A highly effective preconditioner for solving the finite element-boundary integral matrix equation of 3-D scattering

A highly effective preconditioner is presented for solving the system of equations obtained from the application of the hybrid finite element-boundary integral (FE-BI) method to three-dimensional (3-D) electromagnetic scattering problems. Different from widely used algebraic preconditioners, the proposed one is based on a physical approximation and is constructed from the finite element method (FEM) using an absorbing boundary condition (ABC) on the truncation boundary. It is shown that the large eigenvalues of the finite element (FE)-ABC system are similar to those of the FE-BI system. Hence, the preconditioned system has a spectrum distribution clustered around 1 in the complex plane. Consequently, when a Krylov subspace based method is employed to solve the preconditioned system, the convergence can be greatly accelerated. Numerical results show that the proposed preconditioner can improve the convergence of an iterative solution by approximately two orders of magnitude for large problems.     

Experimental study of a flange mounted waveguide as a device for square radiation pattern

A slotted flange mounted on a waveguide has been studied for use as a feed with deep reflectors. TheE-plane patterns have large beamwidths and are reasonably square. A comprehensive device, consisting of a slotted flange mounted on a square aperture, has been designed and fabricated using the optimum slot width values of the slotted flange waveguide system. The amplitude, phase, and bandwidth characteristic of this device satisfy the requirements of a feed for deep reflectors.     

Spectral Two-Step Preconditioning of Multilevel Fast Multipole Algorithm for the Fast Monostatic RCS Calculation

A new spectral two-step preconditioning of multilevel fast multipole algorithm (MLFMA) is proposed to solve large dense linear systems with multiple right-hand sides arising in monostatic radar cross section (RCS) calculations. The first system is solved with a deflated generalized minimal residual (GMRES) method and the eigenvector information is generated at the same time. Based on this eigenvector information, a spectral preconditioner is defined and combined with a previously constructed sparse approximate inverse (SAI) preconditioner in a two-step manner, resulting in the proposed spectral two-step preconditioner. Restarted GMRES with the newly constructed spectral two-step preconditioner is considered as the iterative method for solving subsequent systems and the MLFMA is used to speed up the matrix-vector product operations. Numerical experiments indicate that the new preconditioner is very effective with the MLFMA and can reduce both the iteration number and the computational time significantly.     

Design of a low loss SAW reflector filter with extremely widebandwidth for mobile communication systems

The design and performance of a low-loss surface acoustic wave (SAW) reflector filter are presented. The structure is a dual-track configuration incorporating two interdigital transducers (IDTs) and reflectors in each track. Extremely wide bandwidth can be obtained if chirped IDTs and reflectors are used. From the theoretical conditions for low-loss operation of the reflector filter, a design rule for the distances between the chirped components and for their lengths is derived. Because the transfer function of the filter is predominantly determined by the reflectors, a new synthesis method for chirped reflectors has been developed. For the design of the reflectors, phase-weighting and finger-width-weighting techniques were used to reduce passband distortions and improve the shape factor and stopband rejection. The filter has been fabricated on 128° YX-LiNbO₃ . The center frequency and fractional bandwidth are 200 MHz and 100%, respectively, the minimum insertion loss is 4 dB, a passband ripple is about 1 dB, and the stopband rejection is better than 35 dB     

Calculated scan characteristics of a large spherical reflector antenna

A previously published numerical method to calculate the radiation properties of parabolic reflectors has been modified to also include very large spherical reflectors. The method has been verified by comparing the calculated and the measured results for a 120-wavelength spherical reflector.     

A single-level dual rank IE-QR algorithm to model large microstrip antenna arrays

A single-level dual rank IE-QR algorithm is introduced so that the resulting dense method of moments (MOM) matrix is efficiently compressed. For a system of N equations, an amount of work of the order O(N/sup 2/) has traditionally been required for both matrix assembly and matrix-vector multiplication in an iterative matrix solver. The algorithm of the present paper reduces the memory requirement and CPU time for both matrix assembly and matrix-vector multiplication to O(N/sup 3/2/) making it practical to solve for large antenna arrays with full wave approach. In conjunction with a "geometric-neighboring" preconditioner for matrix solution using GMRES, the current approach solves problems involving large antenna arrays using only a fraction of what are needed by conventional MOM both in term of memory and total CPU time.     

Reduced-order preconditioning for bidomain simulations

Simulations of the bidomain equations involve solving large, sparse, linear systems of the form Ax = b. Being an initial value problems, it is solved at every time step. Therefore, efficient solvers are essential to keep simulations tractable. Iterative solvers, especially the preconditioned conjugate gradient (PCG) method, are attractive since memory demands are minimized compared to direct methods, albeit at the cost of solution speed. However, a proper preconditioner can drastically speed up the solution process by reducing the number of iterations. In this paper, a novel preconditioner for the PCG method based on system order reduction using the Arnoldi method (A-PCG) is proposed. Large order systems, generated during cardiac bidomain simulations employing a finite element method formulation, are solved with the A-PCG method. Its performance is compared with incomplete LU (ILU) preconditioning. Results indicate that the A-PCG estimates an approximate solution considerably faster than the ILU, often within a single iteration. To reduce the computational demands in terms of memory and run time, the use of a cascaded preconditioner was suggested. The A-PCG was applied to quickly obtain an approximate solution, and subsequently a cheap iterative method such as successive overrelaxation (SOR) is applied to further refine the solution to arrive at a desired accuracy. The memory requirements are less than those of direct LU but more than ILU method. The proposed scheme is shown to yield significant speedups when solving time evolving systems.     

预条件共轭梯度法在大型振子阵列天线RCS分析中的应用

本文提出三重Toeplitz线性方程组预条件共轭梯度法,并将该法与快速付里叶变换(FFT)结合.这种结合算法称为PCGFFT.将PCGFFT应用于振子阵列天线的RCS分析中.由于预条件器的使用,系数矩阵的条件数得到了很大改善.数值结果表明,PCGFFT不仅降低了对计算机内存的需求,加快了迭代速度而且提高了算法的收敛性.     

Performance Study of Thermoelectric Solar-Assisted Heat Pump with Reflectors

The simultaneous conversion of solar radiation into thermal and electrical energy in a thermoelectric (TE) solar-assisted heat pump is, for the purposes of this study, referred to as hybrid conversion. To capture more thermal and electrical energy, flat-plate reflectors have been mounted on a TE solar collector. To obtain higher solar radiation intensity on the TE solar collector, the position of the reflectors has been changed and the optimal position of the reflectors determined by both experimental measurements and numerical calculation so as to obtain maximal concentration of solar radiation intensity. The calculated values have been found to be in good agreement with measured ones. Improvements to the thermal energy and electrical power outputs of the system can be achieved by the use of the TE solar-assisted heat pump with reflectors. For the optimum position of the reflectors, the coefficient of performance (COP) of the system formed from a TE solar collector integrated with a heat pump (TESC-HP) was 5.60. The power output and conversion efficiency of the TE modules can reach 10.09 W and 2.40%, respectively, being improved by 34.5% and 18.2%, respectively, compared with the TESC-HP without reflectors.     

一种新型针对快速多极子法(FMM)的预条件技术

提出了一种针对FMM近场作用矩阵块的不完全LU预条件方法。和传统单纯依靠填充参数来控制非零元素个数的ILU分解方法相比，该方法由于引入了数值丢弃阈值，因而可获得性能更好的预条件矩阵。利用该项预条件技术，迭代过程变得更健壮，而且收敛也更快，计算花费的时间也更少。数值实验表明：这种基于双丢弃准则的ILUT预条件技术，是一种非常适合FMM计算的预条件处理方法。     

有耗半空间环境中导体目标电磁散射的快速分析

应用快速多极子方法求解有耗半空间环境中任意三维金属体的雷达散射特性.对于基函数与测试函数的近场组作用,我们用离散复镜像法严格处理半空间并矢格林函数.在处理远场区时,我们利用实镜像源和反射系数近似计算交界面处远场的作用.通过位于有耗半空间三面角反射器、立方体证明了方法的正确性和有效性.另外,将多分辨预处理器和快速多极子方法结合使得矩阵求解器的迭代次数和计算时间减少数倍.     

Diffraction synthesis and experimental verification of a quasi-optical power splitter at 150 GHz

A general and flexible synthesis method based on the physical optics approximation is proposed for computing smooth-surface reliefs of reflectors. As a design example, the method has been applied to a quasi-optical power splitter consisting of two reflectors in a dual-offset configuration that couples a launched beam from a pyramidal horn antenna into a 2/spl times/4 horn antenna array. The two reflectors were treated as diffractive phase elements so that the proposed synthesis method allows reflector designs for many applications. The quasi-optical design has been confirmed at 150 GHz utilizing a vector field measurement system. The measured field distribution in the receiving antenna array plane is compared with the simulated one and shows a very good agreement.     

“邻居单元”为基础的预条件方法及其应用

该文提出了一种具有物理意义的预条件方法--"邻居单元"为基础的预条件方法。该方法充分考虑了矩阵元素中的"主要"信息量,可以有效加快迭代收敛速度。在构造预条件因子时,采用从目标的"几何结构剖分"出发,而不是从"矩阵元素"出发确定"基权函数之间的作用量关系",这样保证了构造预条件矩阵的计算复杂度仅为O(N)。作为实例,该文将这种预条件方法与共轭梯度方法结合应用于矩量法基站天线分析所得方程的求解,数值结果表明了该文方法的有效性。     

大变倍比长波红外连续变焦光学系统设计

针对长波制冷式384×288焦平面探测器,设计了一款大变倍比长波红外连续变焦距光学系统。整个系统由8片透镜及两个反射镜构成,工作波长范围为7.7～9.3 m,F数为3,满足100%冷光阑效率,变倍比为25:1。采用CODE V光学设计软件进行优化设计,设计结果表明,该系统具有结构简单、变倍比大、体积小、像质好等优点。     

求解Helmholtz方程的新型稀疏近似逆预条件算法

提出了一种新型预条件算法,用于对有限元法离散Helmholtz方程所产生的大型稀疏复对称且高度不定的线性系统进行高效迭代求解。该新型预条件子是在复拉普拉斯偏移算子的基础上结合改进的稀疏近似逆算法来得到。通过改善矢量有限元线性系统自身的谱特性,该预条件算法既可避免迭代中的不稳定情况,同时也能较大提高迭代求解效率。数值结果表明,与若干常用预条件算法相比,所提出的预条件算法更加有效。     

基于极化定标的极化隔离度空变分析

极化定标是多极化合成孔径雷达(PolSAR)系统获取真实目标极化散射矩阵的必要步骤。文中针对极化定标过程中存在的极化隔离度距离向空变特性,采用基于无源角反射器的极化定标算法作为仿真工具,对PolSAR系统极化隔离度绝对值及其空变范围对图像中极化隔离度的影响规律进行了分析。分析结果表明:当用于极化修正的极化误差矩阵与PolSAR系统自身极化隔离度不匹配时,极化修正将会使得修正后的图像极化隔离度变差。因此,在进行极化定标时,应当尽可能在定标场沿距离向布设一定间距的多组定标器,从而获取PolSAR系统在整个距离向成像带宽内的极化隔离度拟合曲线,在进行极化修正时对图像中距离向不同的像素点采用曲线中对应位置的极化误差矩阵进行修正,进而得到尽可能接近目标真实极化散射矩阵的估计值。     

An Efficient MAINV Preconditioned COCG Method for FEM Analysis of Millimeter Wave Filters

The modified AINV (MAINV) sparse approximate inverse preconditioner is applied to the conjugate orthogonal conjugate gradient (COCG) iterative method for solving a large systems of linear equations resulting from the use of edge finite element method (FEM). The proposed preconditioner is derived from basic AINV process by adding pivots compensation strategy to avoid the potential breakdowns. Numerical experiments on several typical millimeter wave structrues demonstrate the effectiveness of the MAINV-COCG method, in comparison with other conventional methods.     

Feed-reflector design for large adaptive reflector antenna (LAR)

A novel feed-reflector system for large Cassegrain antennas of radio astronomy and deep-space communication applications is investigated. This feed-reflector is used to illuminate a hyperboloid subreflector with a 5-10 m diameter located 500 m above the ground. Because the subreflector is located in the near field of the feed-reflector antenna, a theory based on the near field focusing properties of paraboloid reflectors is established. The focusing at near distance is formed by moving the feed horn away from the focal point of the feed-reflector. In this theory, the properties of axial defocused paraboloid reflectors at near distance are investigated in more detail. By using equivalence path law, the subreflector shape is obtained. It is found that the hyperbola can approximate the subreflector well. A detailed ray tracing is performed on the entire system which reveals that the feed system uses some part of the subreflector three times. The gain, side lobe level, cross polarization, and aperture distribution are calculated for different feed horn locations and taper at the edge of the feed-reflector and also for different sizes and eccentricities of the subreflector. Peak efficiency in excess of 74.8% and side lobe level around -20 dB are obtained for an unshaped system. The performance of the system over the operating band (1-22 GHz) is also studied and shown that the lower-frequency limit is dependent on subreflector and feed-reflector sizes     

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).