Large Electromagnetic Problems Research Articles

Domain decomposition method with generalized scattering matrix for radiowave propagation analysis

In this paper, we present a novel method based on generalized scattering matrix representation to analyse radiowave propagation. Problem domain is characterized as cascaded two port networks, of which the scattering relations are obtained by the use of Hermite–Gaussian (HG) basis functions. Then the field variation at the boundaries of the problem domain can be calculated by simple matrix operations. The approach is shown to yield accurate results in proposed numerical examples. The method proposed here can be extended to more complex and large domain electromagnetic problems with its systematic methodology.

An Integral Equation-Based Overlapping Domain Decomposition Method Enhanced With Anderson Acceleration

In this letter, an integral equation-based overlapping domain decomposition method enhanced with Anderson acceleration (IE-ODDM-AA) is proposed for the solution of the electrically large electromagnetic problems whose memory consumptions are too large for the user's computer to accommodate. By augmenting the traditional Gauss–Seidel-like iterative scheme of the IE-ODDM with a popular fixed point acceleration technique named Anderson acceleration, the convergence behavior of the IE-ODDM is greatly improved. Particularly, for the domain partitioning cases where the traditional scheme of the IE-ODDM diverges, the presented IE-ODDM-AA can still yield convergent solutions. Several numerical examples are provided to validate the proposed method.

Electromagnetic Backscattering Mechanisms of Frequency Selective Surfaces for Effective Analysis of Radar Cross Section by the First-Order Approximation of Floquet Modes

Full-wave analysis of finite but electrically large frequency selective surfaces (FSSs) substrates for the radar cross section (RCS) estimation is too time-consuming and unbearable for practical applications. Such FSS substrates can be either absorbing or reflective types and are widely used as radomes of antennas for stealth applications, where the electromagnetic (EM) backscattering is of much concern. This large EM problem is simplified by applying Floquet mode decomposition on the scattering fields, where the Kirchhoff approximation is employed to find the backscattering fields for RCS estimation. The resulted formula allows one to explore the scattering mechanism for RCS enhancement or reduction. Besides, the approximation is used to resemble the FSS radome by equivalent substrates. Thus, the transmission and reflection coefficients of the equivalent dielectric substrates are similar to those from FSS elements under an infinite array assumption. Afterward, the resulting EM problems of antenna radiations and scattering can be easily analyzed using the equivalent substrates of EM materials. Numerical examples of planar FSSs to form radomes demonstrate the feasibility of numerical simulations’ proposed work. The presented work can also be directly applied for fast analysis of EM shielding effectiveness by FSS substrates.

An Unconditionally Stable and Energy-Preserving Domain-Decomposition Method for Transient Modeling of Large-Scale Electromagnetic Problems

The purpose of this contribution is to introduce a dual-primal finite-element tearing and interconnecting (DP-FETI) method for the time-domain simulation of large electromagnetic problems. The most distinctive feature of the proposed method is that the continuity of the first-time derivative of the electric field intensity is enforced across the interfaces, unlike the existing formulations in electromagnetics. A theoretical proof is provided to demonstrate that this transmission condition guarantees unconditional stability and energy preservation of the method. Since the condition number of the global interface problem is greatly reduced compared to the standard finite-element time-domain (FETD) method, an iterative solver converges in far fewer iterations. This significantly reduces the simulation time, particularly when implemented on parallel computers. It is numerically shown that the method is scalable with respect to the number of subdomains and the time-step size. The numerical results for simulation of a cavity and bandgap devices are presented to demonstrate capability, accuracy, and efficiency of the proposed time-domain DP-FETI (TD-DP-FETI).

Simulation of Challenging Electromagnetic Problems Using a Massively Parallel Finite Element Method Solver

This communication presents an efficient massively parallel finite element method solver for the solution of complex and electrically large electromagnetic problems with arbitrary structures. The solver makes use of a domain decomposition algorithm to decompose the original problem into several non-overlapping sub-domains that may be solved independently in parallel through the application of the corresponding transmission conditions on the interfaces of the adjacent sub-domains. A numerical exact mesh truncation algorithm called finite element-iterative integral equation evaluation, accelerated with multilevel fast multipole algorithm, is implemented to meet the highly accurate requirements of today's challenging simulations. What's more, a hybrid message passing interface and an open multi-processing parallel framework are designed to achieve large-scale parallel performance on supercomputers. Through several numerical examples, the accuracy, effectiveness, and scalability of the proposed solver will be demonstrated, achieving more than 60% parallel efficiency on an eight times CPU core scale (from 1280 to 10 240 cores).

Speeding-up the CBFM–MLFMA approach for scattering analysis of very large electromagnetic problems

A technique to reduce the CPU-time and computer memory spent in scattering electromagnetic problems when using the Characteristics Basis Function Method (CBFM) combined with the Multilevel Fast Multipole Algorithm (MLFMA) is presented. It is intended for use in very large cases where an iterative solution process cannot be avoided, even considering the matrix size reduction achieved by the CBFM. The technique is based in retaining only the CBFs with a significant impressed field from external sources. Results show that the approach gives accurate results for both canonical and complex bodies.

Novel Extension of SBR–PO Method for Solving Electrically Large and Complex Electromagnetic Scattering Problem in Half-Space

To extend hybrid high-frequency shooting and bouncing rays–physical optics (SBR–PO) method to the modeling of electromagnetic (EM) scattering from an object in half-space, this paper focuses on addressing two key issues: 1) how to accurately obtain the induced electric currents on the object surface by taking into account the EM interactions between the object and half-space and 2) how to accurately calculate far-fields in half-space configuration. First, by introducing virtual interface of half-space, the proposed method avoids physically modeling the underlying ground, and only induced electric currents on the object are effectively taken into account in the SBR process. Second, the closed-form half-space Green’s function is used to calculate scattered far-fields to avoid the time-consuming evaluation of the Sommerfeld integrals. The computational errors are only from the approximation of induced electric currents with the same level of the SBR–PO method for the solution of the free-space problem, so the proposed method is more accurate than the conventional SBR–PO technique. Besides, performing the proposed method on the graphics processing unit platform to further accelerate the ray-tracing process makes the method even more powerful to solve the extra-large-scale scattering problems in the half-space.

Highly efficient parallel direct solver for solving dense complex matrix equations from method of moments

Based on the vectorised and cache optimised kernel, a parallel lower upper decomposition with a novel communication avoiding pivoting scheme is developed to solve dense complex matrix equations generated by the method of moments. The fine-grain data rearrangement and assembler instructions are adopted to reduce memory accessing times and improve CPU cache utilisation, which also facilitate vectorisation of the code. Through grouping processes in a binary tree, a parallel pivoting scheme is designed to optimise the communication pattern and thus reduces the solving time of the proposed solver. Two large electromagnetic radiation problems are solved on two supercomputers, respectively, and the numerical results demonstrate that the proposed method outperforms those in open source and commercial libraries.

A Novel Broadband Multilevel Fast Multipole Algorithm With Incomplete-Leaf Tree Structures for Multiscale Electromagnetic Problems

An efficient and versatile broadband multilevel fast multipole algorithm (MLFMA), which is capable of handling large multiscale electromagnetic problems with a wide dynamic range of mesh sizes, is presented. By invoking a novel concept of incomplete-leaf tree structures, where only the overcrowded boxes are divided into smaller ones for a given population threshold, versatility of using variable-sized boxes is achieved. Consequently, for geometries containing highly overmeshed local regions, the proposed method is always more efficient than the conventional MLFMA for the same accuracy, while it is always more accurate if the efficiency is comparable. Furthermore, in such a population-based clustering scenario, the error is controllable regardless of the number of levels. Several canonical examples are provided to demonstrate the superior efficiency and accuracy of the proposed algorithm in comparison with the conventional MLFMA.

Performance of a Massively Parallel Higher-Order Method of Moments Code Using Thousands of CPUs and Its Applications

The efficiency of a parallel higher-order method of moments is illustrated using up to 4096 CPU cores on a supercomputer. The scattering problems solved include the analysis from two full scale airplanes and the radiation problems include performance of a microstrip patch phased array antenna mounted on an airplane. Both the scattering and radiation problems are simulated to demonstrate the efficiency of the algorithm implementation. Numerical results show that one can achieve above 60% efficiency when the used memory to the total memory ratio is larger than 15%, and the time can reach a theoretical value between O (N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) and O (N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ), where N is the number of unknowns. Due to its high efficiency, the algorithm is able to accurately solve large complex electromagnetic problems including composite and multiscale structures.

Simulation of Airborne Antenna Array Layout Problems Using Parallel Higher-Order MoM

The parallel higher-order Method of Moments based on message passing interface (MPI) has been successfully used to analyze the changes in radiation patterns of a microstrip patch array antenna mounted on different positions of an airplane. The block-partitioned scheme for the large dense MoM matrix and a block-cyclic matrix distribution scheme are designed to achieve excellent load balance and high parallel efficiency. Numerical results demonstrate that the rigorous parallel Method of Moments can efficiently and accurately solve large complex electromagnetic problems with composite structures.

Skin-Effect Loss Models for Time- and Frequency-Domain PEEC Solver

A challenging and interesting issue for the solution of large electromagnetic problems is the efficient, sufficiently accurate modeling of the broadband skin-effect loss for conducting planes and 3-D shapes. The inclusion of such models in an electromagnetic (EM) solver can be very costly in compute time and memory requirements. These issues are particularly important for the class of signal, power, and noise integrity (NI) problems. In this paper, we concentrate on partial element equivalent circuit (PEEC)-type methods which are suitable for the solution of this class of problems. Progress has been made recently in the design of skin-effect models. The difficult issues are broadband frequency-domain or time-domain problems. These models are considered in this paper. We present several solution methods, and we compare results obtained with these approaches.

Hybrid Iterative Approach Combined With Domain Decomposition for the Analysis of Large Electromagnetic Problems

In this paper, we propose a technique for the electromagnetic analysis of large objects considering the interactions between separate parts of the geometry (which in this context will be referred to as domains). A number of unknowns is associated to each domain, and only the basis functions included within the same domain are considered fully coupled (i.e., a full-wave analysis is performed for every domain, isolating it from the rest of the geometry). An iterative process is then applied to determine the total currents over the object, considering the currents induced by the external sources and those due to interactions between different domains. Once a current distribution is obtained over a given domain it is essential to identify those passive domains with which the interaction active-domain-passive-domain will yield a significant contribution to the final result (scattered field, radiation pattern, S-parameters, etc.). In this work, we utilize a ray-tracing method combined with the multipole expansion of the active currents over a number of points located on the radiating surface to speed up the solution of large and realistic problems.

A fast direct matrix solver for surface integral equation methods for electromagnetic wave scattering from non‐penetrable targets

The implementation details of a fast direct solver is described herein for solving dense matrix equations from the application of surface integral equation methods for electromagnetic field scatterings from non‐penetrable targets. The proposed algorithm exploits the smoothness of the far field and computes a low rank decomposition of the off‐diagonal coupling blocks of the matrices through a set of skeletonization processes. Moreover, an artificial surface (the Huygens' surface) is introduced for each clustering group to efficiently account for the couplings between well‐separated groups. Furthermore, a recursive multilevel version of the algorithm is presented. Although asymptotically the algorithm would not alter the bleak outlook of the complexity of the worst case scenario,O(N3) for required CPU time where N denotes the number of unknowns, for electrically large electromagnetic (EM) problems; through numerical examples, we found that the proposed multilevel direct solver can scale as good as O(N1.3) in memory consumption and O(N1.8) in CPU time for moderate‐sized EM problems. Note that our conclusions are drawn based on a few sample examples that we have conducted and should not be taken as a true complexity analysis for general electrodynamic applications. However, for the fixed frequency (h‐refinement) scenario, where the discretization size decreases, the computational complexities observed agree well with the theoretical predictions. Namely, the algorithm exhibits O(N) and O(N1.5) complexities for memory consumption and CPU time, respectively.

GPU‐based acceleration of computational electromagnetics codes

SUMMARYThe solution of large and complex electromagnetic (EM) problems often leads to a substantial demand for high‐performance computing resources and strategies. This is true for a wide variety of numerical methods and applications, ranging from EM compatibility to radio‐coverage, circuit modeling, and optimization of components. In the last decades, graphics processing units (GPUs) have gained popularity in scientific computing as a low‐cost and powerful parallel architecture. This paper gives an overview of the main efforts of researchers to port computational electromagnetics (CEM) codes to GPU. Moreover, GPU implementation aspects of two well‐known techniques, namely the finite‐difference time domain (FDTD) and the method of moments (MoM), are investigated. The impressive speed‐ups achieved (up to 60× and 25× for FDTD and MoM, respectively) demonstrate the effectiveness of GPUs in accelerating CEM codes. Copyright © 2012 John Wiley &amp; Sons, Ltd.

A domain decomposition method for the parallelization of a three-dimensional Maxwell solver based on a constrained formulation

Abstract The numerical solution of very large three-dimensional electromagnetic field problems are challenging for various applications in the industry. In this paper, we propose a nonoverlapping domain decomposition approach for solving the three-dimensional Maxwell equations on MIMD computers, based on a mixed variational formulation. It is especially well adapted for the solution of the Vlasov–Maxwell equations, widely used to simulate complex devices like particle injectors or accelerators. This approach has the important property that it leads to reuse without modification most of an existing sequential code. The continuity at the interfaces is imposed by duality using Lagrange multipliers. Hence, the resulting parallel algorithm requires only to add an external preconditioned Uzawa solver. We present the results of some numerical experiments on a parallel distributed memory machine.

Waveform Relaxation Time Domain Solver for Subsystem Arrays

In this paper we present a waveform relaxation approach for the transient analysis of 3-D electromagnetic problems using the partial element equivalent circuit (PEEC) method. Relying on weaker couplings among separated systems, a waveform relaxation scheme is proposed to accelerate the transient analysis of large electromagnetic problems. The results are compared with those obtained using a conventional PEEC formulation. They exhibit a significant speed-up while preserving the solution accuracy.

A Time-Harmonic Three-Dimensional Vector Boundary Element Model for Electromechanical Devices

In present practice, the most effective way to solve the large electromagnetic (EM) boundary value problems typical in electromechanical device analysis has been with the finite element method (FEM). The sparse, symmetric, and banded structure of FEM system matrices reduces the memory requirements and facilitates several fast and efficient solution algorithms. An alternative, boundary element methods (BEM), is more computationally intensive. Recently, however, fast and efficient solver codes have been developed for BEM solutions of EM scattering problems. These, if effectively implemented in electromechanical device models, can make BEM a more feasible alternative for this purpose than previously. To generate a deeper understanding of this alternative formulation in the context of electromechanics problems, a time-harmonic 3-D vector BEM model for electromechanical devices is presented that is formulated in terms of the field variables and is capable of modeling multiple separated homogeneous regions with or without eddy currents. Extensions to electric machine modeling are given, and the model is assessed using experimental data.

A multilevel Cartesian non-uniform grid time domain algorithm

A multilevel Cartesian non-uniform grid time domain algorithm (CNGTDA) is introduced to rapidly compute transient wave fields radiated by time dependent three-dimensional source constellations. CNGTDA leverages the observation that transient wave fields generated by temporally bandlimited and spatially confined source constellations can be recovered via interpolation from appropriately delay- and amplitude-compensated field samples. This property is used in conjunction with a multilevel scheme, in which the computational domain is hierarchically decomposed into subdomains with sparse non-uniform grids used to obtain the fields. For both surface and volumetric source distributions, the computational cost of CNGTDA to compute the transient field at N s observation locations from N s collocated sources for N t discrete time instances scales as O( N t N s log N s ) and O( N t N s log 2 N s ) in the low- and high-frequency regimes, respectively. Coupled with marching-on-in-time (MOT) time domain integral equations, CNGTDA can facilitate efficient analysis of large scale time domain electromagnetic and acoustic problems.

Parallelized multilevel characteristic basis function method for solving electromagnetic scattering problems

AbstractParallel implementation of the multilevel characteristic basis function method is discussed in this article. The use of this method enables us to solve very large electromagnetic problems in a direct manner via a recursive application of the characteristic basis function method. Furthermore, we show that, unlike the iterative schemes, the present method is very well suited for parallelization. Examples are presented to show that upto one million unknown problems can be solved on a workstation using the present scheme, and that the results show very good agreement with those derived by using analytical or fast multipole methods. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2963–2969, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24767