Fu-Gang Hu

Efficient Calculation of Interior Scattering From Large Three-Dimensional PEC Cavities

Higher order finite element-boundary integral (FE-BI) method is a powerful tool to model the electromagnetic (EM) scattering from three-dimensional large, deep, and arbitrarily-shaped cavities. To further understand the higher order FE-BI method and its applications to the modeling of interior scattering from very large practical perfect electric conductor (PEC) cavity structures, two aspects will be discussed in this paper. The first is on the development of a new integration method to accurately handle singular integrals in calculating BI matrix elements resulted from higher order basis functions defined on higher order elements. The second is on the numerical and experimental verifications of the higher order FE-BI code developed and its applications to the study of the effects of cavity shape, termination and aperture coupling on the interior scattering from large PEC cavities

Preconditioned Formulation of FE-BI Equations With Domain Decomposition Method for Calculation of Electromagnetic Scattering From Cavities

A new formulation of finite element-boundary integral (FE-BI) equations with non-overlapping and non-conforming domain decomposition method (DDM) is proposed to calculate electromagnetic scattering from cavities. The computational domain is divided into two parts: cavity and non-cavity domains. Tetrahedral elements with higher order and lower order vector basis functions are used in the cavity and non-cavity domains, respectively, and they are not conformal on the interface between two sub-domains. The application of Robin transmission condition at the aperture of the cavity relates the fields in the interior and exterior regions of the cavity. In addition, an effective preconditioner is designed to speed up the solution process of iterative solvers. Numerical results obtained show that the proposed method is suitable for this class of problems, and the preconditioner is highly effective to reduce the number of iterations for the solution.

Integral Equation Formulations for Characteristic Modes of Dielectric and Magnetic Bodies

Five types of surface integral equation (IE) formulations are presented to determine the characteristic modes of dielectric and magnetic bodies. It should be noted that these five formulations are derived in a unified manner. Instead of directly using the IE coefficient matrices of scattering problems, this paper presents the formulations in a more natural and rigorous way. The IE formulations result in the generalized real symmetric eigenvalue equations for the characteristic modes. It is found that the eigenvalues of the first four formulations indicate the negative or positive imaginary part of the complex power of the characteristic modes, which are zero at resonance. The first two IE formulations result in two new generalized eigenvalue equations, while the last three IE formulations lead to the same generalized eigenvalue equations as in the references. Moreover, the first two formulations can be immune from spurious modes from which the third and fourth formulations suffer.

Modeling of Waveguide Structures Using DG-FETD Method With Higher Order Tetrahedral Elements

In this paper, the discontinuous Galerkin (DG) finite-element time-domain (FETD) method is developed to model electromagnetic (EM) structures with waveguide excitations. Several specific issues about the DG-FETD modeling are addressed. First, the higher order tetrahedral elements are employed to accurately model the geometry of EM structures and effectively reduce the dispersion error so that the efficiency of the FETD method is increased. To further increase the efficiency of the DG-FETD method, the local time-stepping scheme is applied. Secondly, the conformal perfect matching layer (PML) is applied to terminate the waveguide. The formulation of the conformal PML is presented in this paper. Thirdly, a novel approach is proposed to extract the S-parameters of waveguide structures. This approach applies the surface magnetic current to excite the EM fields in the waveguide structures. Taking advantage of the relationship between the excitation current and excited fields in the uniform waveguide, one can readily obtain the incident electric fields that are required for calculating the S-parameters. This approach avoids the pre-simulation of the uniform waveguide. Finally, the numerical results are given to validate the DG-FETD modeling.

Higher-Order DG-FETD Modeling of Wideband Antennas With Resistive Loading

A discontinuous Galerkin finite-element time-domain (DG-FETD) method with higher-order tetrahedral elements is developed to model wideband antennas with resistive loading. To fully characterize the wideband fundamental parameters of the antennas with multiscaled structures, several schemes are adopted to effectively model resistive loading and accurately calculate return loss, directivity, and radiation pattern. Successful simulation of interesting antennas using the proposed DG-FETD method demonstrates its capability of modeling wideband antennas without or with resistive loading.

Modeling of interior scattering from 3D cavity using FE-BI method with higher-order tetrahedral element

Finite element-boundary integral (FE-BI) method is a powerful tool to model electromagnetic scattering from three-dimensional large, deep, and arbitrarily-shaped cavities. The FE-BI method with higher-order tetrahedral element has been implemented to evaluate the interior electromagnetic scattering from typical and unconventional cavity structure. Using this method, we can understand the underlying phenomena of scattering from various cavities, which will benefit the design of realistic cavity structure

FE-BI formulation for characteristic modes of general bodies

This paper presents a finite element-boundary integral (FE-BI) formulation for determination of the characteristic modes of general bodies. The finite element (FE) method is used to handle the general bodies with composite material, while the boundary integral (BI) method is applied on the boundary of the general bodies to model the open region outside the general bodies. A type of symmetric FE-BI formulation is applied to obtain a generalized Hermitian eigenvalue equation for characteristic modes. Numerical results are provided to validate the proposed FE-BI formulation for characteristic modes.

Preconditioner for modeling EM scattering from cavities using FE-BI equations with domain decomposition method

Electromagnetic scattering from cavities can be accurately simulated using the formulation of finite element-boundary integral (FE-BI) equations with domain decomposition method (DDM). The matrix of its resultant system of equations is usually ill-conditioned and the resultant system of equations has to be preconditioned for speeding up iterative solution process. To precondition the resultant matrix equation, we propose a preconditioner, namely finite element-Robin transmission condition-absorber boundary condition (FE-RTC-ABC) system, which is a natural extension of FE-ABC system developed by Liu and Jin. Preliminary numerical results obtained show the effectiveness of the proposed preconditioner for solving cavity problems.

Formulation of FE-BI equations with domain decomposition method for calculation of em scattering from cavities

In this paper, a new formulation of finite element-boundary integral (FE-BI) equation with domain decomposition method is proposed to compute the electromagnetic (EM) scattering from cavities. The computational domain is divided into two parts: cavity and non-cavity domains. Tetrahedral elements with higher-order and lower-order vector basis functions, which are non-conforming elements, are used in the cavity and non-cavity domains, respectively. The application of Robin transmission condition at the aperture of the cavity relates the fields in the interior and exterior regions of the cavity. Preliminary numerical results obtained show that the proposed method is suitable for this class of problems.

MODAL METHOD ANALYSIS OF MULTILAYERED COATED CIRCULAR WAVEGUIDE USING A MODIFIED CHARACTERISTIC EQUATION

MODALMETHODANALYSISOFMULTILAYEREDCOATEDCIRCULARWAVEGUIDEUSINGAMODIFIEDCHARACTERISTICEQUATIONF.-G.Hu,C.-F.Wang,Y.Xu,andY.-B.GanTemasekLaboratoriesNationalUniversityofSingapore10KentRidgeCrescent,Singapore119260Abstract—In this paper, the modal method is applied to analyzecoated circular waveguide terminated by a perfect electric conductor(PEC) plate. The key to this method is the accurate calculationof the propagation constants of modes in coated circular waveguide.To overcome numerical difficulties, such as overflow, encountered insolvingcharacteristicequation,thecharacteristicequationismodifiedusing Hankel function of the second kind instead of Bessel functionof the first kind in the coated layers. The modified characteristicequationcanbeaccuratelysolvedtoobtainthepropagationconstantseven for very large circular waveguide with highly lossy coatings.To verify the modified characteristic equation, the attenuationand scattering property of circular waveguide structure have beensimulated. Simulationresultsagreewellwiththereferenceresults.1 Introduction2 CharacteristicEquationanditsModification3 ScatteringAnalysisofCircularCoatedWaveguide4 NumericalResults5 ConclusionsReferences