Hypercube matrix computation task

A major objective of the Hypercube Matrix Computation effort at the Jet Propulsion Laboratory (JPL) is to investigate the applicability of a parallel computing architecture to the solution of large-scale electromagnetic scattering problems. Three scattering analysis codes are being implemented and assessed on a JPL/California Institute of Technology (Caltech) Mark 3 Hypercube. The codes, which utilize different underlying algorithms, give a means of evaluating the general applicability of this parallel architecture. The three analysis codes being implemented are a frequency domain method of moments code, a time domain finite difference code, and a frequency domain finite elements code. These analysis capabilities are being integrated into an electromagnetics interactive analysis workstation which can serve as a design tool for the construction of antennas and other radiating or scattering structures. The first two years of work on the Hypercube Matrix Computation effort is summarized. It includes both new developments and results as well as work previously reported in the Hypercube Matrix Computation Task: Final Report for 1986 to 1987 (JPL Publication 87-18)

The Buffered Block Forward Backward technique for solving electromagnetic wave scattering problems

This work focuses on efficient numerical techniques for solving electromagnetic wave scattering problems. The research is focused on three main areas: scattering from perfect electric conductors, 2D dielectric scatterers and 3D dielectric scattering objects. The problem of fields scattered from perfect electric conductors is formulated using the Electric Field Integral Equation. The Coupled Field Integral Equation is used when a 2D homogeneous dielectric object is considered. The Combined Field Integral Equation describes the problem of scattering from 3D homogeneous dielectric objects. Discretising the Integral Equation Formulation using the Method of Moments creates the matrix equation that is to be solved. Due to the large number of discretisations necessary the resulting matrices are of significant size and therefore the matrix equations cannot be solved by direct inversion and iterative methods are employed instead. Various iterative techniques for solving the matrix equation are presented including stationary methods such as the ”forwardbackward” technique, as well its matrix-block version. A novel iterative solver referred to as Buffered Block Forward Backward (BBFB) method is then described and investigated. It is shown that the incorporation of buffer regions dampens spurious diffraction effects and increases the computational efficiency of the algorithm. The BBFB is applied to both perfect electric conductors and homogeneous dielectric objects. The convergence of the BBFB method is compared to that of other techniques and it is shown that, depending on the grouping and buffering used, it can be more effective than classical methods based on Krylov subspaces for example. A possible application of the BBFB, namely the design of 2D dielectric photonic band-gap TeraHertz waveguides is investigated. i

Multi-solver schemes for electromagnetic modeling of large and complex objects

The work in this dissertation primarily focuses on the development of numerical algorithms for electromagnetic modeling of large and complex objects. First, a GPU-accelerated multilevel fast multipole algorithm (MLFMA) is presented to improve the efficiency of the traditional MLFMA by taking advantage of GPU hardware advancement. The proposed hierarchical parallelization strategy ensures a high computational throughput for the GPU calculation. The resulting OpenMP-based multi-GPU implementation is capable of solving real-life problems with over one million unknowns with a remarkable speedup. The radar cross sections (RCS) of a few benchmark objects are calculated to demonstrate the accuracy of the solution. The results are compared with those from the CPU-based MLFMA and measurements. The capability and efficiency of the presented method are analyzed through the examples of a sphere, an aircraft, and a missile-like object. Compared with the 8-threaded CPU-based MLFMA, the OpenMP-CUDA-MLFMA method can achieve from 5 to 20 times total speedup. Second, an efficient and accurate finite element--boundary integral (FE-BI) method is proposed for solving electromagnetic scattering and radiation problems. A mixed testing scheme, in which the Rao-Wilton-Glisson and the Buffa-Christiansen functions are both employed as the testing functions, is first presented to improve the accuracy of the FE-BI method. An efficient absorbing boundary condition (ABC)-based preconditioner is then proposed to accelerate the convergence of the iterative solution. To further improve the efficiency of the total computation, a GPU-accelerated MLFMA is applied to the iterative solution. The RCSs of several benchmark objects are calculated to demonstrate the numerical accuracy of the solution and also to show that the proposed method not only is free of interior resonance corruption, but also has a better convergence than the conventional FE-BI methods. The capability and efficiency of the proposed method are analyzed through several numerical examples, including a large dielectric coated sphere, a partial human body, and a coated missile-like object. Compared with the 8-threaded CPU-based algorithm, the GPU-accelerated FE-BI-MLFMA algorithm can achieve a total speedup up to 25.5 times. Third, a multi-solver (MS) scheme based on combined field integral equation (CFIE) is proposed. In this scheme, an object is decomposed into multiple bodies based on its material property and geometry. To model bodies with complicated materials, the FE-BI method is applied. To model bodies with homogeneous or conducting materials, the method of moments is employed. Specifically, three solvers are integrated in this multi-solver scheme: the FE-BI(CFIE) for inhomogeneous objects, the CFIE for dielectric objects, and the CFIE for conducting objects. A mixed testing scheme that utilizes both the Rao-Wilton-Glisson and the Buffa-Christiansen functions is adopted to obtain a good accuracy of the proposed multi-solver algorithm. In the iterative solution of the combined system, the MLFMA is applied to accelerate computation and reduce memory costs, and an ABC-based preconditioner is employed to speed up the convergence. In the numerical examples, the individual solvers are first demonstrated to be well conditioned and highly accurate. Then the validity of the proposed multi-solver scheme is demonstrated and its capability is shown by solving scattering problems of electrically large missile-like objects. Fourth, a MS scheme based on Robin transmission condition (RTC) is proposed. Different from the FE-BI method that applies BI equations to truncate the FE domain, this proposed multi-solver scheme employs both FE and BI equations to model an object along with its background. To be specific, the entire computational domain consisting of the object and its background is first decomposed into multiple non-overlapping subdomains with each modeled by either an FE or BI equation. The equations in the subdomains are then coupled into a multi-solver system by enforcing the RTC at the subdomain interfaces. Finally, the combined system is solved iteratively with the application of an extended ABC-based preconditioner and the MLFMA. To obtain an accurate solution, both the Rao-Wilton-Glisson and the Buffa-Christiansen functions are employed as the testing functions to discretize the BI equations. This scheme is applied to a variety of benchmark problems and the scattering from an aircraft with a launched missile to demonstrate its accuracy, versatility, and capability. The proposed scheme is compared with the MS-CFIE to illustrate the differences between the two schemes. Fifth, to further improve the modeling capability, an accelerated MS method is developed on distributed computing systems to simulate the scattering from very large and complex objects. The parallelization strategy is to parallelize different subdomains individually, which is different from the parallelized domain decomposition methods, where the subdomains are handled in parallel. The multilevel fast multipole algorithm is parallelized to enable computation on many processors. The modeling strategy using the MS-RTC method is also discussed so that one can easily follow the guideline to model large and complex objects. Numerical examples are given to show the parallel efficiency of the proposed strategy and the modeling capability of the proposed method. Finally, the specific absorption rate (SAR) in a human head at 5G frequencies is simulated by taking advantage of the MS-RTC method. Based on the strong skin effect, the human head model is first simplified to reduce the computation cost. Then the MS-RTC method is applied to model the human head. Numerical examples show that the MS method is very efficient in solving electromagnetic fields in the human head and the simplified human head model can be used in the SAR simulation with an acceptable accuracy

Advanced Diagnosis Techniques for Radio Telescopes in Astronomical Applications

The performance of radio telescopes in astronomical applications can be affected by structural variations due to: 1. Misalignment of the feeding structure, resulting in a lateral or axial displacement of the receiver; 2. Wind stress; 3. Gravitational distortion as the antenna is tilted; 4. Thermal distortion with ambient temperature or sunlight. Diagnosis methods are necessary to estimate any deviation of the antenna system from its nominal behavior in order to guarantee the maximum performance. Several approaches have been developed during the years, and among them the electromagnetic diagnosis appears today as the most appealing, because it allows a relatively simple measurement setup and a reduced human intervention. Electromagnetic diagnosis is based on the acquisition of the antenna Far Field Pattern (FFP), with the Antenna Under Test (AUT) working in receiving mode. A natural radio star or a satellite beacon provides the signal source. The acquisition of the FFP typically requires a very large number of field samples to get the complete information about the AUT, and the subsequent measurement process may span over several hours. A prolonged acquisition has significant drawbacks related to the continuous tracking of the source and the inconstancy of the environmental conditions. The purpose of the PhD activity has been focused on an optimized formulation of the diagnosis of radio telescopes aimed at reducing the number of field samples to acquire, and so at minimizing the measurement time. A diagnosis approach has been developed, based on the Aperture Field method for the description of the AUT radiation mechanism. A Principal Component Analysis (PCA) has been employed to restore a linear relationship between the unknowns describing the AUT status and the far field data. An optimal far field sampling grid is selected by optimizing the singular values behavior of the relevant linearized operator. During the activity, a computational tool based on Geometrical Optics (GO) has been developed to improve the diagnosis approach. Indeed, once the Aperture Field is recovered from the inversion of the measured FFP, an additional step is required to assess the AUT status from the phase distribution. Obviously, the computation of the phase distribution should be based on efficient algorithms in order to properly manage electrically large reflectors. The developed GO technique relies on the Fast Marching Method (FMM) for the direct solution of the eikonal equation. A GO approach based on the FMM is appealing because it shows a favorable computational trend. Furthermore, the explicit solution of the eikonal equation opens the possibility to set up an inverse ray tracing scheme, which proves particularly convenient compared to direct ray tracing because it allows to easily select the minimum number of rays to be traced. The FMM is also amenable for parallel execution. In particular, in the present work, the Fast Iterative Method has been implemented on Graphics Processing Units (GPUs). Moreover, the FMM has been accelerated by introducing a tree data structure. The tree allows to manage the mutual interactions between multiple scattering surfaces and the parallelization of the ray tracing step. The method has been numerically tested on simple canonical cases to show its performance in terms of accuracy and speed. Then, it has been applied to the evaluation of the Aperture Field phase required by the reflector diagnosis. During the research activity, the problem of validating the diagnosis algorithms has been also faced. Obviously, a numerical analysis can been carried out to test the model employed to describe the system and to evaluate the performance of the algorithm. To this end, a reliable commercial software exploited to simulate reflector antennas has been exploited. However, to complete the analysis, the experimental validation becomes mandatory, and an experimental outdoor far field test range is required. Accordingly, a test range has been set up thanks to the collaboration with Istituto Nazionale di Astrofisica (INAF) of Naples, Italy. Its realization has involved the full development of the software to drive an Alt-Azimuth positioner and to remotely control the instrumentation. In addition, an upgrade of the internal connections of a Vector Network Analyzer has been performed in order to allow the interferometric acquisition

Modeling EMI Resulting from a Signal Via Transition Through Power/Ground Layers

Signal transitioning through layers on vias are very common in multi-layer printed circuit board (PCB) design. For a signal via transitioning through the internal power and ground planes, the return current must switch from one reference plane to another reference plane. The discontinuity of the return current at the via excites the power and ground planes, and results in noise on the power bus that can lead to signal integrity, as well as EMI problems. Numerical methods, such as the finite-difference time-domain (FDTD), Moment of Methods (MoM), and partial element equivalent circuit (PEEC) method, were employed herein to study this problem. The modeled results are supported by measurements. In addition, a common EMI mitigation approach of adding a decoupling capacitor was investigated with the FDTD method

Electromagnetic Scattering Characteristics of Composite Targets and Software Development Based on PO Algorithm

Physical optics (PO) algorithm is a high-frequency electromagnetic (EM) algorithm, which is widely used to solve the EM scattering problems of electrically large composite targets. Due to the PO algorithm only considers the induced current in the bright region irradiated by EM wave, the computational memory and time consumption are superior than other high-frequency algorithms, and the calculation accuracy is pretty fine. Based on the PO algorithm, this thesis focuses on the occlusion judgement of PO algorithm and its application in composite targets. The main contents of this thesis are as follows: 1. The occlusion judgement software system for PO algorithm is developed. The main function of this software is to judge the bright region of the target under the irradiation of EM wave. This software uses two judgement methods: ray tracing method based on CPU and Z-Buffer method based on CPU and GPU. Moreover, due to the compromise between patch size and patch number, both methods have errors at the edge of bright and shadow regions. This thesis discusses the error and reduces it. 2. Based on PO algorithm, the EM scattering characteristics of targets covered by plasma sheath are discussed. We simulate the plasma sheath flow field data of hypersonic vehicle by FASTRAN software, compare and analyze the plasma sheath electron number density at different flight heights and speeds. On this basis, the bistatic RCS of hypersonic vehicle head-on irradiation under different flight heights and speeds is calculated by using the PO algorithm of layered medium. 3. SAR image simulation of tree ground composite target is carried out based on PO algorithm and Non-Uniform Fast Fourier Transform (NUFFT) method. Firstly, we introduce the geometric modeling and EM parameter modeling of tree ground composite target, and the scattering characteristics of tree ground composite target are obtained by using PO algorithm. Finally, the scattering field of the target is processed by NUFFT method, and the SAR simulation images of multiple trees scene are obtained

An open-source implementation for full-wave 2D scattering by million-wavelength-size objects

In this contribution, we demonstrate that recent improvements in "fast methods" allow for fully error-controlled full-wave simulations of two-dimensional objects with sizes over a million wavelengths using relatively simple computing environments. We review how a fully scalable parallel version of the Multilevel Fast Multipole Algorithm (MLFMA) is obtained to accelerate a two-dimensional boundary integral equation for the scattering by multiple large dielectric and/or perfectly conducting objects. Several complex and large-scale examples demonstrate the capabilities of the algorithm. This implementation is available as open source under GPL license (http://www.openfmm.net)

International Workshop on Finite Elements for Microwave Engineering

When Courant prepared the text of his 1942 address to the American Mathematical Society for publication, he added a two-page Appendix to illustrate how the variational methods first described by Lord Rayleigh could be put to wider use in potential theory. Choosing piecewise-linear approximants on a set of triangles which he called elements, he dashed off a couple of two-dimensional examples and the finite element method was born. … Finite element activity in electrical engineering began in earnest about 1968-1969. A paper on waveguide analysis was published in Alta Frequenza in early 1969, giving the details of a finite element formulation of the classical hollow waveguide problem. It was followed by a rapid succession of papers on magnetic fields in saturable materials, dielectric loaded waveguides, and other well-known boundary value problems of electromagnetics. … In the decade of the eighties, finite element methods spread quickly. In several technical areas, they assumed a dominant role in field problems. P.P. Silvester, San Miniato (PI), Italy, 1992 Early in the nineties the International Workshop on Finite Elements for Microwave Engineering started. This volume contains the history of the Workshop and the Proceedings of the 13th edition, Florence (Italy), 2016 . The 14th Workshop will be in Cartagena (Colombia), 2018