Hou-Xing Zhou

An IE-ODDM-MLFMA Scheme With DILU Preconditioner for Analysis of Electromagnetic Scattering From Large Complex Objects

For electrically large complex electromagnetic (EM) scattering problems, huge memory is often required for most EM solvers, which is too difficult to be handled by a personal computer (PC) even a workstation. Although the multilevel fast multipole algorithm (MLFMA) effectively deals with electrically large problems to some extent, it is still time and memory consuming for very large objects. In order to further reduce the CPU time and the memory requirement, a hybrid algorithm, based on the overlapped domain decomposition method for integral equations (IE-ODDM), MLFMA and block-diagonal, incomplete lower and upper triangular matrices (DILU) preconditioner, is proposed for the analysis of electrically large problems. The dominant memory requirement for plane wave expansions in the three processes of aggregation, translation and disaggregation in the MLFMA is drastically reduced by the first two techniques. The iterative procedure for each overlapped subdomain solved by the MLFMA is effectively sped up by the DILU preconditioner. After integrating these techniques, the proposed hybrid algorithm is more efficient in computing time and memory requirement compared to the conventional MLFMA and is more suitable for analyzing very large EM scattering problems. Enough accurate solution can be obtained within quite a few outer iterations, where an outer iteration means a complete sweep for all the subdomains. Some numerical examples are presented to demonstrate its validity and efficiency.

A Highly Accurate FGG-FG-FFT for the Combined Field Integral Equation

In this paper, a novel realization of the Integral Equation in combination with the fast Fourier transform for the CFIE is established by Fitting both the Greens function and its Gradient onto the nodes of a uniform Cartesian grid. The new method has been compared with several existing popular FFT-based methods, including the AIM, the IE-FFT, and the p-FFT. The accuracy of the proposed method is significantly higher than other FFT-based methods, and the method is not sensitive to both the grid spacing and the expansion order. The outstanding merit of the proposed method is that the fitting procedure is independent of the basis functions. Therefore, when the higher order basis functions would be adopted in the method of moments, only one fitting procedure for the Greens function and its gradient on a basis function support is needed to meet all of basis functions defined on this support. Some numerical examples are provided in this paper to demonstrate the accuracy and efficiency of the proposed method.

Higher Order Method of Moments With a Parallel Out-of-Core LU Solver on GPU/CPU Platform

In this paper, a full realization of the higher order method of moments (HMoM) with a parallel out-of-core LU solver on GPU/CPU platform is presented in detail, mainly including three parts: In the first part, both global-auxiliary table and local-auxiliary table are introduced for reducing a lot of tedious and repetitive calculations, and then a realization for GPU-oriented programming is proposed and optimized. In the second part, an overlapped grouping of all the curved quadrilaterals is proposed. With this scheme, all the submatrices can be efficiently generated one by one without wasting any calculations with the help of both the video memory and the host memory. In the third part, a GPU-based out-of-core algorithm for LU decomposition is proposed and further developed into a hybrid GPU/CPU algorithm. Numerical examples are provided to test the robustness of the proposed algorithm by comparison with the measurement and/or the traditional MoM with RWG basis functions, and to demonstrate the overall performance of the proposed algorithm by comparison with the existing algorithm for dealing with similar problems. The speedup ratio of the proposed algorithm for generating the HMoM matrix can achieve about from 7 to 12 compared with the GPU-based algorithm in literatures. Also compared with the 8-threaded CPU-based algorithm, the speedup ratio of the proposed algorithm for LU decomposition can exceed 13 for the single precision case and 7 for the double precision case.

An Accurate Interpolation Scheme With Derivative Term for Generating MoM Matrices in Frequency Sweeps

A new accurate impedance matrix interpolation algorithm is proposed for frequency sweeps arising in the method of moments (MoM). Its performance is optimized by specifying the choice of the internal frequency sample within a given frequency band. The modified matrix element employed in this scheme is a product of the normalized frequency and the remaining part of the impedance matrix element after factoring out the dominant phase term, where the normalized frequency means that the frequency is normalized by the highest frequency. Based on the modified matrices at three normalized frequency samples and the derivative of the modified matrix at the internal sample, the matrices over the frequency band are fast generated via interpolation. The proposed scheme requires the same storage as the Hermite scheme and 25% storage more than the improved Lagrange scheme. Numerical examples indicate that it yields more accurate matrices over the frequency band than both the Hermite scheme and the improved Lagrange scheme.

Accurate Evaluation of Green's Functions for a Lossy Layered Medium by Fast Extraction of Surface- and Leaky-Wave Modes

In this paper, a method based on consecutive perturbation for the fast and accurate extraction of all useful surface- and leaky-wave modes for a lossy layered medium is proposed. The algorithm consists of two perturbation stages. In the first stage, according to the relationship for the frequency variation between the surface- and leaky-wave modes, the leaky-wave modes for a lossless medium can be tracked by consecutive frequency perturbation, with the surface-wave modes at a proper high frequency as starting points. All the surface-wave modes are extracted by a modified dichotomy method. In the second stage, a consecutive loss perturbation is performed, in which the mediums loss is increased step by step. In each perturbation step of both of the two stages, Newton-Raphson iterations are employed to update the modes on the corresponding Riemann sheet. With these discrete modes accurately extracted, a combination of the Discrete Complex-Image Method (DCIM) and the All-Modes Method can be realized for accurate evaluation of the Greens functions in the near-field and non-near-field regions, respectively. Several numerical examples demonstrated the high accuracy and efficiency of this method.

A novel FG-FFT method for the EFIE

In this paper, a novel realization of the FFT-based methods for the EFIE with high accuracy is established by fitting the Greens function onto the nodes of a uniform Cartesian grid. Like the IE-FFT, the focus of the proposed method is the Green function, but the accuracy of new method is significantly higher than that of the IE-FFT. Some numerical examples are provided to demonstrate the accuracy and efficiency of the proposed method.

Analysis of Multiscale Problems Using the MLFMA With the Assistance of the FFT-Based Method

A new method for analysis of multiscale problems using the multilevel fast multipole algorithm (MLFMA) is proposed. In this method, the MLFMA bears the main part of the computation at the macro level, while some FFT-based method is responsible for the computation on the subregion with liner meshes. With this strategy, a reasonable balance between the computational efficiency and storage efficiency can be achieved in the case when the local regions with tiny geometry features are relatively centralized. The new method has been compared with several existing methods, including the hybrid method of the MLFMA and LFFIPWA, the MLFMA equipped with the hybrid tree structure (HTS), and the MLFMA with the near-matrix compression, such as the ID-MLFMA and the MLFMA-ACA. Numerical examples are provided to demonstrate the correctness and efficiency of the proposed method.

Microstrip Folded Dipole Antenna for 35 GHz MMW Communication

A microstrip asymmetric folded dipole antenna on chip is proposed in this paper. The construction of balun feed line is adopted to provide wideband. A new design procedure based on the odd-even mode method to calculate the input impedance of an asymmetric strip folded dipole antenna is presented. The folded dipole antenna has the advantage of small size, low profile, low cost, and so forth. The measured results show that a miniaturized antenna has the bandwidth of more than 14.2% (VSWR 2); gain of the antenna is 5.7 dB at 35 GHz.

Accuracy Improvement of Cubic Polynomial Inter/Extrapolation of MoM Matrices by Optimizing Frequency Samples

A cubic polynomial inter/extrapolation method is investigated to improve the inter/extrapolation accuracy of the matrix over a frequency band in the method of moments (MoM). In the method, the error of the MoM matrix in the Frobenius norm can be expressed as a product of the error coefficient and the polynomial component. The error coefficient is insensitive to the positions of the frequency samples and the operating frequency, and hence it is practical to minimize the amplitude of the polynomial component rather than the error of matrix by optimizing the frequency samples. Actually, the amplitude of the polynomial component attains the minimum when the frequency samples are analytically expressed in terms of the roots of the Chebyshev polynomial of degree 4. Numerical examples are presented to validate the proposed method.

Accurate location of all surface wave modes for Green's functions of a layered medium by consecutive perturbations

In this paper, an efficient method is proposed to quickly and accurately locate all the surface wave modes of spectral Green’s functions of a layered medium. This method consists of two parts. In the first part, all the surface wave poles without considering the medium loss are located by a modified dichotomy on the real axis in the complex plane. In the second part, consecutive perturbations with respect to the medium loss are performed, which means that the medium loss is increased step by step from zero to the given value, and at each step, the Newton-Raphson algorithm is employed to find all the current poles, with the poles at the previous step as initial values. The residues of the surface wave poles are analytically calculated without any contour integral. The whole procedure is based on the recursively rational forms of spectral Green’s functions. As an application, all the surface wave poles and their residues obtained by the method proposed in this paper are applied in evaluation of the spatial Green’s functions by the discrete complex image method. Some numerical examples are provided to validate the correctness and efficiency of the proposed method.