波导混合模问题的修正边界元法分析

本文建立了分析波导混合模问题的修正边界元模型;导出了关于混合模的耦合边界积分方程组及其退化形式,并用矩量法将之离散为齐次代数方程组,从而得波导的混合模传输常数;最后以部分介质填充波导为例进行了计算,所得结果与横向谐振法结果吻合得很好。     

Finite element computation of electromagnetic fields [hyperthermiatreatment]

A three dimensional finite element solution scheme is developed for numerically computing electromagnetically induced power depositions. The solution method is applicable to those problems for which it can be reasonably assumed that the magnetic permeability is homogeneous. The method employs an incident field/scattered field approach where the incident field is precalculated and used as the forcing function for the computation of the scattered field. A physically logical condition is used for the numerical boundary conditions to overcome the fact that electromagnetic problems are generally unbounded (i.e., the boundary condition is applied at infinity) but numerical models must have a boundary condition applied to some finite location. At that numerical boundary, an outgoing spherical wave is simulated. Finally, an alternate to a direct solution scheme is described. This alternate method, a preconditioned conjugate gradient solver, provides both a storage and CPU time advantage over direct solution methods. For example, a one-thousand fold decrease in CPU time was achieved for simple test cases. Unlike most iterative methods, the preconditioned conjugate gradient technique used has the important property of guaranteed convergence. Solutions obtained from this finite element method are compared to analytic solutions demonstrating that the solution method is second-order accurate     

Indirect boundary element method applied to generalizedmicrostripline analysis with applications to side-proximity effect inMMIC's

A novel analysis of the electrical properties of the microstrip-like structures with generalized configuration by means of the indirect boundary element method (BEM) is proposed. In this method, the basic boundary-integral equation is derived by choosing an appropriate fundamental solution and the numerical calculation is done by considering the root-singularity of the boundary distribution on the strip conductor. As an application, the proximity effects in monolithic microwave integrated circuits (MMICs) are calculated. By curve-fitting, the numerical results are expressed in a polynomial suitable for CAD for MMICs     

Efficient analytical and numerical methods for the computation of bent loss in planar waveguides

In this paper, we present new analytical and numerical modal analyses of bent planar waveguides allowing precise computation of the bending loss. The analytical method is based on an accurate algorithm for evaluating Bessel and Hankel functions. The numerical one relies on a finite-element model derived from the cylindrical coordinates version of the Maxwell system. To eliminate spurious reflections from the artificial boundary of the computational domain, an efficient perfectly matched layer technique is adapted to the formulation. A thorough comparison shows that our analytical approach is both simple and highly accurate whereas the numerical method is cheap and easily extendible to higher dimensions and other geometries.     

The novel boundary integral equation method for solving arbitrary cross-section waveguides

A novel method for solving arbitrary cross-sectionn waveguides is presented. The novel method is a modification of the eigen-weighted boundary integral equation method; the EWBIEM is modified by using the eigenfunction of a fictitious regular boundary as weighting function, whose eigenvalue may be the known value, and meanwhile using the domain-bases. To confirm the validity of the novel method, numerical analysis are presented for circular groove guide as an example.     

Equivalent Boundary Conditions for Isotropic Arrays

Inductive and capacitive isotropic ribbon arrays with a period small compared with the wavelength, placed at the interface between two media, are considered. Boundary value problems for the scattering of plane waves of two polarizations, incident onto the arrays at arbitrary angles, are formulated. The boundary value problems are solved by the Galerkin method. A model of an array is proposed in the form of a semitransparent film on the surfaces of which equivalent boundary conditions relating the fields on both sides of the surfaces are imposed. The theoretical solution is compared with a numerical solutions obtained using a standard system of electromagnetic simulation. It is shown that, in the low-frequency region, the equivalent boundary conditions describe the behavior of the arrays with good accuracy.     

An efficient numerical method for the small-signal AC analysis of MOS capacitors

A numerical method for the small-signal ac analysis of MOS capacitors is presented. The equations describing device operation, which comprise a boundary value problem, are formulated as an initial value problem and are solved by a shooting method. This results in a numerically stable and efficient algorithm for their solution. The recognized ill-conditioning of the boundary value problem, manifesting itself in numerical instabilities in the conductance-voltage characteristics of MOS capacitors is addressed. Calculated small-signal ac admittance as a function of gate bias for homogeneously doped and ion-implanted devices is shown. The high- "and low-frequency" positional dependence of convection and displacement current densities is determined.     

Analysis of the Scattering Characteristic of Several Waveguide Components Using Boundary Element Method

Several kinds of waveguide components such as curved waveguide bends, arbitrary angle waveguide bends and T-junctions have been analyzed with boundary element method in this paper. A new discretization method for the boundary element method to solve the waveguide discontinuities has been given. The numerical results obtained agree well with the experimental results and numerical results in other literature. Especially, the scattering characteristics of Forded E-, H-plane T-junctions in 3mm band have been analyzed using boundary element method and the calculation results are presented.     

The time-domain discrete Green's function method (GFM)characterizing the FDTD grid boundary

For a given FDTD simulation space with an arbitrarily shaped boundary and an arbitrary exterior region, most existing absorbing boundary conditions become inapplicable. A Green's function method (GFM) is presented which accommodates arbitrarily shaped boundaries in close proximity to a scattering object and an arbitrary composition in the exterior of the simulation space. Central to this method is the numerical precomputation of a Green's function tailored to each problem which represents the effects of the boundary and the external region. This function becomes the kernel for a single-layer absorbing boundary operator, it is formulated in a manner which naturally incorporates numerically induced effects, such as the numerical dispersion associated with the FDTD scheme. The Green's function is an exact absorber in the discretized space. This property should be contrasted with other methods which are initially designed for the continuum and are subsequently discretized, thereby incurring inherent errors in the discrete space which cannot be eliminated unless the continuum limit is recovered. In terms of accuracy, the GFM results have been shown to be of a similar quality to the PML, and decidedly superior to the Mur (1981) condition. The properties of the GFM are substantiated by a number of numerical examples in one, two, and three dimensions     

Investigation of diffraction of an electromagnetic wave arbitrarily incident on a locally inhomogeneous medium interface

The 3D problem of reflection of a plane electromagnetic wave by an irregular boundary containing a locally inhomogeneous well conducting section is considered. The boundary value problem for the system of Maxwell equations in an infinite section with an irregular boundary is reduced to the solution of systems of singular equations. A numerical algorithm for their solution is developed. Results of calculation of the currents induced on the irregularity and reflected field patterns are presented for the case of the E polarization.     

Computing scattering amplitudes for arbitrary cylinders under incident plane waves

A numerical method to compute scattering amplitudes for time harmonic waves scattered from infinite cylinders with arbitrary uniform cross section is described. A nonlocal boundary condition is used to develop a variational formulation of the scattering problem, and the finite element method is applied to determine approximations to the near field. Scattering amplitudes are then determined by means of an integral representation obtained from Green's formula and properties of the nonlocal boundary operator. Computational results are presented to illustrate the method's application.     

Full-Vectorial Mode Solver for Bending Waveguides Using Multidomain Pseudospectral Method in a Cylindrical Coordinate System

A full-vectorial mode solver for bending waveguides using a spectral collocation method in a local cylindrical coordinate system is described. The perfectly matched layers' absorption boundary conditions are incorporated into the present method for effectively demonstrating the leaky nature of the bending waveguides. The domain decomposition technique is utilized for improving the computational accuracy and stability. A bending rib waveguide with high index contrast is considered as a numerical example to validate the established method.      

The on-surface radiation condition applied to three-dimensionalconvex objects

A numerical method is described for obtaining solutions for electromagnetic scattering from convex three-dimensional objects by invoking the on-surface radiation condition (OSRC). The set of objects for which the numerical method can be employed are those that are describable as bodies of revolution and have surfaces that are perfect electrical conductors. The numerical method is sufficiently general to allow arbitrary angles of incident radiation. In the development of the numerical method the three-dimensional form of OSRC was transformed from a coupled vector partial differential equation to an ordinary differential equation to ease computation. Issues of numerical tractability and boundary conditions also had to be addressed. Comparisons of the numerical solutions of OSRC with accepted scattering results are provided. The objects used in these comparisons are spheres, spheroids, disks, wires, and conespheres     

Solution of the time-optimal control problem for systems of similar structure

A method for the solution of the time-optimal control problem is outlined. It is based on calculating the changes in the unknown boundary conditions with system structure. A simple fourth-order numerical example for the control of a swinging load is given.     

A New Approach to Volumes Irradiated by Unknown Sources

We suggest an approach to the characterization of electromagnetic (EM) environments irradiated by unknown sources. The approach is based on the numerical solution of Maxwell's equations subject to the constraints imposed by the measured values of the field at a small number of measurement points and by boundary conditions. A thorough examination of a method for the numerical solution is presented. The examples attempted demonstrate the approach but reveal deficiencies in the numerical method. Possible future directions are suggested.     

Investigation of a method for numerical solution of nonstationary waveguide equations

Results of numerical time-domain calculation of propagation and transformation of ultrawideband electromagnetic pulses in irregular metal waveguides with a variable section are presented for the example of a coaxial corrugated structure. The calculation is performed with the use of a system of nonstationary waveguide equations. A method for estimation of the computation error is described. The method involves the following components (below, referred to as features): monitoring the energy balance, integral estimation of the error in the calculated field, and estimation of the accuracy of the computational realization of the boundary condition on the boundary of the perfect conductor. With the use of a coaxial corrugated structure as an example, it is shown that, for each of the above features, the application of the proposed polynomial basis in the calculations guarantees an accuracy that substantially exceeds the accuracy of measurements. It is shown that the basis of comparison waveguides provides for highly accurate computations in the rms approximation, in spite of the fact that the application of the third feature is impeded because, for a waveguide with a variable section, the boundary conditions cannot be satisfied on perfectly conducting boundary Γ.     

Scattering analysis of a large body with deep cavities

A numerical scheme is presented for simulating electromagnetic scattering from a large and arbitrarily shaped body, coated with inhomogeneous composite materials, with large and deep cavities. This numerical scheme employs the higher order vector finite-element method (FEM) to discretize the fields inside the cavities and coatings and the higher order boundary integral (BI) method to terminate the FEM computational domain. A highly efficient special solver is designed to eliminate the unknowns inside the cavities, which yields a computed relation (CR) matrix over the cavity's aperture between the tangential electric and magnetic fields. This CR matrix is then combined with the finite element-boundary integral (FE-BI) matrix equation to form a complete linear system for the discrete fields everywhere in the computational domain. The resulting system is solved iteratively using a novel preconditioner derived by replacing the BI with a corresponding absorbing boundary condition (ABC).     

An FDTD model for calculation of gradient-induced eddy currents in MRI system

In most magnetic resonance imaging (MRI) systems, pulsed magnetic gradient fields induce eddy currents in the conducting structures of the superconducting magnet. The eddy currents induced in structures within the cryostat are particularly problematic as they are characterized by long time constants by virtue of the low resistivity of the conductors. This paper presents a three-dimensional (3-D) finite-difference time-domain (FDTD) scheme in cylindrical coordinates for eddy-current calculation in conductors. This model is intended to be part of a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The singularity apparent in the governing equations is removed by using a series expansion method and the conductor-air boundary condition is handled using a variant of the surface impedance concept. The numerical difficulty due to the "asymmetry" of Maxwell equations for low-frequency eddy-current problems is circumvented by taking advantage of the known penetration behavior of the eddy-current fields. A perfectly matched layer absorbing boundary condition in 3-D cylindrical coordinates is also incorporated. The numerical method has been verified against analytical solutions for simple cases. Finally, the algorithm is illustrated by modeling a pulsed field gradient coil system within an MRI magnet system. The results demonstrate that the proposed FDTD scheme can be used to calculate large-scale eddy-current problems in materials with high conductivity at low frequencies.     

ANALYSIS OF 2-D EM PROBLEMS ON A COMPOUND RECTANGULAR REGION BY THE METHOD OF LINES

In this paper an extended method of lines for analyzing the electromagnetic boundary valueproblems is presented and applied to the waveguide with a compound rectangular cross-section.A number ofnumerical results are given for the higher mode analysis in a rectangular waveguide with ridges or fins,and in ashielded stripline.In the computation practice,the random errors caused by the discretization of theboundary conditions are decreased by a least-square procedure.