MULTISCALE COMPUTATIONAL ELECTROMAGNETICS

Many problems in Computational Electromagnetics (CEM) and Computational Fluid Dynamics (CFD) require millions of grid cells to properly represent the physics. Advances in parallel computing, both in hardware and software, make it feasible to solve such large scale simulations in a timely manner. The objective of this paper is to describe some of the recent work at Rockwell in performing parallel computing for providing quick-turnaround solutions to problems in CFD, CEM and other computational disciplines.

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.

Recent years have seen a spectacular increase in our capability to model, simulate the performance of, and design complex electromagnetic systems. Much progress has been made in enhancing the available numerical techniques, viz., the method of moments (MoM), the finite-element method (FEM), and the finite-difference time-domain (FDTD) or its variants. Great strides have recently been made in enlarging the scope of MoM via the use of the fast multipole method (FMM), which has made it feasible for us to solve problems that require the handling of 106 degrees of freedom, or even higher, and distributed processing has enabled the FDTD to handle upward of 109 degrees of freedom on a moderate-size computing platform. Despite this recent progress, many practical computational electromagnetic (CEM) modeling problems of interest present formidable challenges, and the search for numerically efficient techniques to solve large problems involving complex structures continues unabated. The objectives of this paper are to identify some of these challenging problems encountered by the author during the last five years, and to present the results of application of a technique called CBFM - developed at the EMC Laboratory at Penn State - that has been found useful for addressing them.

Computation of scattering by large, complex, composite targets is one of most challenging problems in computational electromagnetics (CEM). A formulation of hybrid FE/BI/MLFMA is presented for this kind of problem. The numerical performance of the hybrid FE/BI/MLFMA is investigated by computation of a conducting sphere coated with anisotropic material and a conducting brick with deep material-filled cavity.

Surface-integral-equation (SIE) approaches are presented for the accurate solution of different problems in computational electromagnetics. First, an efficient message passing interface (MPI)/OpenMP parallel implementation of the multilevel fast multipole algorithm-fast Fourier transform (MLFMA-FFT) is presented for the solution of large-scale conducting bodies. Second, looking for the extension of these rigorous approaches to new demanded areas, the SIE method is successfully applied to the solution of left-handed metamaterials and plasmonic nanostructures.

Electromagnetic wave scattering from large and complex bodies is currently the most challenging problem in computational electromagnetics. There is an increasing need for more efficient algorithms with reduced computational complexity and memory requirements. In this work we solve the problem of electromagnetic wave scattering involving three-dimensional, homogeneous, arbitrarily shaped dielectric objects. The fast multipole method (FMM) is used along with the algebraic multigrid (AMG) method, that is employed as a preconditioner, in order to accelerate the convergence rate of the Krylov iterations. Our experimental results suggest much faster convergence compared to the non preconditioned FMM, and hence significant reduction to the overall computation time.

The analysis of electromagnetic diffraction phenomena in arbitrarily linear media is a challenging problem in computational electromagnetics either with numerical, analytical, semi-analytical and asymptotic techniques.

The growing significance, technical development and employment of electromagnetic (EM) methods in exploration geophysics have led to the increasing need for reliable and fast techniques of interpretation of 3-D EM data sets acquired in complex geological environments. The first and most important step to creating an inversion method is the development of a solver for the forward problem. In order to create an efficient, reliable and practical 3-D EM inversion, it is necessary to have a 3-D EM modelling code that is highly accurate, robust and very fast. This thesis focuses precisely on this crucial and very demanding step to building a 3-D EM interpretation method. The thesis presents as its main contribution a highly accurate, robust, very fast and extremely scalable numerical method for 3-D EM modelling in geophysics that is based on finite elements (FE) and designed to run on massively parallel computing platforms. Thanks to the fact that the FE approach supports completely unstructured tetrahedral meshes as well as local mesh refinements, the presented solver is able to represent complex geometries of subsurface structures very precisely and thus improve the solution accuracy and avoid misleading artefacts in images. Consequently, it can be successfully used in geological environments of arbitrary geometrical complexities. The parallel implementation of the method, which is based on the domain decomposition and a hybrid MPI-OpenMP scheme, has proved to be highly scalable - the achieved speed-up is close to the linear for more than a thousand processors. Thanks to this, the code is able to deal with extremely large problems, which may have hundreds of millions of degrees of freedom, in a very efficient way. The importance of having this forward-problem solver lies in the fact that it is now possible to create a 3-D EM inversion that can deal with data obtained in extremely complex geological environments in a way that is realistic for practical use in industry. So far, such imaging tool has not been proposed due to a lack of efficient, parallel FE solutions as well as the limitations of efficient solvers based on finite differences. In addition, the thesis discusses physical, mathematical and numerical aspects and challenges of 3-D EM modelling, which have been studied during my research in order to properly design the presented software for EM field simulations on 3-D areas of the Earth. Through this work, a physical problem formulation based on the secondary Coulomb-gauged EM potentials has been validated, proving that it can be successfully used with the standard nodal FE method to give highly accurate numerical solutions. Also, this work has shown that Krylov subspace iterative methods are the best solution for solving linear systems that arise after FE discretisation of the problem under consideration. More precisely, it has been discovered empirically that the best iterative method for this kind of problems is biconjugate gradient stabilised with an elaborate preconditioner. Since most commonly used preconditioners proved to be either unable to improve the convergence of the implemented solvers to the desired extent, or impractical in the parallel context, I have proposed a preconditioning technique for Krylov methods that is based on algebraic multigrid. Tests for various problems with different conductivity structures and characteristics have shown that the new preconditioner greatly improves the convergence of different Krylov subspace methods, which significantly reduces the total execution time of the program and improves the solution quality. Furthermore, the preconditioner is very practical for parallel implementation. Finally, it has been concluded that there are not any restrictions in employing classical parallel programming models, MPI and OpenMP, for parallelisation of the presented FE solver. Moreover, they have proved to be enough to provide an excellent scalability for it.

This publication documents the proceedings of the first Workshop on Computational Electromagnetics (CEM) and Applications, hosted by the Institute for Computer Applications in Science and Engineering (ICASE) and the NASA Langley Research Center, Hampton, Virginia, 29-31 May, 1996, and attended by approximately 70 people from academia, government laboratories, and industry. ICASE's charter mission in 1972 remains today - to explore novel computer environments (vector in the 1970s; parallel in the 1990s) for scientific computing. These proceedings provide a necessary foundation for symposia in computational electromagnetics for future aerospace applications. The objectives of this CEM Workshop were to provide a forum for many of the leaders of the community to assess the state of CEM technology and to discuss areas of research for future programmatic planning activities. Workshop sessions included topics on optimization, industrial applications, algorithms, and a special panel session was provided during which issues were discussed and future research areas were identified. Hopefully, this publication will stimulate and improve communication among multidisciplinary researchers as well as highlighting several CEM areas that need improvement - especially for highly challenging problems. The two most important criteria in the selection of speakers for the workshop were their substantial contribution to large-scale CEM problems and their ability to articulate the issues confronting the CEM research community. Based on the results obtained, it is anticipated that this publication will be useful to government, industry, and university researchers to plan future research tasks in CEM analytical methods and applications.

This study investigates and evaluates applications of the adjoint problem and its solution in frequency-domain computational electromagnetics (CEM). The study establishes and validates adjoint-based applications including higher order parameter sampling, a posteriori error estimate evaluation, and p- and h-refinements. These applications can improve the efficiency, automation, and robustness of CEM methods. We employ a 1-D finite-element-method scattering solver, simplifying the implementation, replicability, clarity, and intuitiveness of analysis results and conclusions, which then extend naturally to higher dimensional solvers and more complicated CEM problems. While demonstrated with a higher order solver, the derived techniques apply to low-order methodology as well. This is the first demonstration of the applicability of adjoint-based a posteriori error estimation techniques to adaptive discretization refinement in frequency-domain CEM with arbitrary-order basis functions. This work introduces the application of dual-weighted residual error estimation and selective adaptivity based on error cancellation. The proposed targeted, adaptive mesh/model p- and/or h-refinement heuristics informed by adjoint element-wise error contribution estimates show near-monotonic reduction of the quantity-of-interest error with increased numbers of refined elements. In general, adjoint techniques are underutilized in CEM, and another goal of this work is to promote their future use for refinement, optimization, and uncertainty quantification.

近年来国内森林生态系统服务功能研究较多,但应用价值不高,其科学性受到诸多质疑。从森林水源涵养功能的多尺度内涵、过程以及其计量方法出发,对国内外研究动态和发展趋势进行了总结分析,重新审视森林水源涵养功能的研究意义,探讨森林水源涵养功能的多尺度特征。从森林水源涵养功能作用的空间尺度上看,其拦蓄洪水削减洪峰的功能仅在较小尺度上有效,而调节径流的功能只有当森林土壤的入渗量超过蒸散量时,才可能有更多地下水补给河道径流,进而增加旱季河道流量。同时森林水源涵养功能也具有明显的时间尺度特征,具体表现为在次降水事件中,由于蒸散发量较小,森林水源涵养功能的物质量等于森林不同层次的截留量,在功能上表现为拦蓄降水;在长时间尺度上,由于林地蒸散要耗去大量水分,森林水源涵养功能的物质量等于森林不同层次的截留量减去林地蒸散发量,在功能上表现为净化水质和调节径流。大多数研究仅对单一林分的个别层次蓄水功能进行研究,缺乏流域尺度或者更大空间尺度的森林水源涵养功能研究。建议从区域降尺度到流域或将坡面尺度上推到流域,集中在流域尺度解决森林水源涵养空间异质性将是解决森林水源涵养功能尺度外推的有效办法。就目前国内流行的森林水源涵养功能计量方法而言,其与尺度及研究目的有较大相关性,在研究中应根据研究目的、研究尺度和可获取的数据情况选择合适的计量方法。研究突出了不同尺度作用下森林水文过程的复杂性及重要性,并结合森林与水关系的争论问题,分析目前国内对森林水源涵养功能研究的一些误区,提出森林水源涵养功能研究的一些关键科学问题及未来可能的发展方向,主要包括:1)明确界定森林水源涵养功能的边界,探索森林水源涵养功能计量的新方法;2)加强不同时空尺度关联的森林水源涵养功能研究,包括正确评价森林水源涵养功能的时空变异规律,森林生态系统水源涵养功能的尺度效应,森林水源涵养与下游水生态安全,森林水源涵养研究范式转变等核心问题。;Forest water conservation as an important ecosystem function has caused a rising interests in the scientific community in recent years. However, there remain some arguments in several aspects regarding the forest water conservation function. For the concept of the forest water conservation, there is no clear definition about its connotation. Another concern is the scaling issue. It is a challenge to scale up the estimation for the forest water conservation from the plot scale to larger scale, e.g., watershed scale or regional scale. Many quantification methods have been developed, but their suitability, performance, advantages and disadvantages are unknown. Many of such argument issues are significant limits of the forest water conservation in science and management. On the basis of the literature review, we clarify the important role of the water conservation in forest ecosystem function. We also summarize and analyze the concepts of the forest water conservation and its multi-scale connotation, processes and quantification methods. On the spatial scale, function of the forest in mitigating peak flow is effective at a smaller scale but not necessarily at a larger scale. More groundwater recharges into stream flow when forest soil infiltration exceeds evapotranspiration, thus increasing stream flow in the dry season. During a rainfall event, forest water conservation has different features at different temporal scales. For example, the amount of the forest conservation during a rainfall event dominates by the forest canopy interception and most water is stored in the forest due to less evapotranspiration in the rainfall event scale. At the longer temporal scale, the forest water conservation can be determined by the forest canopy interception subtracting evapotranspiration. The functional roles of the forest water conservation at longer temporal scale dominate by purifying water from natural rainfall and mitigating seasonal flow peaks of the river discharges. Most previous studies of the forest water conservation focused on water storage function at the plot scale, but lack better understanding in the forest water conservation function at the watershed or regional scales. We suggest the approach that combines downscaling from the regional to watershed scales and upscaling from the hillside to the watershed scales can an effective way of the scale extrapolation. This idea can be used to address the heterogeneity issue of the forest water conservation function at different spatio-temporal scales. Among the existing quantification approaches of the forest water conservation function, each one highly relies on the temporal and spatial scales and its application goal. An appropriate calculation method should be carefully evaluated and considered based on the objectives, data availability, temporal and spatial scales of each study case. The suitability difference in different calculation methods of the forest water conservation demonstrates the complexity and importance of the multi-scale consideration in forest hydrological processes. In the context of the long-term debates about the relationship between the forest and water, we figure out a few confusing points in the current studies of the forest water conservation function. We also propose the critical scientific questions that should be addressed and a few directions in future studies of forest water conservation function including: 1) to clearly define the connotation and boundary of the forest water conservation function, and develop innovatory methods for determining the forest water conservation function; 2) to pay more attentions on the forest water conservation function studies associated with the different spatial and temporal scales, including evaluation of the spatio-temporal variations in forest water conservation function, the scaling effects on estimation of the water conservation function, the trade-off relationship between the upstream forest water conservation and the downstream ecological water need, and the development of the innovatory ways of forest water conservation practices.

—By employing the analysis of storage and computation time in fast multi-pole algorithm, this article introduces a new fast multi-pole algorithm to solve the problem of large computation time in multi-pole transfer process of the original fast multi-pole boundary element method. The new method uses the index expansion form to complete the transfer process of multi-pole moments at the expense of a small amount of storage. The obtained computational efficiency is significantly improved. Finally, the two-dimensional plate capacitor model is used to verify the precision of the authors’ method, and the three-dimensional spherical capacitor model is used to verify the superiority of the new fast multi-pole algorithm in solving multi-freedom electric field distribution problems. The electric field distribution of a 110 kV substation switching field model is calculated by using the new fast multi-pole algorithm. Compared with the calculated and measured values, the error is less than 10% upon optimization of the model; therefore, this method is better able to solve large-scale, multi degree-of-freedom problems.

This study focused on the structure of the aquatic insect community in spatial and temporal scales in the Esparza River. The river was sampled for one full year throughout 2007. During the dry season low flow months, five sampling points were selected in two different habitats (currents and pools), with five replicates per sample site. During the wet season with peak rain, only the data in the "current habitat" were sampled at each site. Specimens present in the different substrates were collected and preserved in situ. A nested ANOVA was then applied to the data to determine richness and density as the response variables. The variations in temporal and spatial scales were analyzed using width, depth and discharge of the river, and then analyzed using a nested ANOVA. Only a correlation of 51% similarity in richness was found, while in spatial scale, richness showed significant variation between sampling sites, but not between habitats. However, the temporal scale showed significant differences between habitats. Density showed differences between sites and habitats during the dry season in the spatial scale, while in the temporal scale significant variation was found between sampling sites. Width varied between habitats during the dry season, but not between sampling points. Depth showed differences between sampling sites and season. This work studies the importance of community structure of aquatic insects in rivers, and its relevance for the quality of water in rivers and streams.

Broadband electromagnetic (EM) modeling increases in importance for virtual prototyping of advanced power electronics systems (PES), enabling a more accurate prediction of fast switching converter operation and its impact on energy conversion efficiency and EM interference. With the aim to predict and reduce an adverse impact of parasitics on the dynamic performance of fast switching power semiconductor devices, the circuit-oriented EM modeling based on the extraction of equivalent lumped R-L-C-G circuits is frequently selected over the Finite Element Method (FEM)-based EM modeling, mainly due to its lower computational complexity. With requirements for more accurate virtual prototyping of fast-switching PES, the modeling accuracy of the equivalent-RLCG-circuit-based EM modeling has to be re-evaluated. In the literature, the equivalent-RLCG-circuit-based EM techniques are frequently misinterpreted as the quasi-static (QS) 3-D Partial Element Equivalent Circuit (PEEC) method, and the observed inaccuracies of modeling HF effects are attributed to the QS field assumption. This paper presents a comprehensive analysis on the differences between the QS 3-D PEEC-based and the equivalent-RLCG-circuit-based EM modeling for simulating the dynamics of fast switching power devices. Using two modeling examples of fast switching power MOSFETs, a 3-D PEEC solver developed in-house and the well-known equivalent-RLCG-circuit-based EM modeling tool, ANSYS Q3D, are compared to the full-wave 3-D FEM-based EM tool, ANSYS HFSS. It is shown that the QS 3-D PEEC method can model the fast switching transients more accurately than Q3D. Accordingly, the accuracy of equivalent-RLCG-circuit-based modeling approaches in the HF range is rather related to the approximations made on modeling electric-field induced effects than to the QS field assumption.

Electromagnetic Environment Associated with Lightning Strikes to Tall Strike Objects