Radar cross section (RCS) modeling and simulation, part 1: a tutorial review of definitions, strategies, and canonical examples

Modeling and simulation strategies for radar cross section (RCS) prediction are reviewed, and a novel FDTD-based virtual RCS prediction tool is introduced in this two-part paper. Part 1 is reserved for a tutorial review. Concepts and definitions related to RCS modeling are outlined. Analytical approaches, i.e., high-frequency asymptotics (HFA), as well as powerful time- and frequency-domain numerical methods, are given. Canonical examples using the finite-difference time-domain (FDTD) Method, the method of moments (MoM), and physical optics (PO) are presented.     

A parallel FFT accelerated transient field-circuit simulator

A novel fast electromagnetic field-circuit simulator that permits the full-wave modeling of transients in nonlinear microwave circuits is proposed. This time-domain simulator is composed of two components: 1) a full-wave solver that models interactions of electromagnetic fields with conducting surfaces and finite dielectric volumes by solving time-domain surface and volume electric field integral equations, respectively, and 2) a circuit solver that models field interactions with lumped circuits, which are potentially active and nonlinear, by solving Kirchoff's equations through modified nodal analysis. These field and circuit analysis components are consistently interfaced and the resulting coupled set of nonlinear equations is evolved in time by a multidimensional Newton-Raphson scheme. The solution procedure is accelerated by allocating field- and circuit-related computations across the processors of a distributed-memory cluster, which communicate using the message-passing interface standard. Furthermore, the electromagnetic field solver, whose demand for computational resources far outpaces that of the circuit solver, is accelerated by a fast Fourier transform (FFT)-based algorithm, viz. the time-domain adaptive integral method. The resulting parallel FFT accelerated transient field-circuit simulator is applied to the analysis of various active and nonlinear microwave circuits, including power-combining arrays.     

A FDTD-based modal PML

The finite-difference time-domain (FDTD) method is one of the most popular numerical methods for solving electromagnetic problems because of its algorithmic simplicity and flexibility. For an open waveguide structure, modal perfectly matched layer (PML) schemes have been developed as efficient absorbing terminations. However, since these PML schemes are not derived directly from the FDTD algorithm, they do not perform as well as the original three-dimensional (3-D) PMLs. In this letter, a FDTD-based one-dimensional modal PML is proposed. Because it is derived directly from the FDTD formulation, its numerical dispersion characteristics are very close to the original FDTD method. Relative differences between results obtained with the proposed method and the original 3-D PML are found to be less than -220dB, and the proposed modal PML is shown to perform at least the same as the original PML if not better.     

Correction to the analysis of dielectric guides by transversemagnetic field finite element penalty function method with extensions

Recently a method to obtain the propagation constants of lossless dielectric waveguides using the Helmholtz equation with the finite element method and penalty function method was presented. The advantage of using this approach is that only one final eigenvalue matrix needs to be solved for only two components of the H-fields. We have determine that the results were obtained using an eigenvalue solver that did not account for the asymmetry in the final eigenvalue matrix. In this paper, we present the results of the same cases simulated using the correct eigenvalue solver, and the results obtained are in good agreement with previously published ones. We also show by simulation of appropriate cases, a high penalty factor is correlated to highly coupled modes, while weakly coupled modes may be correlated to small penalty factors. Finally, we have extended the penalty function method to include the complex case without the use of the perturbation method. The gain results obtained for a channel waveguide are in good agreement with previously published ones     

Solution of large complex problems in computational electromagnetics using higher-order basis in MoM with out-of-core solvers

In a recent invited paper in the IEEE Antennas and Propagation Magazine, some of the challenging problems in computational electromagnetics were presented. One of the objectives of this note is to simply point out that challenging to one may be simple to another. This is demonstrated through an example cited in that article. The example chosen is a Vivaldi antenna array. What we discuss here also applies to the other examples presented in that article, but we have chosen the Vivaldi antenna array to help us make our point. It is shown in this short article that a higher-order basis using a surface integral equation a la a PMCHWT (Poggio-Miller-Chu-Harrington-Wu-Tsai) method-of-moments formulation may still be the best weapon that one have in today's arsenal to deal with challenging complex electromagnetic analysis problems. Here, we have used the commercially available code WIPL-D to carry out all the computations using laptop/desktop systems. The second objective of this paper is to present an out-of-core solver. The goal is to demonstrate that an out-of-core 32-bit-system-based solver can be as efficient as a 64-bit in-core solver. This is quite contrary to the popular belief that an out-of-core solver is generally much slower than an in-core solver. This can be significant, as the difference in the cost of a 32-bit system can be 1/30 of a 64-bit system of similar capabilities using current computer architectures. For the 32-bit system, we consider a Pentium 4 system, whereas for the 64-bit system, we consider an Itanium 2 system for comparison. The out-of-core solver can go beyond the 2 GB limitation for a 32-bit system and can be run on ordinary laptop/desktop; hence, we can simultaneously have a much lower hardware investment while better performance for a sophisticated and powerful electromagnetic solver. The system resources and the CPU times are also outlined.     

加速SPICE进行三维电磁分析

互连结构的电磁分析越来越受到人们的重视.针对三维互连,A.E.Ruehli提出了部分元等效电路法.但该法生成的等效电路具有紧耦合性,用SPICE进行分析时稀疏矩阵技术已失去原先的优越性.本文采用广义残量法作为大型紧耦合线性方程组的求解工具以取代SPICE中的LU分解法,并辅以初值预估.实际计算表明,本文的方法提高了运算速度.广义残量法也可用于矩量法的方程求解中.     

Two-dimensional computational model of discharge uniformity in radio-frequency-excited CO/sub 2/ slab lasers with high aspect ratio electrodes

A finite difference scheme for the numerical solution of Maxwell's equations in the time domain is utilized for the optimization of discharge uniformity in radio frequency (RF)-excited CO/sub 2/ slab lasers with high aspect ratio electrodes. The field solver can be coupled to standard RF discharge models. The model may be regarded as a natural generalization of the successful transmission line method to two dimensions.     

A Generalized 2-D Multiport Model for Planar Circuits With Slots in Ground Plane

A new approach for multiport network modeling (MNM) of multilayer planar circuits coupled through slots in ground plane is introduced. Generalized network formulation for aperture problems is combined with Okoshi's model for planar circuits to obtain a unified circuit model for two irregularly shaped planar circuits coupled through a slot of arbitrary shape in their common ground plane. The methodology, which can be generalized to structures having more than two layers, is described by applying the method to a two-layer structure. Results for several sample structures will also be presented     

Solving the Coupled System Improves Computational Efficiency of the Bidomain Equations

The bidomain equations are frequently used to model the propagation of cardiac action potentials across cardiac tissue. At the whole organ level, the size of the computational mesh required makes their solution a significant computational challenge. As the accuracy of the numerical solution cannot be compromised, efficiency of the solution technique is important to ensure that the results of the simulation can be obtained in a reasonable time while still encapsulating the complexities of the system. In an attempt to increase efficiency of the solver, the bidomain equations are often decoupled into one parabolic equation that is computationally very cheap to solve and an elliptic equation that is much more expensive to solve. In this study, the performance of this uncoupled solution method is compared with an alternative strategy in which the bidomain equations are solved as a coupled system. This seems counterintuitive as the alternative method requires the solution of a much larger linear system at each time step. However, in tests on two 3-D rabbit ventricle benchmarks, it is shown that the coupled method is up to 80% faster than the conventional uncoupled method-and that parallel performance is better for the larger coupled problem.     

Fast and Rigorous Analysis of EMC/EMI Phenomena on Electrically Large and Complex Cable-Loaded Structures

A fast and comprehensive time-domain method for analyzing electromagnetic compatibility (EMC) and electromagnetic interference (EMI) phenomena on complex structures that involve electrically large platforms (e.g., vehicle shells) along with cable-interconnected antennas, shielding enclosures, and printed circuit boards is proposed. To efficiently simulate field interactions with such structures, three different solvers are hybridized: (1) a time-domain integral-equation (TDIE)-based field solver that computes fields on the exterior structure comprising platforms, antennas, enclosures, boards, and cable shields (external fields); (2) a modified nodal-analysis (MNA)-based circuit solver that computes currents and voltages on lumped circuits approximating cable connectors/loads; and (3) a TDIE-based transmission line solver that computes transmission line voltages and currents at cable terminations (guided fields). These three solvers are rigorously interfaced at the cable connectors/loads and along the cable shields; the resulting coupled system of equations is solved simultaneously at each time step. Computation of the external and guided fields, which constitutes the computational bottleneck of this approach, is accelerated using fast Fourier transform-based algorithms. Further acceleration is achieved by parallelizing the computation of external fields. The resulting hybrid solver permits the analysis of electrically large and geometrically intricate structures loaded with coaxial cables. The accuracy, efficiency, and versatility of the proposed solver are demonstrated by analyzing several EMC/EMI problems including interference between a log-periodic monopole array trailing an aircraft's wing and a monopole antenna mounted on its fuselage, coupling into coaxial cables connecting shielded printed circuit boards located inside a cockpit, and coupling into coaxial cables from a cell phone antenna located inside a fuselage.     

Nested multigrid vector and scalar potential finite element method for fast computation of two-dimensional electromagnetic scattering

Nested multigrid techniques are combined with the ungauged vector and scalar potential formulation of the finite-element method to accelerate the convergence of the numerical solution of two-dimensional electromagnetic scattering problems. The finite-element modeling is performed on nested meshes of the same computational domain. The conjugate gradient method is used to solve the resultant finite-element matrix for the finest mesh, while the nested multigrid vector and scalar potential algorithm acts as the preconditioner of the iterative solver. Numerical experiments are used to demonstrate the superior numerical convergence and efficient memory usage of the proposed algorithm.     

Modeling of smart devices

The precise numerical modeling of electromechanical smart structures and devices is reported. This modeling is performed on the basis of finite and boundary element procedures solving coupled field problems arising in transducer technology. Furthermore, the controler is embedded within the simulation process. Therewith, the numerical computation of the closed loop starting with the sensor and ending with the actuator is performed. Results are shown for an electrostatic excited plate as well as an electromagnetic excited tube, which are both actively damped by controlled piezoelectric actuators.     

Stationary, nonstationary, and hybrid iterative method of momentssolution schemes

The purpose of this paper is to report on the convergence rates of two iterative matrix solution methods individually and then to combine the two methods into a hybrid scheme to achieve additional convergence rate benefits. One iterative matrix solver investigated is the sparse iterative method (SIM) which is a stationary, Jacobi-like solver but uses a sparse and not a banded matrix, with matrix elements corresponding to strong interactions, rather than position in the matrix. In this paper, the SIM is modified to include an adaptive relaxation scheme to improve its convergence speed and numerical stability. Another iterative scheme investigated is the nonstationary biconjugate gradient stabilized (BiCGSTAB) method. It is shown that the BiCGSTAB is considerably improved when the method is preconditioned by the sparse matrix used in the SIM method. Finally, a hybrid scheme is proposed which combines both SIM-AR and BiCGSTAB-precon and it is shown that the hybrid gives best results on the problems considered. Examples giving convergence time versus accuracy are presented for two problems: a wire-grid plate, and a wire-grid partial helicopter     

Hybrid finite element method for describing the electrical response of biological cells to applied fields

A novel hybrid finite element method (FEM) for modeling the response of passive and active biological membranes to external stimuli is presented. The method is based on the differential equations that describe the conservation of electric flux and membrane currents. By introducing the electric flux through the cell membrane as an additional variable, the algorithm decouples the linear partial differential equation part from the nonlinear ordinary differential equation part that defines the membrane dynamics of interest. This conveniently results in two subproblems: a linear interface problem and a nonlinear initial value problem. The linear interface problem is solved with a hybrid FEM. The initial value problem is integrated by a standard ordinary differential equation solver such as the Euler and Runge-Kutta methods. During time integration, these two subproblems are solved alternatively. The algorithm can be used to model the interaction of stimuli with multiple cells of almost arbitrary geometries and complex ion-channel gating at the plasma membrane. Numerical experiments are presented demonstrating the uses of the method for modeling field stimulation and action potential propagation.     

Parallel GMRES solver for fast analysis of large linear dynamic systems on GPU platforms

In this paper, we propose an efficient parallel dynamic linear solver, called GPU-GMRES, for transient analysis of large linear dynamic systems such as large power grid networks. The new method is based on the preconditioned generalized minimum residual (GMRES) iterative method implemented on heterogeneous CPU–GPU platforms. The new solver is very robust and can be applied to power grids with different structures as well as for general analysis problems for large linear dynamic systems with asymmetric matrices. The proposed GPU-GMRES solver adopts the very general and robust incomplete LU based preconditioner. We show that by properly selecting the right amount of fill-ins in the incomplete LU factors, a good trade-off between GPU efficiency and convergence rate can be achieved for the best overall performance. Such tunable feature can make this algorithm very adaptive to different problems. GPU-GMRES solver properly partitions the major computing tasks in GMRES solver to minimize the data traffic between CPU and GPUs to enhance performance of the proposed method. Furthermore, we propose a new fast parallel sparse matrix–vector (SpMV) multiplication algorithm to further accelerate the GPU-GMRES solver. The new algorithm, called segSpMV, can enjoy full coalesced memory access compared to existing approaches. To further improve the scalability and efficiency, segSpMV method is further extended to multi-GPU platforms, which leads to more scalable and faster multi-GPU GMRES solver. Experimental results on the set of the published IBM benchmark circuits and mesh-structured power grid networks show that the GPU-GMRES solver can deliver order of magnitudes speedup over the direct LU solver, UMFPACK. The resulting multi-GPU-GMRES can also deliver 3–12× speedup over the CPU implementation of the same GMRES method on transient analysis.     

A modeling methodology for thermal analysis of the PCB structure

A modeling methodology is proposed for the thermal analysis of the PCB structure based on integrating both the FVM-based numerical solution and the Fourier-series-based analytical solution of temperature. The heat spreading through tracks and the vertical heat transfer through vias are taken into account in a numerical way and regarded as the additional thermal boundary conditions of insulating layers, which are assumed to be homogeneous from an analytical point of view. A methodology based on the vertex-centered Cartesian-grid Finite Volume Method is also proposed for the electric analysis of PCB tracks in order to take into account the temperature-dependent Joule heating effect, thus the current carrying capacity of tracks can be estimated as well. The necessary and sufficient condition for solving electric distributions in multi-terminal tracks is discussed, described and verified through both the analysis of the equivalent resistor network in a multi-terminal track and the mathematical analysis of a matrix equation, which correlates terminal currents with terminal electric potentials. In addition, the method for analyzing the multilayer structure is also discussed. A thermal solver was developed in MATLAB based on the methodology. Several layouts were modeled in the solver and COMSOL to test the validity of the methodology and to investigate the influence factors of the solution. Based on the analysis and comparisons, mesh density and the number of eigenvalues are the main influence factors. The vertical and horizontal heat transfer contributions of vias were also investigated by modeling the footprint layout of a power mosfet in order to test the modeling assumptions. Finally, the consistency between the modeling results and the reference results was found. Both the advantages and disadvantages of the methodology are discussed throughout the analysis.     

AIM Analysis of Electromagnetic Scattering by Arbitrarily Shaped Magnetodielectric Object

A fast solution to the electromagnetic scattering by large-scale three-dimensional magnetodielectric objects with arbitrary permittivity and permeability is presented. The scattering problem is characterized by using coupled field volume integral equation (CF-VIE). By considering the total electric and magnetic fields, i.e., the sum of incident fields and the radiated fields by equivalent electric and magnetic volume currents, the CF-VIE can be established in the volume of the scatterers. The resultant CF-VIE is discretized and solved by using the method of moments (MoM). For large-scale scattering problems, the adaptive integral method (AIM) is then applied in the MoM in order to reduce the memory requirement and accelerate the matrix-vector multiplication in the iterative solver. The conventional AIM has been modified to cope with the two sets of equivalent volume currents.     

Realistic and efficient simulation of electro-thermal effects inVLSI circuits

Needs for electro-thermal simulation of VLSI circuits, as opposed to both the system and device levels, are analyzed. A system capable of modeling these effects in a realistic and sufficiently accurate way that uses a reasonable amount of CPU resources is presented. An innovative solver is also proposed. The system is used to study the importance of some three dimensional (3-D) effects as well as metallic connections. A complete example was treated to have an insight on the type of results to be expected and the corresponding costs in terms of CPU     

Scalable Compact Circuit Model for Differential Spiral Transformers in CMOS RFICs

A new compact circuit model for differential spiral transformers in CMOS radio frequency integrated circuits (RFICs) is developed in this paper. The model consists of two coupled “$hbox2-pi$” subcircuits for each inductor coil in the transformer. All the values of the circuit elements can be analytically calculated according to the process parameters and the device's geometric dimensions, making the model highly scalable and predictive. The model has very good accuracy as validated by comparison to a 2.5-dimensional full-wave numerical electromagnetic field solver.     

An FDTD/MoM hybrid technique for modeling complex antennas in thepresence of heterogeneous grounds

Calculating the current distribution and radiation patterns for ground-penetrating radar antennas is a challenging problem because of the complex interaction between the antenna, the ground, and any buried scatterer. Typically, numerical techniques that are well suited for modeling the antennas themselves are not well suited for modeling the heterogeneous grounds, and visa versa. For example the finite-difference time-domain (FDTD) technique is well suited for modeling fields in heterogeneous media, whereas the method of moments (MoM) is well suited for modeling complex antennas in free space. This paper describes a hybrid technique, based upon the equivalence principle, for calculating an antenna's current distribution radiation pattern when the antenna is located near an air-ground interface. The original problem is decomposed into two coupled equivalent problems: one for the antenna geometry and the other for the ground geometry, with field information passing between them via a rapidly converging iterative procedure. The fields in each region may be modeled using numerical techniques best suited to them. Results for several test cases are presented, using FDTD to model the ground problem and MoM for the antenna problem, that demonstrate the accuracy of this hybrid technique