Keynote Speech 1
: Prof. Dan Jiao (Purdue University)
Keynote Speech 2
: Prof. Tapan K. Sarkar (Syracuse University)
Keynote Speech 3
: Prof. Michel M. Ney (Telecom Bretagne Institute)
Keynote Speech 4
: Prof. Mahta Moghaddam (University of Southern California)
Keynote Speech 5
: Prof. Makoto Ando (Tokyo Institute of Technology)
Keynote Speech 6
: Prof. Qing Huo Liu (Duke University)
Keynote Speech 7
: Prof. Magdalena Salazar-Palma (Carlos III University of Madrid)
Keynote Speech 8
: Prof. Roberto Graglia (Polytechnic of Turin)
Recent Progress on Optimal-Complexity Direct Solvers
Prof. Dan Jiao (Purdue University)
Dan Jiao received her Ph.D. degree in electrical engineering from the University of Illinois at Urbana-Champaign, in 2001. She then worked at the Technology Computer-Aided Design (CAD) Division, Intel Corporation, until September 2005, as a Senior CAD Engineer, Staff Engineer, and Senior Staff Engineer. In September 2005, she joined Purdue University, West Lafayette, IN, as an Assistant Professor with the School of Electrical and Computer Engineering, where she became a tenured Associate Professor in 2009, and a Full Professor in 2013. She has authored over 240 papers in refereed journals and international conferences.
Prof. Jiao received the 2013 S. A. Schelkunoff Prize Paper Award of the IEEE Antennas and Propagation Society. She was among the 21 women faculty selected across the country as the 2014-2015 Fellow of ELATE at Drexel, a national leadership program for women in the academic STEM fields. She was one of the 85 engineers selected throughout the nation for the National Academy of Engineering's 2011 US Frontiers of Engineering Symposium. She was the recipient of the 2010 Ruth and Joel Spira Outstanding Teaching Award, the 2008 National Science Foundation (NSF) CAREER Award, the 2006 Jack and Cathie Kozik Faculty Start up Award, a 2006 Office of Naval Research (ONR) Award under the Young Investigator Program, the 2004 Best Paper Award presented at the Intel Corporation's annual corporate-wide technology conference (Design and Test Technology Conference), the 2003 Intel Corporation's Logic Technology Development (LTD) Divisional Achievement Award, the Intel Corporation's Technology CAD Divisional Achievement Award, the 2002 Intel Corporation's Components Research the Intel Hero Award (Intel-wide she was the tenth recipient), the Intel Corporation's LTD Team Quality Award, and the 2000 Raj Mittra Outstanding Research Award presented by the University of Illinois at Urbana-Champaign. Prof. Jiao has served on a number of Technical Program Committees of premium conferences, and editorial boards of journals in electromagnetics, microwave, and circuits. She is an IEEE Fellow.
In general, to solve problems with N parameters, the optimal computational complexity is linear complexity O(N). State-of-the-art fast computational electromagnetic methods rely on iterative matrix solutions to solve large-scale problems. The optimal complexity of an iterative solver is O(NNitNrhs) with N being matrix size, Nit the number of iterations and Nrhs the number of right hand sides. How to invert or factorize a dense matrix or a sparse matrix of size N in O(N) (optimal) complexity has been a challenging research problem, but of critical importance to the continual advancement of computational electromagnetics. In this talk, I will present recent progresses in developing both direct finite element solvers and integral equation based solvers of optimal complexity for fast and large-scale electromagnetic analysis.
Solving Complex Electromagnetic Problems on Supercomputers using a Parallel Higher-Order
Method of Moments with a Reduced Communication LU (RCLU) Solver
Prof. Tapan K. Sarkar (Syracuse University)
Dr. Xunwang Zhao (Xidian University)
Dr. Yu Zhang (Xidian University)
Tapan K. Sarkar received the B.Tech. degree from the Indian Institute
of Technology, Kharagpur, in 1969, the M.Sc.E. degree from the
University of New Brunswick, Fredericton, NB, Canada, in 1971, and the
M.S. and Ph.D. degrees from Syracuse University, Syracuse, NY, in 1975.
From 1975 to 1976, he was with the TACO Division of the General
Instruments Corporation. He was with the Rochester Institute of
Technology, Rochester, NY, from 1976 to 1985. He was a Research Fellow
at the Gordon McKay Laboratory, Harvard University, Cambridge, MA, from
1977 to 1978. He is now a Professor in the Department of Electrical and
Computer Engineering, Syracuse University. His current research
interests deal with numerical solutions of operator equations arising in
electromagnetics and signal processing with application to system
design. He obtained one of the "best solution" awards in May 1977 at the
Rome Air Development Center (RADC) Spectral Estimation Workshop. He
received the Best Paper Award of the IEEE Transactions on
Electromagnetic Compatibility in 1979 and in the 1997 National Radar
Conference. He has authored or coauthored more than 360 journal articles
and numerous conference papers and 32 chapters in books and fifteen
books, including his most recent ones, /Iterative and Self Adaptive
Finite-Elements in Electromagnetic Modeling /(Boston, MA: Artech House,
1998), /Wavelet Applications in Electromagnetics and Signal Processing/
(Boston, MA: Artech House, 2002), /Smart Antennas /(IEEE Press and John
Wiley & Sons, 2003), /History of Wireless/ (IEEE Press and John Wiley &
Sons, 2005), and /Physics of Multiantenna Systems and Broadband Adaptive
Processing/ (John Wiley & Sons, 2007),/Parallel Solution of Integral
Equation-Based EM Problems in the Frequency Domain /(IEEE Press and John
Wiley & Sons, 2009), /Time and Frequency Domain Solutions of EM Problems
using Integral Equations and a Hybrid Methodology /(IEEE Press and John
Wiley & Sons, 2010), and /Higher Order Basis Based Integral equation
Solver/ (HOBBIES) (John Wiley & Sons 2012) .
Dr. Sarkar is a Registered Professional Engineer in the State of New
York. He was the 2014 President of the IEEE Antennas and Propagation
He received Docteur Honoris Causa from Universite Blaise Pascal,
Clermont Ferrand, France in 1998, from Politechnic University of Madrid,
Madrid, Spain in 2004, and from Aalto University, Helsinki, Finland in
2012. He received the medal of the /friend of the city of Clermont
Ferrand/, France, in 2000.
A parallel higher-order method of moments (HOMoM) in conjunction with a newly developed reduced communication lower-upper (RCLU) decomposition solver will be presented. The problem will be solved using 201,600 CPU cores on the world's largest and fastest supercomputer located in Guangzhou (used to be: not any more as of June 2016). Our code achieves a parallel efficiency of nearly 70% when simulating a large aircraft discretized into approximately 1.06 million unknowns for the current distribution on the structure and solved on Tianhe 2 using LU decomposition. Tianhe-2, a supercomputer developed by China's National University of Defense Technology, used to be the world's No. 1 system with a performance of 33.86 petaflop/s (quadrillions of calculations per second) on the LINPAC benchmark. It was built by China's National University of Defense Technology (NUDT) in collaboration with the Chinese IT firm Inspur. With 16,000 computer nodes, each comprising two Intel Ivy Bridge Xeon processors and three Xeon Phi chips, it used to represent the world's largest installation of Ivy Bridge and Xeon Phi chips, counting a total of 3,120,000 cores. Each of the 16,000 nodes possess 88 gigabytes of memory (64 used by the Ivy Bridge processors, and 8 gigabytes for each of the Xeon Phi processors). The total CPU plus coprocessor memory is 1,375 TiB (approximately 1.34 PiB, 1 Pebibyte = 1050 bytes).
In this paper, we will present a review of the in-core and out-of-core algorithms of HOMoM, focusing on the details of the RCLU parallel implementation and demonstrating its performance using some challenging applications.
Computational Electromagnetics in Complex Linear Media with the TLM Method
Prof. Michel M. Ney (Telecom Bretagne Institute)
Dr. Abdelrahman Ijjeh (Telecom Bretagne Institute)
Michel M. Ney (S'80-M'82-SM'91-F'11-LF'16) received the Engineering Diploma from the Swiss Federal Institute of Technology of Lausanne (EPFL), Switzerland in 1976 and then obtained his M.Sc. degree from the University of Manitoba, Canada, in 1978. After working two years at the Laboratory of Electromagnetism and Acoustics (LEMA) at the EPFL as a research engineer, he pursued his studies and obtained his Ph. D. degree in 1983 from the University of Ottawa, Canada where he started his academic career as an assistant professor. Professor Ney spent his sabbatical year at the Swiss Federal Institute of Technology, Lausanne, as a Guest Professor in 1989. He became a full professor in June 1993 and shortly after joined the Mines-Telecom Institute (Telecom Bretagne) a graduate engineering school in Brest, France. He was Head of the Laboratory for Electronics and Communication Systems associated to the French National Research Council (CNRS) from 1998 to 2007. His research interests include antenna and scattering, time domain numerical techniques applied to electromagnetic engineering.
Abdelrahman IJJEH received the bachelor and the M.S degrees in communication engineering from Yarmouk University, Jordan in 2008, and 2011, and the Ph.D degree in communication engineering from Institut Mines-Telecom, France, in 2014. From 2014 he has been a post-doc researcher in Institut Mines-Telecom, France, working in collaboration with the University Nice Sophia Antipolis, France. His research topics are in computational electromagnetic in general complex linear media, with applications to dosimetry and hyperthermia.
Volumic time-domain computational methods such as FDTD or Transmission-Line Matrix method (TLM) are widely used for full-wave simulation of structures with arbitrary geometry. While FDTD is a direct discretization of curl Maxwell's equation using finite-difference operators, TLM is seen as a discretized version of Huygens' principle of wave propagation. Fields are computed by linear combination of local ordinary waves. Local medium properties are accounted for by correcting the field values at every time step in a way that can be fundamentally described by a filtering process. Generally, the Symmetrical Condensed Node (SCN) proposed by Johns is used, owing to its very good dispersion characteristics and the fact that it always operates at the maximum time-step, computes all field components at the cell center and at the same time-step. Another advantage of the SCN is that continuity of tangential field components is automatically enforced at interfaces between media as fields are always updated in a homogeneous medium. As a result, SCN-TLM remains very accurate for high contrast of constitutive parameters. The price to pay is larger computer expenditure per iteration than when using FDTD, for instance. However, some recent work have shown that, even if the SCN-TLM requires more operations and storage, it substantially outperforms FDTD in terms of computer cost for high contrasted media or zones with irregular mesh with large mesh size ratio. This is due to the local properties of the SCN-TLM. In this paper, a brief review of the TLM method is presented. Then, a unified TLM algorithm for complex linear media is described. These media include dispersive, anisotropic or media with both characteristics. Some aspects of the TLM method regarding its performances for high contrast heterogeneous media are discussed. Also, some issues regarding dispersion and stability when dealing with complex media are presented. Examples in the case of dispersive, non-isotropic media such as ferrite will be shown. Finally, when dealing with highly heterogeneous medium such as encountered in human dosimetry, the use of block- meshing brings some obvious advantage. However, when local time-step is used some stability issue occurs. Some current results and related discussion are presented.
Clinical Microwave Imaging, Therapy, and Monitoring Applications Through Computational Electromagnetics
Prof. Mahta Moghaddam (University of Southern California)
Mahta Moghaddam is Professor of electrical engineering at the University of Southern California (USC) Ming Hsieh department of electrical engineering. She received the Ph.D. degree in electrical and computer engineering from the University of Illinois, Urbana, in 1991. From 1991 to 2003, she was with the Jet Propulsion Laboratory (JPL), Pasadena, CA, and at the University of Michigan from 2003 to 2011. During the past ~25 years of involvement in microwave sensing for environmental and medical applications, Prof. Moghaddam has introduced new measurement concepts and quantitative interpretation approaches for monostatic and multistatic microwave observations . Her most recent contributions include the development of new radar measurement technologies for subsurface and subcanopy characterization, development of forward and inverse scattering techniques for complex and random media, developing sensor web technologies for environmental and body-area sensing, and transforming concepts of radar remote sensing to medical imaging and therapy applications. She is a member of the NASA Soil Moisture Active and Passive (SMAP) mission Science Team, member of the Arctic-Boreal Vulnerability Experiment (ABoVE) Science Team, and the PI for AirMOSS NASA Earth Ventures Suborbital 1 Mission. She is a Fellow of IEEE, Editor-in-Chief of the IEEE Antennas and Propagation Magazine, and a member of the NASA Advisory Council Earth Science Subcommittee. She is currently serving as the Interim Vice Dean for Research at the USC Viterbi School of Engineering.
Electromagnetic waves in the microwave regime have been proposed for a variety of medical applications in the past several decades. Microwave imaging was perhaps the first such application, motivated by the goal of enhancing imaging depth as compared to, for example, ultrasound, and enhancing imaging specificity and safety as compared to, for example, X-ray modalities. Relatively low resolution and high computational complexity even for idealized renditions of microwave imagers have been some of the impediments in their widespread adoption. More recently, non-contact hyperthermia (microwave) and invasive probe-based ablation (radio frequency (RF) and microwave) methods have seen clinical use for thermal therapeutic purposes. The attraction of such methods is the highly efficient and deep heat deposition property of microwaves in biological tissue, especially those with high water content. A main challenge with such systems, however, is monitoring the temporal and spatial progress of heat deposition for proper treatment: real-time thermal monitoring is necessary to guide the location, intensity, and time of heat delivery such that the desired elevated temperature is reached long enough to achieve cell death throughout the target region, as well as to monitor and prevent inadvertent heating up of surrounding tissue. In this talk, we will describe our recent work on the development of microwave imaging, thermal therapy, and thermal monitoring systems, with emphasis on the latter. We will present a realistic novel computational method that allows us to fully represent the therapy and monitoring system, including antennas and other elements of the hardware setup. The results show successful retrieval of temperature fields with a precision of about 0.5o C and spatial resolution of about 2-3 cm. Acceleration of computations via state-of the-art GPU clusters are expected to allow a temperature map refresh rate of about 1 frame per second, which makes this method realistically useful in a clinical setting. Furthermore, the temperature mapping method is independent of the method of heat delivery, and therefore useful in conjunction with most any thermal therapy modality.
Compact Range Communication for 60 GHz Integrated 5G Heterogeneous Networks
and Fast Estimation of Shadowing Effects by Modified Edge Representation (MER)
Prof. Makoto Ando (Tokyo Institute of Technology)
Makoto Ando received the D.E. degrees in electrical engineering from Tokyo Institute of Technology, Tokyo, Japan in 1979. He joined Yokosuka Electrical Communication Laboratory, Nippon Telegraph and Telephone Public Corporation (NTT), and was engaged in development of antennas for satellite communication. He moved to Tokyo Institute of Technology in 1983 and is currently a Professor and Executive Vice President for Research.
His main interests have been field and waves in radio science, especially high frequency diffraction theory, the design of waveguide planar arrays and millimeter-wave antennas for future wireless communication.
He was the Program Officer in Research Center for Science Systems, the Japan Society for the Promotion of Science (JSPS) in 2006-2009. He was the 2007 President of Electronics Society and the 2014 Vice President of The Institute of Electronics, Information and Communication Engineers Japan (IEICE). His international activities covered the member of Scientific Council for Antenna Centre of Excellence in EU's 6'th framework (2004-2006), the 2002-2005 Chair of Commission B of the International Union of Radio Science (URSI) and the 2009 President of IEEE Antennas and Propagation Society. He is currently the Chair of ISAP International Steering Committee and the vice-president of URSI.
He received the Distinguished Achievement and Contributions Award in 2014, the Paper Awards in 1993, 2003, 2009 and 2016, all from IEICE. He won the Best paper awards of 2011, 2012 and 2013 Asia Pacific Microwave Conferences and in 2011 from International Millimeterwave Workshop (IMWS) of IEEE. He is the recipient of the 8th Inoue Prize for Science in 1992, the Meritorious Award of the Minister of Internal Affairs and Communications (MIC) and the Board of the Association of Radio Industries and Businesses (ARIB) in 2004 and the Award in Information Promotion Month 2006, MIC.
He is the Fellow IEEE and IEICE.
The 60 GHz band compact-range communication is very promising for short-time, short distance communication. This system consists of 60 GHz 32x32 massive elements antenna to provide special shape of communication area. This is applied to the PoC demonstration of mmWave integrated 5G heterogeneous networks (HetNet). It provides the world fastest mmWave access at 60 GHz band between a small-cell BS and a smartphone terminal achieving 6.1 Gbps. Pedestrian users experience to download 1 GB file with just 1.3 s. The seamless service between Wi-fi and mmWave accesses is demonstrated first.
Unfortunately, due to the short wavelengths in this frequency band the shadowing effects caused by human bodies, furniture, etc are severe and need to be modeled properly. Fresnel zone number (FZN) adopted modified edge representation (MER) equivalent edge current (EEC) is an accurate and fast high frequency diffraction technique which expresses the fields in terms of line integration. In the second half of the talk, FZN MER EEC is used to compute field distribution in the millimeter-wave compact range communication in the presence of scatterer, where shadowing effects rather than multi-path dominate the radio environments.
Multiscale and Multiphysics Computation for Subsurface Sensing and Super-Resolution Imaging
Prof. Qing Huo Liu (Duke University)
Qing Huo Liu (S'88-M'89-SM'94-F'05) received his B.S. and M.S. degrees in physics from Xiamen University in 1983 and 1986, respectively, and Ph.D. degree in electrical engineering from the University of Illinois at Urbana-Champaign in 1989. His research interests include computational electromagnetics and acoustics, inverse problems, and their applications in geophysics, nanophotonics, and biomedical imaging. He has published over 300 refereed journal papers and 450 conference papers in conference proceedings. He was with the Electromagnetics Laboratory at the University of Illinois at Urbana-Champaign as a Research Assistant from September 1986 to December 1988, and as a Postdoctoral Research Associate from January 1989 to February 1990. He was a Research Scientist and Program Leader with Schlumberger-Doll Research, Ridgefield, CT from 1990 to 1995. From 1996 to May 1999 he was an Associate Professor with New Mexico State University. Since June 1999 he has been with Duke University where he is now a Professor of Electrical and Computer Engineering.
Dr. Liu is a Fellow of the IEEE, Fellow of the Acoustical Society of America, Fellow of Electromagnetics Academy, and Fellow of the Optical Society of America. Currently he serves as the founding Editor in Chief of the IEEE Journal on Multiscale and Multiphysics Computational Techniques, and an Editor for the Journal of Computational Acoustics. He received the 1996 Presidential Early Career Award for Scientists and Engineers (PECASE) from the White House, the 1996 Early Career Research Award from the Environmental Protection Agency, and the 1997 CAREER Award from the National Science Foundation. He serves as an IEEE Antennas and Propagation Society Distinguished Lecturer for 2014-2016.
Acoustic/seismic and electromagnetic waves have widespread applications in geophysical subsurface sensing and imaging, and they are also coupled with subsurface fluid flow. In these applications, often the problems of understanding the underlying wave phenomena, designing the sensing and imaging measurement systems, and performing data processing and image reconstruction require multiscale and multiphysics computation involving acoustics and electromagnetics. It is very challenging to solve such problems with the traditional finite difference and finite element methods. In this presentation (an IEEE Antennas and Propagation Society Distinguished Lecture), several high-performance computational methods and super-resolution imaging in acoustics and electromagnetics will be discussed along with their applications in oil exploration and subsurface imaging.
Parallel Finite Element Method Solver for the Analysis of Large Scale Objects
Prof. Magdalena Salazar-Palma (Carlos III University of Madrid)
Dr. D. García-Doñoro (Xidian University)
Dr. A. Amor-Martín (Carlos III University of Madrid)
Dr. L. E. García-Castillo (Carlos III University of Madrid)
Magdalena Salazar-Palma received his MS and PhD from Polytechnic University of Madrid, Spain. She is a Professor at the Department of Signal Theory and Communications, Carlos III University of Madrid, and co-director of the Radiofrequency, Electromagnetics, Microwaves and Antennas Research Group (GREMA).
She has developed her research in electromagnetic field theory, advanced computational and numerical methods, advanced network (passive devices, filters and multiplexers) theory and design, antenna arrays and smart antennas, novel materials for the implementation of devices and antennas with improved performance (multiband, miniature size, etc.), millimeter, submillimeter and THz frequency band technologies; radio waves propagation theory; and history of telecommunications.
She has co-authored 7 scientific books and 30 book contributions published by international editorial companies, 103 articles in scientific journals, 370 contributions for international symposia and other publications. She has coauthored 2 European/USA patents and several software packages for the analysis and design of microwave and millimeter wave passive components, antennas and antenna arrays, advanced filters and multiplexers, under exploitation by multinational companies. She has participated (as PI or researcher) in a total of 93 research projects (43) and contracts (50) financed by Spanish, European, and USA public institutions and companies. She received two individual research awards. In 2016 she got an Honorary Doctorate from Aalto University, Finland. She has received recognitions, among them the elevation to IEEE Fellow.
Since 1989 she has served IEEE in different positions. Among them: Spain AP-S/MTT-S Joint Chapter Chair, Spain Section Chair, Region 8 Committee member, WIE Committee Chair, AP-S AdCom member, 2011 AP-S President, TAB member, 2014 Sections Congress Chair, member of TAB Society Review Committee, several Awards committees, MGAB, SIGHT (Special Interest Group on Humanitarian Technologies) Communities of Practice Committee, IEEE Fellow Committee, MTT-S AdCom, and IEEE Ethics Committee Chair.
Nowadays, the analysis of large scale objects is of crucial interest in military (and also civil) nautical and aeronautical industry. The use of higher frequencies in modern radars makes the analysis a challenge, despite the constant enhancements in computer power, especially due to the large electrical sizes of the objects. Thus, different computer techniques for electromagnetic analysis have been used in the past years. In this context, Finite Element Method (FEM) has demonstrated to be a powerful computational tool in a wide number of problems of different physics and, specifically, in electromagnetics , . During recent years, the authors have been focus on the development of a parallel FEM electromagnetic code able to analyze large scale objects on high performance computing (HPC) clusters. The code, namely HOFEM , is part of commercial electromagnetic suite HOBBIES .
HOFEM makes use of a weak formulation based on the double curl vector wave equation. The discretization of the computation domain is performed by using our own implementations of higher-order curl-conforming tetrahedral and triangular prismatic finite elements of Nedelec first family. The parallelization of HOFEM is achieved by the use of the Message Passing Interface (MPI) paradigm with multi-thread execution. The code employs a traditional direct solver algorithm that, together with an appropriate conformal decomposition method, provides a good efficiency for large-scale analysis. The use of these techniques entails higher computational requirements in the form of larger amount of RAM memory than those based on iterative or Domain Decomposition techniques. However, the code is able to maximize its performance of HPC systems to relieve this issue.
 M. Salazar-Palma, T. K. Sarkar, L. E. García-Castillo, T. Roy, and A. R. Djordjevic, Iterative and Self-Adaptive Finite-Elements in Electromagnetic Modeling, Norwood, MA: Artech House Publishers, Inc., 1998.
 M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. John Wiley & Sons, Inc., 2002.
 D. García-Doñoro, I. Martínez-Fernández,
L. E. García-Castillo, and M. Salazar-Palma, "HOFEM: A higher order fnite element method electromagnetic simulator," in International Conference on Computational Electromagnetics, ICCEM 2015, City University of Hong Kong, Hong Kong, China, Feb. 2015.
 Y. Zhang, T. K. Sarkar, X. Zhao, D. García-Doñoro, W. Zhao, M. Salazar, and S. Ting, Higher Order Basis Based Integral Equation Solver (HOBBIES), John Wiley & Sons, Inc., 2012, ISBN: 9781118140659.
Hierarchical Basis Functions for the Numerical Modeling of Edge-Field Singularities
Prof. Roberto D. Graglia (Polytechnic of Turin)
Prof. Andrew F. Peterson (Georgia Institute of Technology)
Prof. Paolo Petrini (Polytechnic of Turin)
Roberto D. Graglia received the Laurea degree (summa cum laude) in electronic engineering from the Polytechnic of Turin in 1979, and the Ph.D. degree in electrical engineering and computer science from the University of Illinois at Chicago in 1983. He is now Professor of Electrical Engineering at the Polytechnic of Turin, Italy. He was the President of the IEEE AP-S during 2015. He is a Fellow of the IEEE. His areas of interest comprise numerical methods for high- and low-frequency electromagnetics, theoretical and computational aspects of scattering and interactions with complex media, waveguides, antennas, electromagnetic compatibility, and low-frequency phenomena. He has organized and offered several short courses in these areas.
Andrew F. Peterson received the B.S., M.S., and Ph.D. degrees in electrical engineering from the University of Illinois at Urbana-Champaign in 1982, 1983, and 1986, respectively. He is now Professor and Associate Chair for Faculty Development at the Georgia Institute of Technology, Atlanta. He conducts research in the development of computational techniques for microwave frequency electromagnetic applications. He was the President of the IEEE AP-S during 2006 and the President of ACES from 2011-2013. He is a Fellow of the IEEE and a Fellow of ACES, and a member of URSI Commission B, the American Society for Engineering Education, and the American Association of University Professors. He is also a recipient of the IEEE Third Millennium Medal.
Paolo Petrini received the Laurea degree (summa cum laude) in electronic engineering from the Polytechnic of Turin, Italy, in 1979. In 1980-1981, he was Research Engineer at CSELT, Italy,
while in 1981-1982 was Research Engineer at CERN (European Center for Nuclear Research, Geneva, Switzerland). From 1983 to 2012, he worked as a registered engineer working in the fields of RF-Microwave and Aerospace engineering, with customers among the most important Companies in Europe. He is now a Research Assistant with the Department of Electronics and Telecommunications, Polytechnic of Turin.
Basis functions have been developed that permit accurate modeling of certain types of singularities in electromagnetic fields at geometric edges and corners. For example, the authors recently introduced hierarchical (scalar and vector) basis functions to represent vertex singularities in two-dimensional cells, designed to be used in connection with hierarchical polynomial representations for adaptive p-refinement on domains meshed with cells of various shape. Singular bases and their derivatives may contain multiple fractional exponents as needed in different field components. Hierarchical bases of this flexibility and adaptive refinement provide a powerful modeling capability that combines an efficient distribution of unknowns throughout the domain with a generality that, as an example, can facilitate the analysis of multiscale problems. There is considerable interest in extending this type of approach to edge singularities on surfaces in three dimensions, problems that are often treated by surface integral equations. While basis functions have been proposed for dominant edge singularities of this type, additional work is necessary before a hierarchical and adaptive framework can be assembled.
In this presentation we will briefly review the development of hierarchical basis functions for vertex singularities and present results that demonstrate their value. Then, we present new divergence-conforming vector basis functions for surface edges that are hierarchical in nature and offer the flexibility to handle multiple fractional exponents to better model singular currents and charges. Preliminary results will show the utility of the new approach.