing platforms in analyzing electrically large planar conducting structures via a parallel computed method of moments technique

The analysis of electrically large planar conducting structures is examined by employing parallel computations of an integral equation technique in conjunction with a method of moments. The integral equation, in terms of the induced conductivity currents, is solved using an entire domain Galerkin technique, with Chebyshev‐type basis fonctions. The resulting algorithm parallelization enables extension of the proposed methodology above the resonance region. Numerical results are computed for several scatterer sizes and excitations source types on varying high‐performance computing platforms: Silicon Graphics Power Challenge, Intel Paragon XP/S, CRAY C‐90, and CRAY T3D. A comparison is made among these diverse computing platforms for their applicability‐suitability in solving electromagnetic problems in the domain of electrically large planar scattering structures. Their suitability is not only judged on performance obtained but also on ease of code portation.