Table of Contents
Overview
Definition and Importance
Computational Electromagnetics (CEM) is a field that focuses on the application of computational methods to solve problems related to electromagnetic fields, particularly those described by partial differential equations. The roots of computational physics, which encompasses CEM, can be traced back to the foundational work of early scientists such as Bernoulli, Newton, and Gauss, long before the advent of modern computers.[2.1] The significance of CEM is underscored by its close relationship with the IEEE Antennas and Propagation Society (AP-S), which has celebrated 75 years of research in this domain. This milestone highlights the intertwined histories of CEM and AP-S, reflecting a shared evolution that spans half of the history of Maxwell's equations.[4.1] The development of CEM has been driven by the need for effective designs in antennas and electromagnetic systems, which in turn has necessitated the creation of accurate simulation tools that leverage the capabilities of available computer resources.[5.1] CEM employs a variety of computational techniques to address complex electromagnetic problems. These methods include time-stepping through equations over the entire domain, banded matrix inversion for finite element methods, and numerical integration techniques such as the method of moments. Additionally, advanced techniques like the Cagniard-deHoop method of moments and the finite integration technique are utilized to solve electromagnetic field problems in both time and frequency domains.[6.1] The continuous advancement of these computational tools is crucial for the ongoing development and optimization of electromagnetic applications.Applications in Various Fields
Computational electromagnetics (CEM) has a wide range of applications across various fields, particularly in the design and optimization of antennas. The high fidelity of Maxwell's equations in describing electromagnetic phenomena often results in numerical solutions that are more reliable than traditional laboratory experiments, making CEM a crucial tool in this domain.[8.1] For instance, advancements in computational methods have significantly enhanced the accuracy and efficiency of antenna pattern measurements. By employing a simple dipole antenna as a probe to scan over the measurement plane, researchers have achieved improved accuracy in planar near-field to far-field transformations compared to classical Fourier-based methods.[19.1] Moreover, the integration of cutting-edge computational techniques has been pivotal in the design of antennas for emerging technologies such as 5G, 6G, and the Internet of Things (IoT). These advancements reflect the dynamic nature of antenna research, which increasingly relies on sophisticated computational methods to meet the demands of interconnected systems.[23.1] In addition to antenna design, CEM is instrumental in modeling and simulating electromagnetic fields around complex structures. This capability is essential for understanding how antennas interact with their environments, which can significantly modify their characteristics.[20.1] Various numerical methods, including the finite element method (FEM) and the method of moments (MOM), are commonly employed to solve Maxwell's equations and analyze electromagnetic behavior in different scenarios.[28.1]In this section:
Computational ElectromagneticsElectromagnetic FieldsPartial Differential EquationsComputational PhysicsAntennas
History
Early Developments
The field of computational electromagnetics (CEM) began to take shape in the mid-1960s, coinciding with the advent of powerful mainframe computers and an increasing demand for antenna modeling capabilities across various sectors, including rural television reception, commercial and space communications, and defense applications.[62.1] This period marked a significant transition from traditional analytical methods to numerical methods, which allowed for more complex and accurate modeling of electromagnetic phenomena.[73.1] The development of CEM was influenced by earlier computational physics efforts, which date back to the work of pioneers such as Bernoulli, Newton, and Gauss. However, the true application of numerical methods, particularly stochastic algorithms and finite difference techniques for solving partial differential equations, became feasible only with the rise of modern computing technology.[1.1] The 1960s saw the emergence of various numerical methods, including the Method of Moments (MoM), which was notably advanced by Harrington, who is often regarded as the "father of MoM" for his contributions to its foundational principles and applications.[63.1] During this era, significant advancements in computer science and engineering were driven by military funding, which facilitated the rapid evolution of computational techniques.[64.1] The introduction of algorithms capable of numerically modeling Maxwell's equations with high accuracy was a pivotal breakthrough that laid the groundwork for future developments in CEM.[65.1] As researchers began to explore these numerical methods, they faced challenges related to the simulation and calculation of electromagnetic-mechanical coupled physical fields, which remained a critical focus within the CEM community.[76.1]Key Figures and Contributions
The history of Computational Electromagnetics (CEM) is marked by significant contributions from key figures who have shaped the field through their innovative approaches and foundational work. Harrington, often referred to as the "father of the Method of Moments" (MoM), is a pivotal figure in this domain. His work was crucial in establishing the foundations of MoM, demonstrating its generality and power, and developing techniques applicable to a wide range of electromagnetic problems. Notably, a 1967 article by Harrington was initially rejected by the IEEE Transactions on Antennas and Propagation due to skepticism about representing continuous physical quantities and the limitations of early computational capabilities, such as matrix inversion.[78.1] The mid-1960s marked a turning point for CEM, coinciding with the advent of mainframe computers and the growing demand for antenna modeling across various sectors, including rural television, commercial communications, and defense applications. This period catalyzed the development of computational methods that could effectively address complex electromagnetic problems.[79.1] In the realm of computational methods, various techniques have emerged, including time-stepping through equations, banded matrix inversion, and the use of fast Fourier transforms. The Cagniard-deHoop method of moments (CdH-MoM) and the finite integration technique (FIT) are notable examples illustrating the evolution of numerical approaches in solving electromagnetic field problems.[80.1] The IEEE Antennas and Propagation Society (AP-S) has been instrumental in fostering collaboration among researchers and practitioners in CEM. Over the past 75 years, the society has facilitated numerous initiatives that have advanced the field, including promoting research and organizing conferences that highlight breakthroughs in computational methods.[70.1]Theoretical Foundations
Maxwell's Equations
Maxwell's equations serve as the cornerstone of electromagnetism and have been pivotal in advancing computational electromagnetics, particularly in the context of metamaterials. Recent analyses have derived a simple integro-differential vector wave equation from the metamaterial Maxwell's equations, highlighting the evolving nature of these foundational principles in modern applications.[114.1] The reliability of Maxwell's equations in providing accurate predictions in electromagnetism is well established. Numerical solvers extend the reach of electromagnetic solutions beyond traditional analytical closed-form solutions, which is especially critical in the design of metamaterials. Here, the objective is to identify geometries that yield optimal electromagnetic properties.[115.1] The primary allure of metamaterials lies in their potential applications, which include the construction of perfect lenses, sub-wavelength imaging, and cloaking technologies. Since the year 2000, extensive numerical simulations based on Maxwell's equations have been conducted to explore these applications, underscoring the equations' relevance in contemporary engineering and physics.[116.1]Numerical Techniques in CEM
Numerical techniques in computational electromagnetics (CEM) are essential for solving Maxwell's equations, which describe the behavior of electric and magnetic fields. The evolution of CEM has been significantly influenced by the development of numerical methods that leverage the computational power of modern digital computers. These methods allow for the efficient resolution of complex electromagnetic problems, particularly in layered media and various engineering applications.[85.1] Three primary full-wave numerical methods are widely utilized in CEM: the Method of Moments (MoM), the Finite Element Method (FEM), and the Finite-Difference Time-Domain (FDTD) method. Each of these methods provides unique advantages in simulating electromagnetic fields and obtaining valid approximations to the solutions of Maxwell's equations.[95.1] The MoM is particularly effective for problems involving surface currents, while FEM is favored for complex geometries and boundary conditions. The FDTD method excels in time-domain simulations, making it suitable for transient analysis.[95.1] The application of these numerical methods involves discretizing Maxwell's equations, which is a crucial step due to the limitations of digital computer arithmetic that can only process a finite number of values.[96.1] This discretization allows for the transformation of continuous equations into a form that can be solved numerically, facilitating the analysis of electromagnetic phenomena in various contexts, including optical devices and biomedical engineering.[94.1] Despite the advancements in numerical techniques, challenges remain in applying these methods to real-world scenarios. Issues such as computational efficiency, accuracy, and the handling of complex boundary conditions are prevalent.[89.1] Future directions in CEM emphasize the integration of hybrid approaches, machine learning, and high-performance computing to overcome these limitations and enhance the capabilities of numerical simulations.[89.1]Recent Advancements
New Algorithms and Techniques
Recent advancements in computational electromagnetics (CEM) have led to the development of new algorithms and techniques that significantly enhance the ability to solve complex electromagnetic problems. These advancements are particularly evident in the emergence of highly scalable algorithms designed to tackle large-scale and intricate electromagnetic challenges, which are often not efficiently addressed by traditional methods.[121.1] The classical CEM methods, such as the method of moments (MoM), finite element method (FEM), and finite-difference time-domain (FDTD), have seen substantial improvements in recent years, allowing for more accurate modeling and simulation of electromagnetic systems.[158.1] Additionally, the integration of machine learning techniques into CEM has shown disruptive potential, enabling unprecedented speeds in evaluating solutions to CEM problems.[123.1] This augmentation through artificial intelligence not only enhances computational efficiency but also addresses various challenges faced in practical applications, such as multiscale modeling and simulation.[157.1] Moreover, a comprehensive review of 75 years of research within the IEEE Antennas and Propagation Society highlights the interwoven history of CEM and its continuous evolution, showcasing the significant breakthroughs achieved over the decades.[124.1] These advancements reflect a concerted effort within the engineering community to innovate and refine computational techniques, ultimately benefiting researchers, engineers, and graduate students engaged in contemporary topics in CEM.[121.1]Applications in Emerging Technologies
Recent advancements in computational electromagnetics (CEM) have catalyzed significant progress in emerging technologies by integrating machine learning techniques to enhance the efficiency of solving complex electromagnetic problems. Machine learning, particularly through deep neural networks, has enabled the development of specialized CEM algorithms that can evaluate solutions at unprecedented speeds, which is crucial for applications requiring rapid and accurate computations, such as antenna array processing, microwave circuit design, remote sensing, and radar systems.[126.1][129.1] In the realm of metamaterial device design and simulation, machine learning has been pivotal in overcoming the computational expense and slow pace of traditional modeling methods. By streamlining the modeling process, machine learning accelerates design and reduces costs, making it indispensable for a wide range of applications.[128.1] Telecommunications have also benefited from CEM advancements, particularly in the development of Multiple Inputs Multiple Outputs (MIMO) systems, which are essential for modern wireless communication technologies like 5G. Efficient CEM algorithms are critical for designing and controlling MIMO antenna arrays, facilitating high-throughput communication and effective beamforming.[138.1] Furthermore, high-performance computing architectures have significantly improved the accuracy and efficiency of CEM simulations. The development of parallel finite-element codes, such as the ACE3P suite, allows for high-fidelity simulations that integrate multi-physics effects, essential for applications in particle accelerators and other complex systems. The use of GPU-accelerated programs has demonstrated substantial improvements in computational efficiency, achieving speedup ratios of 5 to 13 times compared to traditional CPU programs.[141.1][142.1]Computational Techniques
Finite Difference Time Domain (FDTD)
The Finite Difference Time Domain (FDTD) method is a prominent numerical technique used in computational electromagnetics (CEM) for solving Maxwell's equations. This method discretizes both time and space, allowing for the simulation of electromagnetic wave propagation in complex environments. FDTD has gained popularity due to its straightforward implementation and ability to handle a wide range of electromagnetic problems, from antenna design to waveguide analysis.[169.1] FDTD operates by approximating the derivatives in Maxwell's equations using finite differences, which leads to a set of difference equations that can be solved iteratively over time. This approach enables the modeling of transient electromagnetic phenomena, making it particularly useful for applications where time-varying fields are of interest.[171.1] The method's versatility allows it to be applied across various frequency ranges, from radio frequencies to optical wavelengths, thus catering to a broad spectrum of engineering applications.[170.1] One of the key advantages of FDTD is its ability to model complex geometries and materials, including anisotropic and nonlinear media. This capability is essential for accurately predicting the behavior of electromagnetic fields in real-world scenarios, such as in the design of advanced antennas and metamaterials.[168.1] However, FDTD also faces challenges, particularly regarding computational efficiency and memory requirements, especially when simulating large-scale problems or high-resolution models.[179.1] Recent advancements in computational power and algorithmic techniques have significantly enhanced the performance of FDTD simulations. The integration of parallel computing and high-performance computing resources has allowed for the handling of larger simulations with greater detail, thereby improving the accuracy and applicability of the FDTD method in modern engineering practices.[182.1] As a result, FDTD continues to be a vital tool in the field of computational electromagnetics, contributing to the ongoing development of innovative electromagnetic devices and systems.In this section:
Challenges And Limitations
Computational Complexity
The computational complexity in computational electromagnetics (CEM) arises from the need to solve large-scale problems involving intricate structures and high degrees of freedom. Recent advancements, such as the implementation of the Fast Multipole Method (FMM), have significantly expanded the capabilities of the Method of Moments (MoM), allowing for the resolution of problems that require handling up to 10^6 degrees of freedom or more.[206.1] Additionally, distributed processing techniques have enabled Finite-Difference Time-Domain (FDTD) methods to manage upwards of 10^9 degrees of freedom on moderate computing platforms, showcasing the increasing computational demands of modern CEM applications.[206.1] Despite these advancements, many practical CEM modeling problems remain challenging due to their inherent complexity. For instance, the analysis of large arrays covered by frequency selective radomes presents formidable difficulties, necessitating the development of numerically efficient techniques to address these issues.[205.1] Furthermore, the design of stealth technologies and precision guidance systems in military applications is particularly affected by the computational costs associated with optimizing a large number of design variables.[214.1] The challenges of modeling complex environments and processing real-time data further complicate the effectiveness of these systems.[216.1] Moreover, the intricate geometrical features of radar systems, including electrically large scattering entities, contribute to a variety of electromagnetic phenomena such as diffraction and reflection, which complicate the computational modeling process.[219.1] The performance of modern radar systems, which integrate electrical, mechanical, and structural components, is influenced by the collective behavior of these subsystems under various conditions, adding another layer of complexity to CEM.[221.1] As a result, the ongoing search for efficient computational techniques remains a critical focus in the field, particularly as the demand for high-fidelity simulations continues to grow.[207.1]Accuracy and Reliability of Solutions
The accuracy and reliability of solutions in computational electromagnetics (CEM) are significantly influenced by various challenges inherent in numerical methods and modeling techniques. One of the primary challenges is the numerical simulation and calculation of electromagnetic-mechanical coupled physical fields, which poses technological difficulties particularly relevant in applications such as electromagnetic launch and braking engineering.[76.1] As computational methods for solving Maxwell's equations mature, the focus has shifted towards tackling complex multiphysics problems that encompass a wide range of applications in science and technology.[229.1] However, these multiphysics modeling challenges often lead to limitations in accuracy and efficiency, especially when dealing with electrically large objects that possess fine structures.[227.1] The integration of advanced numerical methods, such as the Finite Difference Time Domain (FDTD), Finite Element Method (FEM), and Method of Moments (MoM), is essential for addressing these complex electromagnetic problems.[77.1] Despite these advancements, the computational burden remains high, with some methods requiring the handling of millions to billions of degrees of freedom, which can strain computational resources.[230.1] Moreover, the emergence of realistic applications in engineering design has introduced new challenges, including multiscale modeling and the need for accurate simulations that reflect real-world scenarios.[227.1] These challenges are compounded by the limitations of current numerical methods, which may not always provide reliable solutions under varying conditions, thereby impacting the overall effectiveness of technologies developed for military and security applications.[231.1]In this section:
Computational ComplexityDistributed ProcessingGuidance SystemsReal-time DataCollective Behavior
Future Directions
Trends in Research and Development
Recent advancements in Computational Electromagnetics (CEM) have highlighted several key trends in research and development, particularly in the integration of machine learning techniques and hybrid numerical methods. The CEM community has made significant progress in addressing complex electromagnetic problems through the development of new algorithms and applications that are not easily solvable with traditional techniques such as the Finite Element Method (FEM), Finite Difference Time Domain (FDTD), and Method of Moments (MoM).[248.1] One notable trend is the increasing use of machine learning to augment CEM methodologies. This integration has shown disruptive potential, enabling the evaluation of solutions to CEM problems at unprecedented speeds.[258.1] Recent developments in machine learning hardware and software are enhancing conventional CEM techniques, allowing for the creation of specialized algorithms that leverage deep neural networks.[272.1] These advancements are particularly relevant in applications such as antenna design, radar, communication, and imaging, where intelligent algorithms are being developed to improve performance and efficiency.[259.1] Moreover, hybrid approaches that combine traditional numerical methods with newer techniques are gaining traction. These hybrid methods aim to overcome the limitations of classical techniques by integrating the strengths of various approaches, such as combining MoM with Uniform Theory of Diffraction (UTD) or other asymptotic methods.[270.1] The advantages of these hybrid strategies include improved accuracy and efficiency in solving complex electromagnetic problems, which are increasingly relevant in engineering designs that require multiscale modeling and simulation.[271.1] As the field continues to evolve, future directions emphasize the importance of high-performance computing alongside these innovative methodologies. The ongoing research aims to expand the scope of CEM applications while addressing current limitations, thereby advancing both electromagnetic theory and practical applications.[271.1]Integration with Emerging Technologies
The integration of machine learning (ML) techniques into computational electromagnetics (CEM) is poised to significantly enhance simulation accuracy and efficiency across various engineering applications. Recent advancements in ML hardware and software have the potential to augment conventional CEM methods, enabling the development of specialized algorithms that utilize deep neural networks for improved problem-solving capabilities.[252.1] This integration allows for the creation of generalized surrogate electromagnetic solvers, which can be realized through the training of deep convolutional neural networks using simulated data.[253.1] Moreover, the application of ML in CEM is not limited to traditional methods; it also addresses challenges in power system applications, providing valuable insights into the efficiency and capabilities of machine learning in electromagnetics.[254.1] The transformative impact of ML is evident in its ability to evaluate solutions to CEM problems at unprecedented speeds, thereby revolutionizing the field.[103.1] In addition to machine learning, the integration of multiscale modeling techniques with emerging computational methods is enhancing the accuracy and efficiency of simulations in electromagnetics. This synergy is particularly beneficial in managing complex data sets and uncovering correlations between multifaceted phenomena, which is crucial for advancing human health and other applications.[265.1] The combination of ML and multiscale modeling creates robust predictive models that effectively integrate underlying physics, thereby addressing ill-posed problems and exploring extensive design spaces.[265.1] As the demand for advanced computational tools grows, particularly with the rise of connected devices and platforms such as 5G and 6G, CEM tools have become integral to the product design cycle. Numerical simulations now facilitate the evaluation of various factors, including antenna design and electromagnetic compatibility (EMC), offering greater flexibility compared to traditional testing methods.[267.1] Companies like Ansys have been at the forefront of this evolution, providing simulation software that allows for virtual prototyping, which is essential for designing high-performance electronics.[268.1] However, challenges remain in accurately simulating the electromagnetic properties of emerging materials, such as metamaterials and nanomaterials. The complexity of these materials, characterized by their unique physical structures rather than their chemistry, necessitates sophisticated multiscale modeling approaches to effectively capture their behavior across different scales.[279.1] The future of CEM will likely involve overcoming these challenges through continued advancements in deep learning and multiscale modeling, paving the way for innovative applications in the field.[279.1]In this section:
References
[1] A Brief History of Computational Electromagnetics - IEEE Xplore — A Brief History of Computational Electromagnetics Abstract: Computational Physics, i.e. computational methods applied to physics, is much older than computers, dating back to Bernoulli, Newton and Gauss. Yet true application of stochastic algorithms or applications of finite differences to partial differential equations is feasible only by
[2] A Brief History of Computational Electromagnetics — This work will briefly review the development of Computational Physics, with a focus on the solution of partial differential equations and boundary value problems and a particular attention to the field of Computatory Electromagnetics. Computational Physics, i.e. computational methods applied to physics, is much older than computers, dating back to Bernoulli, Newton and Gauss.
[4] PDF — in computational electromagnetics (CEM) within the IEEE Antennas and Propagation Society (AP-S) and the AP community at large on the occasion of the 75th anniversary of AP-S, where both CEM and AP-S have similar and interwoven histories of 75 years, a half of the history of Maxwell's equations. The article discusses the discoveries,
[5] Computational Electromagnetics and the IEEE Antennas and ... - IEEE Xplore — Computational Electromagnetics is heavily intertwined with the IEEE Antennas and Propagation Society. Effective designs for antennas and electromagnetic systems motivated accurate simulation tools that continuously exhausted the available computer resources. This 2-part article traces the development of computational tools and techniques and ties them to milestones in computer hardware, the
[6] Computational electromagnetics - Wikipedia — Some typical methods involve: time-stepping through the equations over the whole domain for each time instant; banded matrix inversion to calculate the weights of basis functions (when modeled by finite element methods); matrix products (when using transfer matrix methods); calculating numerical integrals (when using the method of moments); using fast Fourier transforms; and time iterations (when calculating by the split-step method or by BPM). The Cagniard-deHoop method of moments (CdH-MoM) is a 3-D full-wave time-domain integral-equation technique that is formulated via the Lorentz reciprocity theorem. The finite integration technique (FIT) is a spatial discretization scheme to numerically solve electromagnetic field problems in time and frequency domain.
[8] PDF — 36.1 Computational Electromagnetics and Numerical Meth-ods Due to the high delity of Maxwell's equations in describing electromagnetic physics in na-ture, often time, a numerical solution obtained by solving Maxwell's equations is more reliable than laboratory experiments. This eld is also known as computational electromagnet-ics.
[19] Use of Computational Techniques in Electromagnetics to Enhance the ... — The objective of this paper is to demonstrate that computational techniques in electromagnetics can be used very effectively to enhance the accuracy and efficiency of antenna pattern measurements. It is illustrated that this is carried out by using a simple dipole antenna used as a single probe to scan over the measurement plane in front of the near field of the antenna. Then using the
[20] Low-frequency computational electromagnetics for antenna analysis — Low-frequency computational electromagnetics for antenna analysis . × ... followed by a consideration of some computational issues that affect model accuracy, efficiency, and utility. ... Modeling Antenna-Structure Effects: Antennas are often mounted on complex structures, the effect of which can greatly modify the antenna's characteristics.
[23] Antenna Design and Optimization for 5G, 6G, and IoT - MDPI — Collectively, these contributions offer a comprehensive perspective on the latest advancements in antenna design and optimization, specifically for 5G, 6G, and IoT applications. ... The fusion of advanced materials, miniaturization techniques, and cutting-edge computational methods signifies the vibrant and dynamic nature of antenna research
[28] Computational Electromagnetics - SpringerLink — Access this book Buy Hardcover Book About this book This book introduces three of the most popular numerical methods for simulating electromagnetic fields: the finite difference method, the finite element method and the method of moments. In particular it focuses on how these methods are used to obtain valid approximations to the solutions of Maxwell's equations, using, for example, "staggered grids" and "edge elements." The main goal of the book is to make the reader aware of different sources of errors in numerical computations, and also to provide the tools for assessing the accuracy of numerical methods and their solutions. Search within this book Book Title: Computational Electromagnetics Authors: Thomas Rylander, Par Ingelström, Anders Bondeson Access this book About this book
[62] Early Development of Computational Electromagnetics-A Perspective — It may be said that computational electromagnetics (CEM) began in earnest around the mid-1960s, spurred by the simultaneous emergence of available mainframe computers and the increasing need for antenna modeling capabilities to support such diverse sectors as rural TV reception, commercial and space communications, and defense.
[63] Computational Electromagnetics and the IEEE Antennas and ... - IEEE Xplore — To better understand this historical period, a 1967 article by Harrington was previously rejected by IEEE Transactions on Antennas and Propagation for reasons including that “it is not possible to represent continuous physical quantities, such as current, using discontinuous quantities,” and “it is not possible for a computer to invert even a 100 × 100 matrix because the magnetic tape will wear out going back and forth.” Harrington is sometimes considered the “father of MoM,” not only for having first named the method but, above all, because he was instrumental in consolidating its foundations, understanding its generality and power, and developing and applying appropriate techniques to a wide variety of problems .
[64] PDF — Important advances in computer science, aerospace and materi-als engineering, and telecommunications originated from these programs and other lesser-known military programs, such as the development of stealth technology. The rapid evolution of computers beginning in the early 1960s was enabled by huge funding allocated for the devel-
[65] PDF — The field of computational electromagnetics (CEM) involves the development of algorithms that can numerically model Maxwell's equations with high accuracy. It initiated during the first computing revolution in the 1960's, during which a wide range of partial differential equation solvers were developed across many fields of science and engineering, including structural analysis, fluid flow
[70] 75 Years of IEEE AP-S Research in Computational Electromagnetics: A ... — This article presents an overview of 75 years of research in computational electromagnetics (CEM) within the IEEE Antennas and Propagation Society (AP-S) and the AP community at large on the occasion of the 75th anniversary of AP-S, where both CEM and AP-S have similar and interwoven histories of 75 years, a half of the history of Maxwell's equations. The article discusses the discoveries
[73] PDF — 37.1 Computational Electromagnetics and Numerical Meth-ods Numerical methods exploit the blinding speed of modern digital computers to perform calcu-lations, and hence to solve large system of equations. These equations are partial di erential equations or integral equations. When these methods are applied to solving Maxwell's equa-tions and related equations, the eld is known as computational
[76] A numerical simulation method for solving electromagnetic-mechanical ... — The challenge of numerical simulation and calculation of electromagnetic-mechanical coupled physical fields has always been a hot topic in the computational electromagnetics community, as well as a technological difficulty that must be taken into account in electromagnetic launch and braking engineering.
[77] Advanced Numerical Methods in Electromagnetics: Techniques and ... — This research paper provides an in-depth exploration of advanced numerical methods in electromagnetics, including the Finite Difference Time Domain (FDTD), Finite Element Method (FEM), Boundary Element Method (BEM), and Method of Moments (MoM). These methods are essential for solving complex electromagnetic problems that are not feasible with traditional analytical approaches, enabling precise
[78] Computational Electromagnetics and the IEEE Antennas and Propagation ... — To better understand this historical period, a 1967 article by Harrington was previously rejected by IEEE Transactions on Antennas and Propagation for reasons including that “it is not possible to represent continuous physical quantities, such as current, using discontinuous quantities,” and “it is not possible for a computer to invert even a 100 × 100 matrix because the magnetic tape will wear out going back and forth.” Harrington is sometimes considered the “father of MoM,” not only for having first named the method but, above all, because he was instrumental in consolidating its foundations, understanding its generality and power, and developing and applying appropriate techniques to a wide variety of problems .
[79] Early Development of Computational Electromagnetics-A Perspective — It may be said that computational electromagnetics (CEM) began in earnest around the mid-1960s, spurred by the simultaneous emergence of available mainframe computers and the increasing need for antenna modeling capabilities to support such diverse sectors as rural TV reception, commercial and space communications, and defense.
[80] Computational electromagnetics - Wikipedia — Some typical methods involve: time-stepping through the equations over the whole domain for each time instant; banded matrix inversion to calculate the weights of basis functions (when modeled by finite element methods); matrix products (when using transfer matrix methods); calculating numerical integrals (when using the method of moments); using fast Fourier transforms; and time iterations (when calculating by the split-step method or by BPM). The Cagniard-deHoop method of moments (CdH-MoM) is a 3-D full-wave time-domain integral-equation technique that is formulated via the Lorentz reciprocity theorem. The finite integration technique (FIT) is a spatial discretization scheme to numerically solve electromagnetic field problems in time and frequency domain.
[85] ESSENTIALS OF COMPUTATIONAL ELECTROMAGNETICS - Wiley Online Library — Computational electromagnetics (CEM) has evolved as an independent, vibrant ... which play a key role. The landmarks of progress in CEM are achieved by ... the numerical methods are introduced and the essential principles, i.e., the techniques improving the numerical efficiency, and the skills in writing computer programs, are detailed. In
[89] Advanced Numerical Methods in Electromagnetics: Techniques and Applications — Future directions are identified, emphasizing the potential of hybrid approaches, machine learning integration, and high-performance computing to address current limitations and expand the scope of these methods. The insights gained underline the critical role of numerical techniques in advancing electromagnetic theory and applications.
[94] Computational Electrodynamics | Modeling, Methods & Applications — Computational Electrodynamics, often referred to as computational electromagnetics (CEM), explores the numerical methods used for solving Maxwell's equations - the core principles that explain how electric and magnetic fields are generated and altered by charges and currents.
[95] Computational Electromagnetics for Rf and Microwave Engineering — The numerical approximation of Maxwell's equations, computational electromagnetics (CEM), has emerged as a crucial enabling technology for radio-frequency, microwave, and wireless engineering. The three most popular "full-wave" methods - the Finite Difference Time Domain method, the Method of Moments, and the Finite Element Method - are introduced in this book by way of one- or two
[96] PDF — With the introduction of computers, new mathematical tools and engineering disciplines had to be devised to actually solve the electromagnetics equations. Since digital computer arithmetics typically just allows to process a finite number of real and integer values, the crucial step of almost any computational solution method is a discretization of Maxwell's equations. In the past decades
[103] PDF — This chapter explores the emerging topic of computational electromagnetics (CEM) augmentation using machine learning techniques, which has disruptive potential due to its ability to evaluate solutions to CEM problems with unprecedented speeds. We dis-cuss how recent developments in machine learning hardware and software can enhance
[114] Solving metamaterial Maxwell's equations via a vector wave integro ... — This paper presents a new analysis of Maxwell's equations in metamaterials. The new contribution is that a simple integro-differential vector wave equation is derived from the metamaterial Maxwell's equations.
[115] Fast approximate solvers for metamaterials design in electromagnetism — In electromagnetism, the model of Maxwell's equations yields accurate and trustworthy predictions. Numerical solvers can reach electromagnetic solutions far beyond the set of analytical closed-form solutions; this is crucial in metamaterials design where the goal is to find the geometry that generates an optimal electromagnetic solution for a desired property. Then why do we still need to
[116] Development of discontinuous Galerkin methods for Maxwell's equations ... — The main interest in metamaterials comes from their potential applications in diverse areas such as construction of a perfect lens, sub-wavelength imaging and cloaking. Since 2000, engineers and physicists have carried out many numerical simulations for Maxwell's equations when metamaterials are involved.
[121] Computational Electromagnetics: Recent Advances and Engineering ... — Computational Electromagnetics: Recent Advances and Engineering Applications | SpringerLink Access this book The book examines new algorithms, and applications of these algorithms for solving problems of current interest that are not readily amenable to efficient treatment by using the existing techniques. Efficient Numerical Techniques for Analyzing Microstrip Circuits and Antennas Etched on Layered Media via the Characteristic Basis Function Method “This book collects in 19 chapters new computational techniques, developed in the engineering community, to solve large-scale and complex electromagnetic problems by using highly scalable algorithms. … The material in this book is useful to researchers, engineers, and graduate students who work on contemporary topics and recent developments in computational electromagnetics. Book Title: Computational Electromagnetics Access this book
[123] Machine Learning Advances in Computational Electromagnetics — Machine Learning Advances in Computational Electromagnetics | part of Advances in Electromagnetics Empowered by Artificial Intelligence and Deep Learning | Wiley-IEEE Press books | IEEE Xplore Machine Learning Advances in Computational Electromagnetics is part of: Advances in Electromagnetics Empowered by Artificial Intelligence and Deep Learning This chapter explores the emerging topic of computational electromagnetics (CEM) augmentation using machine learning techniques, which has disruptive potential due to its...Show More This chapter explores the emerging topic of computational electromagnetics (CEM) augmentation using machine learning techniques, which has disruptive potential due to its ability to evaluate solutions to CEM problems with unprecedented speeds. About IEEE Xplore | Contact Us | Help | Accessibility | Terms of Use | Nondiscrimination Policy | IEEE Ethics Reporting | Sitemap | IEEE Privacy Policy
[124] 75 Years of IEEE AP-S Research in Computational Electromagnetics: A ... — This article presents an overview of 75 years of research in computational electromagnetics (CEM) within the IEEE Antennas and Propagation Society (AP-S) and the AP community at large on the occasion of the 75th anniversary of AP-S, where both CEM and AP-S have similar and interwoven histories of 75 years, a half of the history of Maxwell's equations. The article discusses the discoveries
[126] Machine Learning Advances in Computational Electromagnetics — We discuss how recent developments in machine learning hardware and software can enhance conventional CEM techniques and enable specialized CEM algorithms using deep neural networks. We also review how generalized surrogate electromagnetic solvers can be realized by the training of deep convolutional neural networks using simulated data
[128] Machine Learning for Electromagnetic — ABSTRACT Computational electromagnetics has found success in the design and simulation of metamaterial devices for many applications. This work explores machine learning as a tool for computationally efficiently modeling metamaterial devices. Conventional methods have proven effective, though computationally expensive and slow, for
[129] Machine Learning in Electromagnetics: A Review and Some Perspectives ... — We review machine learning and its applications in a wide range of electromagnetic problems, including radar, communication, imaging and sensing. We extensively discuss some recent progress in development and use of intelligent algorithms for antenna design, synthesis, and characterization. We also provide some perspectives for future research directions in this emerging field of study.
[138] Computational Electromagnetics for Efficient Control Design of Massive ... — As Multiple Inputs Multiple Outputs (MIMO) is becoming one of the enable techniques in modern wireless communication like 5G/6G and beyond, it is important to design efficient controls for the MIMO antenna arrays to realize critical functions such as high-throughput communication and beamforming. Efficient and rigorous Computational Electromagnetics (CEM) algorithms are key for such control
[141] High Performance Computing in Parallel Electromagnetics Simulation Code ... — High Performance Computing in Parallel Electromagnetics Simulation Code suite ACE3P | IEEE Conference Publication | IEEE Xplore A comprehensive set of parallel finite-element codes suite ACE3P (Advanced Computational Electromagnetics 3D Parallel) is developed by SLAC for multi-physics modeling of particle accelerators running on massively parallel computer platforms for high fidelity and high accuracy simulation. Through the support of Department of Energy (DOE), SLAC has developed a comprehensive set of conformal, higher-order, parallel finite element electromagnetics modelling code suite ACE3P (Advanced Computational Electromagnetics 3D Parallel) for accelerator cavity and structure design including integrated multi-physics effects in electromagnetic, thermal, and mechanical characteristics with two unique features: (1) Based on higher order curved finite elements for high-fidelity modelling and improved solution accuracy; (2).
[142] High-efficiency computation for electromagnetic forming process: An ... — Finally, numerical results show that the efficiency of parallel computing (i.e., speedup ratio = T CPU /T GPU) of the proposed GPU-accelerated program is 5∼13 times higher than that of the CPU program in the simulation of the EMF process. It means that a large improvement of computational efficiency in EMF process is achieved.
[157] Application of Artificial Intelligence Techniques on Computational ... — This paper provides a review of the most recent advances in artificial intelligence (AI) as applied to computational electromagnetics (CEM) to address challenges and unlock opportunities in power system applications. It is intended to provide readers and practitioners in electromagnetics (EM) and related applicable fields with valuable perspectives on the efficiency and capabilities of machine
[158] A look at some challenging problems in computational electromagnetics ... — 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
[168] COMPUTATIONAL EM » IT'IS Foundation — In particular, computational electromagnetics (CEM) techniques are vital to the analysis and design of highly complex devices and applications as well as to predict and analyze the interaction mechanisms of electromagnetic fields within complex environments.
[169] New Trends in Computational Electromagnetics | IET Digital Library — Computational electromagnetics is an active research area on the development and implementation of numerical methods and techniques for rigorous solutions of physical problems in the entire spectrum of electromagnetic waves from radio frequencies to gamma rays. While a set of Maxwell's equations are sufficient to model most of the electromagnetic scenarios, analytical solutions are available
[170] 75 Years of IEEE AP-S Research in Computational Electromagnetics: A ... — Abstract: This article presents an overview of 75 years of research in computational electromagnetics (CEM) within the IEEE Antennas and Propagation Society (AP-S) and the AP community at large on the occasion of the 75th anniversary of AP-S, where both CEM and AP-S have similar and interwoven histories of 75 years, a half of the history of Maxwell's equations. The article discusses the
[171] PDF — The numerical approximation of Maxwell's equations, the subject of this book, is known as computational electromagnetics (CEM). CEM techniques have been available for close on four decades now. These techniques have gestated, grown and matured to the point where they form an invaluable part of current RF and microwave engineering practice .
[179] A survey of machine learning and evolutionary computation for antenna ... — To lower the computational overhead, machine learning (ML) methods have been incorporated to accelerate antenna optimization by building surrogate model of EM simulation from the way of expensive EM theories (called response model) and expensive objective or constrained functions (called specification model). From perspective of assisting optimization (refer to Fig. 5), response modeling (Wu et al., 2023) typically increases freedom in problem formulation in antenna design field (see Fig. 5(a)) while specification modeling (Liu et al., 2014) fails to decouple expensive costs from problem formulation (see Fig. 5(b)). To highlight their differences to specification modeling and present essential difficulties of the problem, we categorize existing methods that how ML methods are introduced to learn mapping f from antenna design parameters x to response vector R as Eq.
[182] PDF — variational methods, computational electromagnetics. I. INTRODUCTION ARIATIONAL techniques like finite element method (FEM), method of moments (MoM), and finite difference (FD) method are dominant for solving numerical physics problems in computational electromagnetics (CEM) and computational science/engineering (CSE) due to their
[205] A look at some challenging problems in computational electromagnetics — 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. Q. Ho, " A Novel Approach to Analyzing Truncated Frequency Selective Surface Radomes Operating in the Proximity of Array Antennas, " Electromagnetic Code Consortium (EMCC) Annual Meeting, Kawai, HI, May, 2001. Characteristic Basis Function Method for Analyzing Large Arrays Covered by Frequency Selective Radomes with Dissimilar Periods R. Mittra, " Characteristic Basis Function Method for Analyz-ing Large Arrays Covered by Frequency Selective Radomes with Dissimilar Periods, " 2003 EM Code Consortium Annual Meeting, May 2003. R. Mittra, " Solution of Large array and Radome Problems using the Characteristic Basis Function Approach, " USNC/URSI National Radio Science Meeting, Columbus, Ohio, June 2003.
[206] A look at some challenging problems in computational electromagnetics ... — 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. Great strides have recently been made in enlarging the scope of the 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. About IEEE Xplore | Contact Us | Help | Accessibility | Terms of Use | Nondiscrimination Policy | IEEE Ethics Reporting | Sitemap | IEEE Privacy Policy
[207] Ten problems in computational electromagnetics - cjors.cn — This paper aims to extract ten computational electromagnetic problems from the development of several electronic systems, including radar, stealth, precision guidance, naval ships, automobiles. The research status and future objectives of these ten problems are briefly analyzed to provide samples of considering future research directions of computational electromagnetics.
[214] PDF — computational cost of optimization with a large number of design variables. A two-rounds multi-fidelity aerodynamic/stealth design optimization method based on hierarchical Kriging (HK) model is developed in this paper by using the validated RANS solver and computational electromagnetics (CEM) methods based on the
[216] Electromagnetic Research and Challenges for Tactical Communication — The challenges associated with the operation of a military communications system in a congested and contested electromagnetic spectrum have spawned intensive research. The focus is on radio-frequency (RF) propagation, interference, and antenna system performance, and different techniques developed for sustained tactical communication.
[219] Radar Cross-Section (RCS) Estimation and Reduction — Scattering entities, especially electrically large ones, give rise to a wide variety of electromagnetic phenomena like refraction, reflection, traveling waves, leaky waves, diffraction effects, etc. In addition to the complex geometrical features of the primary reflecting surface, ground planes as well as other proximal structures contribute to
[221] PDF — Modern radar systems are a good example of a complex product - comprising electrical, mechanical and structural components. The overall radar performance, as measured by the electromagnetic (EM) radiation profile, is influenced by each subsystem - both individually and collectively - under a range of hostile, environmental conditions.
[227] Recent Advances in Computational Electromagnetics for Emerging ... — Aims & Scope: With the development of computational electromagnetics (CEM) methods and high-performance computers, the CEM community has achieved a great number of breakthroughs. However, regarding the emerging realistic applications in engineering designs, many new challenges are arising, e.g. multiscale modeling and simulation for electrically-large objects with fine structures, modeling and
[229] Multiphysics Modeling with Computational Electromagnetics — As computational methods for solving Maxwell's equations become rather mature, the time has come to tackle much more challenging multiphysics problems, which have a great range of applications in science and technology. In this chapter, we use four examples to illustrate the challenges and resolutions of multiphysics modeling. The first example is related to electromagnetic hyperthermia for
[230] A look at some challenging problems in computational electromagnetics ... — 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. Great strides have recently been made in enlarging the scope of the 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. About IEEE Xplore | Contact Us | Help | Accessibility | Terms of Use | Nondiscrimination Policy | IEEE Ethics Reporting | Sitemap | IEEE Privacy Policy
[231] Recent Trends in Computational Electromagnetics for Defence Applications — of the recent trends in computational electromagnetics are presented highlight the challenges ... Some of these limitations can ... military and security applications. In Proceedings of SPIE
[248] Computational Electromagnetics: Recent Advances and Engineering ... — Computational Electromagnetics: Recent Advances and Engineering Applications | SpringerLink Access this book The book examines new algorithms, and applications of these algorithms for solving problems of current interest that are not readily amenable to efficient treatment by using the existing techniques. Efficient Numerical Techniques for Analyzing Microstrip Circuits and Antennas Etched on Layered Media via the Characteristic Basis Function Method “This book collects in 19 chapters new computational techniques, developed in the engineering community, to solve large-scale and complex electromagnetic problems by using highly scalable algorithms. … The material in this book is useful to researchers, engineers, and graduate students who work on contemporary topics and recent developments in computational electromagnetics. Book Title: Computational Electromagnetics Access this book
[252] Machine Learning Advances in Computational Electromagnetics — We discuss how recent developments in machine learning hardware and software can enhance conventional CEM techniques and enable specialized CEM algorithms using deep neural networks. We also review how generalized surrogate electromagnetic solvers can be realized by the training of deep convolutional neural networks using simulated data
[253] PDF — communication, and ultimately in electromagnetics, namely in antenna array processing and microwave circuit design, remote sensing, and radar. The advancements in machine learning of the last two decades, in particular in kernel methods and deep learning, together with the progress in the computational
[254] Application of Artificial Intelligence Techniques on Computational ... — This paper provides a review of the most recent advances in artificial intelligence (AI) as applied to computational electromagnetics (CEM) to address challenges and unlock opportunities in power system applications. It is intended to provide readers and practitioners in electromagnetics (EM) and related applicable fields with valuable perspectives on the efficiency and capabilities of machine
[258] Machine Learning Advances in Computational Electromagnetics — Machine Learning Advances in Computational Electromagnetics | part of Advances in Electromagnetics Empowered by Artificial Intelligence and Deep Learning | Wiley-IEEE Press books | IEEE Xplore Machine Learning Advances in Computational Electromagnetics is part of: Advances in Electromagnetics Empowered by Artificial Intelligence and Deep Learning This chapter explores the emerging topic of computational electromagnetics (CEM) augmentation using machine learning techniques, which has disruptive potential due to its...Show More This chapter explores the emerging topic of computational electromagnetics (CEM) augmentation using machine learning techniques, which has disruptive potential due to its ability to evaluate solutions to CEM problems with unprecedented speeds. About IEEE Xplore | Contact Us | Help | Accessibility | Terms of Use | Nondiscrimination Policy | IEEE Ethics Reporting | Sitemap | IEEE Privacy Policy
[259] Machine Learning in Electromagnetics: A Review and Some Perspectives ... — We review machine learning and its applications in a wide range of electromagnetic problems, including radar, communication, imaging and sensing. We extensively discuss some recent progress in development and use of intelligent algorithms for antenna design, synthesis, and characterization. We also provide some perspectives for future research directions in this emerging field of study.
[265] Integrating machine learning and multiscale modeling ... - Nature — There is a critical need for time- and cost-efficient strategies to analyze and interpret these data to advance human health. The recent rise of machine learning as a powerful technique to integrate multimodality, multifidelity data, and reveal correlations between intertwined phenomena presents a special opportunity in this regard. Multiscale modeling is a successful strategy to integrate multiscale, multiphysics data and uncover mechanisms that explain the emergence of function. Here we demonstrate that machine learning and multiscale modeling can naturally complement each other to create robust predictive models that integrate the underlying physics to manage ill-posed problems and explore massive design spaces.
[267] (PDF) EMC computer modelling and simulation of integrated circuits in ... — In contrast to the tradi-tional EMC product testing, which are both time-consuming and expensive, computational modeling and simulation offer more flexibility in design modification and are
[268] It Was Impossible - Until Now. Computational Electromagnetic ... — Ansys has developed simulation software tools for over 50 years, helping their customers virtually prototype their products within a simulation before they ever build a physical prototype and test in the real world. This simulation process is critical in designing high performance electronics from cell phones to computers to complex radar systems.
[270] On hybrid methods for modeling complex electromagnetic problems — This paper presents a review of selected hybrid numerical methods for efficient solution to complex electromagnetic problems. First, recent developments in computational electromagnetics are briefly reviewed and several remaining challenges are addressed. Second, advantages of hybrid numerical methods are highlighted and hybridization strategies are described. Recent developments in hybrid
[271] Advanced Numerical Methods in Electromagnetics: Techniques and ... — Future directions are identified, emphasizing the potential of hybrid approaches, machine learning integration, and high-performance computing to address current limitations and expand the scope of these methods. The insights gained underline the critical role of numerical techniques in advancing electromagnetic theory and applications.
[272] PDF — Abstract This chapter explores the emerging topic of computational electromagnetics (CEM) augmentation using machine learning techniques, which has disruptive potential due to its ability to evaluate solutions to CEM problems with unprecedented speeds. We dis- cuss how recent developments in machine learning hardware and software can enhance conventional CEM techniques and enable specialized
[279] Novel techniques for numerically efficient solution of multiscale ... — Numerical electromagnetic modeling and simulation of structures with multiscale features are highly challenging due to the fact that electrically small as well as large features are simultaneously present in the model that demands for discretization of the computational domain such that the number of degrees of freedom is very large, thus