George W. Pan

Application of Physical Spline Finite Element Method (PSFEM) to Fullwave Analysis of Waveguides

In this paper, the physical spline finite element method (PSFEM) is applied to the fullwave analysis of inhomogeneous waveguides. Combining (rectangular) edge element and the PSFEM, the cubic spline interpolation is successfully applied to the wave equation. For waveguide problems, the resulting nonlinear eigenvalue problem is solved by a simple iteration method in which the initial estimate is taken as the linear Lagrange interpolation, and then the solutions are improved by a few iterations. The bandwidth of the resultant matrix from the PSFEM is the same as that of linear Lagrange interpolation and is sparse. As a result, sparse matrix solver can be used. Three typical examples are demonstrated and compared with the analytical solutions and with the linear Lagrange interpolation results. It is observed that the present method converges much faster than the Lagrange interpolation method.

Smooth local cosine based Galerkin method for scattering problems

The smooth local trigonometric (SLT) functions are employed as the basis and testing functions in the Galerkin based method of moments (MoM), and sparse impedance matrices are obtained. The basic idea of SLT is to use smooth cutoff functions to split the function and to fold overlapping parts back into the intervals so that the orthogonality of the system is preserved. Moreover, by choosing the correct trigonometric basis, rapid convergence in the case of smooth functions is ensured. The SLT system is particularly suitable to handle electrically large scatterers, where the integral kernel behaves in a highly oscillatory manner. Numerical examples demonstrate the scattering of electromagnetic waves from two-dimensional objects with smooth contours as well as with sharp edges. A comparison of the new approach versus the traditional MoM and wavelet methods is provided.

Examination, Clarification, and Simplification of Stability and Dispersion Analysis for ADI-FDTD and CNSS-FDTD Schemes

We describe a rigorous analysis of unconditional stability for the alternating-direction-implicit finite-difference time-domain (ADI-FDTD) and Crank-Nicholson split step (CNSS-FDTD) schemes avoiding use of the von Neumann spectral criterion. The proof is performed in the spectral domain, and uses skew-Hermitivity of matrix terms in the ADI and CNSS total amplification matrices. A bound for the total ADI amplification matrix is provided. While the CN and CNSS-FDTD amplification matrices are unitary, the bound on the ADI-FDTD depends on the Courant number. Importantly, we have found that the ADI-FDTD amplification matrix is not normal, i.e., the unit spectral radius alone cannot be used to prove the ADI-FDTD unconditional stability. The paper also shows that the ADI-FDTD and CNSS-FDTD schemes share the same dispersion equation by a similarity of their total amplification matrices, and the two schemes have identical numerical dispersion in the frame of plane waves.

Full-wave analysis of coupled lossy transmission lines using multiwavelet-based method of moments

Full-wave analysis for coupled lossy transmission lines with finite thickness is conducted using a multiwavelet-based method of moments (MBMM). We use the multiscalets with multiplicity r=2 as the basis and testing functions, and take the discrete Sobolev-type inner products to discretize the integral equation and its derivative at the testing points. Since the numerical integration is not needed in the testing procedure, the new approach is faster, yet preserves high accuracy due to the derivative sampling. In the new approach, we compute the incoming fields in the spatial domain directly without resorting to the inverse Fourier transform. Hence, the local coordinate system used to perform the Sommerfeld integral is avoided and the computational cost is reduced remarkably. In addition, a coarser mesh can be used owing to the smoothness of the multiscalets. Numerical examples show that the MBMM speeds up the traditional method of moments 3 /spl sim/ 10 times.

ON SAMPLING-BIORTHOGONAL TIME-DOMAIN SCHEME BASED ON DAUBECHIES COMPACTLY SUPPORTED WAVELETS

The multi-resolution time domain (MRTD) technique for electromagnetic field equations was proposed by Krumpholz, Katehi et al., using Battle-Lemarie wavelets. The basis principle behind the MRTD is the wavelet-Galerkin time domain (WGTD) approach. Despite its effectiveness in space discretization, the complexity ofthe MRTD makes it unpopular. Recently, the WGTD was significantly simplified by Cheong et al. based on the approximate sampling property ofthe shifted versions ofthe Daubechies compactly supported wavelets. In this paper, we provide a rigorous analysis ofthe MRTD, employing positive sampling functions and their biorthogonal dual. We call our approach as the sampling biorthogonal time-domain (SBTD) technique. The introduced sampling and dual functions are both originated from Daubechies scaling functions of order 2 (referred as to D2), and form a biorthonormal system. This biorthonormal system has exact interpolation properties and demonstrates superiority over the FDTD in terms ofmemory and speed. Numerical examples and comparisons with the traditional FDTD results are provided.

MALVAR WAVELET BASED POCKLINGTON EQUATION SOLUTIONS TO THIN-WIRE ANTENNAS AND SCATTERERS

Malvar wavelets are often referred to as smooth local cosine (SLC) functions. In this paper the SLC functions are employed as the basis and testing functions in the Galerkin-based Method of Moments (MoM) for the Pocklington equation of thin-wire antennas and scatterers. The SLC system has rapid convergence and is particularly suitable to handle electrically large scatterers, where the integral kernel behaves in a highly oscillatory manner. Numerical examples demonstrate the scattering of electromagnetic waves from a thin-wire scatterer as well as wave radiation from the gull-shaped antenna. A comparison of the new approach versus the traditional MoM is provided.

Coifman wavelets in electromagnetic wave scattering by a groove in a conducting plane

Scattering of electromagnetic waves from a groove in an infinite conducting plane is studied using the Coifman wavelets (Coiflets) under the integral equation formulation. The induced current is expressed in terms of the known Kirchhoff solution plus a localized correction current in the vicinity of the groove. The Galerkin procedure is implemented, employing the Coiflets as expansion and testing functions to find the correction current numerically. Owing to the vanishing moments, the Coiflets lead to a one-point quadrature formula in O(h5), which reduces the computational effort in filling the impedance matrix entries. The resulting matrix is sparse, which is desirable for iterative algorithms. Numerical results show that the new method is 2 to 5 times faster than the pulse based method of moments.

Time Harmonic Fields Produced by Circular Current Loops

New analytic expressions for the magnetic and electric fields generated by circular current loops (magnetic dipoles) are derived. They apply to near-zone, Fresnel-zone, and far-zone conditions; they asymptotically reduce to the popular small-loop equations in the far-zone. Analytical expressions for the fields produced by current-carrying conductors are valuable because of their rarity. They offer physical insight and a way to test the numerical methods needed for solving more complex problems. Areas for application include medicine, weapons, and nondestructive testing.

Lens-enhanced phased array antenna system for high directivity beam-steering

This paper investigates a hybrid steerable antenna topology composed of a small phased array and a significantly larger planar lens-array. The phased array antenna creates an electronically steerable beam, and the lens-array further confines the beam to enhance its directivity. The feasibility of this approach is examined via a 60 GHz design example based on a 4 × 4 phased array and a 24 × 24 lens-array. It is observed that adding the lens-array improves the directivity by 2.5–6 dB for beams within 45° of the boresight direction. Since the lens consumes no power and it may be manufactured inexpensively, this improvement comes at very little cost. The overall depth of the system in this example is 1 cm, which is quite small compared to typical lens-based systems. These characteristics make the proposed topology suitable for applications in laptop computers, tablets PCs, PDAs, flat screen TVs and similar products.

A novel subgridding technique for unconditionally stable time domain method

For inhomogeneous electromagnetic (EM) problems, subgridding techniques have been introduced [1, 2], in which coarse grid is used for homogeneous background, while fine grid is employed in the denser area. In the traditional approach, the interface between the two areas is considered as the boundary condition by each other. Recently, a new subgridding technique called HSG (Huygens sub-griding) method is proposed by Berenger [3], in which the physical connection between two areas is realized by means of Huygens surfaces. Instead of EM components, equivalent currents on the Huygens surface become the commuter between the coarse and fine grid regions. In a macroscopic view, EM fields are teleported from the coarse grid region (source domain) to the fine grid one (problem domain) via equivalent currents. The two major features HSG achieved are arbitrarily large spatial ratio and insignificant spurious reflection from the interface. However the drawback of the late time instability restricts its applicability. The oscillation period associated with this phenomenon depends on the spatial size of the source domain and the ratio between time step and the Courant limit.