S. Barmada, A. Musolino and M. Raugi
The analysis of multiconductor transmission lines excited by an electromagnetic field is investigated here by the use of the wavelet expansion. The exciting field is taken into…
Abstract
The analysis of multiconductor transmission lines excited by an electromagnetic field is investigated here by the use of the wavelet expansion. The exciting field is taken into account considering its contribution in terms of equivalent distributed voltage and current along the line. The resulting equations are expanded in the wavelet domain on both the variables (space and time), leading to an algebraic system in a Lyapunov form which is solved by the use of standard techniques.
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Sami Barmada, Alessandro Formisano, Dimitri Thomopulos and Mauro Tucci
This study aims to investigate the possible use of a deep neural network (DNN) as an inverse solver.
Abstract
Purpose
This study aims to investigate the possible use of a deep neural network (DNN) as an inverse solver.
Design/methodology/approach
Different models based on DNNs are designed and proposed for the resolution of inverse electromagnetic problems either as fast solvers for the direct problem or as straightforward inverse problem solvers, with reference to the TEAM 25 benchmark problem for the sake of exemplification.
Findings
Using DNNs as straightforward inverse problem solvers has relevant advantages in terms of promptness but requires a careful treatment of the underlying problem ill-posedness.
Originality/value
This work is one of the first attempts to exploit DNNs for inverse problem resolution in low-frequency electromagnetism. Results on the TEAM 25 test problem show the potential effectiveness of the approach but also highlight the need for a careful choice of the training data set.
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Sami Barmada, Nunzia Fontana, Leonardo Sandrolini and Mattia Simonazzi
The purpose of this paper is to gain a better understanding on how metasurfaces behave, in terms of currents in each unit cell. A better knowledge of their behavior could lead to…
Abstract
Purpose
The purpose of this paper is to gain a better understanding on how metasurfaces behave, in terms of currents in each unit cell. A better knowledge of their behavior could lead to an ad-hoc design for specific applications.
Design/methodology/approach
The methodology used is both theoretical and numerical; it is based on circuit theory and on an optimization procedure.
Findings
The results show that when the knowledge of the current in each unit cell of a metasurface is needed, the most common approximations currently used are often not accurate. Furthermore, a procedure for the termination of a metasurface, with application-driven goals, is given.
Originality/value
This paper investigates the distribution of the currents in a 2D metamaterial realized with magnetically coupled resonant coils. Different models for the analysis of these structures are illustrated, and the effects of the approximations they introduce on the current values are shown and discussed. Furthermore, proper terminations of the resonators on the boundaries have been investigated by implementing a numerical optimization procedure with the purpose of achieving a uniform distribution of the resonator currents. The results show that the behavior of a metasurface (in terms of currents in each single resonator) depends on different properties; as a consequence, their design is not a trivial task and is dependent on the specific applications they are designed for. A design strategy, with lumped impedance termination, is here proposed.
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Mohammad Mushfiqur Rahman, Arbaaz Khan, David Lowther and Dennis Giannacopoulos
The purpose of this paper is to develop surrogate models, using deep learning (DL), that can facilitate the application of EM analysis software. In the current status quo…
Abstract
Purpose
The purpose of this paper is to develop surrogate models, using deep learning (DL), that can facilitate the application of EM analysis software. In the current status quo, electrical systems can be found in an ever-increasing range of products that are part of everyone’s daily live. With the advances in technology, industries such as the automotive, communications and medical devices have been disrupted with new electrical and electronic systems. The innovation and development of such systems with increasing complexity over time has been supported by the increased use of electromagnetic (EM) analysis software. Such software enables engineers to virtually design, analyze and optimize EM systems without the need for building physical prototypes, thus helping to shorten the development cycles and consequently cut costs.
Design/methodology/approach
The industry standard for simulating EM problems is using either the finite difference method or the finite element method (FEM). Optimization of the design process using such methods requires significant computational resources and time. With the emergence of artificial intelligence, along with specialized tools for automatic differentiation, the use of DL has become computationally much more efficient and cheaper. These advances in machine learning have ushered in a new era in EM simulations where engineers can compute results much faster while maintaining a certain level of accuracy.
Findings
This paper proposed two different models that can compute the magnetic field distribution in EM systems. The first model is based on a recurrent neural network, which is trained through a data-driven supervised learning method. The second model is an extension to the first with the incorporation of additional physics-based information to the authors’ model. Such a DL model, which is constrained by the laws of physics, is known as a physics-informed neural network. The solutions when compared with the ground truth, computed using FEM, show promising accuracy for the authors’ DL models while reducing the computation time and resources required, as compared to previous implementations in the literature.
Originality/value
The paper proposes a neural network architecture and is trained with two different learning methodologies, namely, supervised and physics-based. The working of the network along with the different learning methodologies is validated over several EM problems with varying levels of complexity. Furthermore, a comparative study is performed regarding performance accuracy and computational cost to establish the efficacy of different architectures and learning methodologies.
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Keywords
- Finite element analysis (FEA)
- Field analysis
- Partial differential equations (PDEs)
- Magnetic device
- Recurrent neural network (RNN)
- Physics-informed neural network (PINN)
- Gated recurrent unit (GRU)
- Physics-informed recurrent neural network (PI-RNN)
- Deep learning (DL)
- Finite elements (FE)
- Finite element method (FEM)
- Electromagnetics (EM)
- Magnetic flux density
Luca Di Rienzo, Sergey Yuferev, Nathan Ida and Cesare Mario Arturi
To provide a time domain formulation for reconstruction of transient currents flowing in massive parallel conductors from magnetic data collected in the dielectric space…
Abstract
Purpose
To provide a time domain formulation for reconstruction of transient currents flowing in massive parallel conductors from magnetic data collected in the dielectric space surrounding the conductors.
Design/methodology/approach
A boundary integral equation (BIE) formulation involving Mitzner's and Rytov's high order surface impedance boundary conditions (SIBCs) is used. Input data of the inverse problem are the magnetic fields at given locations near the conductors. In order to validate the inversion algorithm, the magnetic field data are computed solving the direct problem with FEM for given current waveforms.
Findings
The improvement in reconstruction accuracy of the new time domain BIE formulation employing high order SIBCs has been demonstrated numerically in a simple test case. The range of validity of the technique has been extended to current pulses of longer duration and the computational burden has shown to increase only by a factor of 4.
Research limitations/implications
The proposed formulation can be compared with other possible formulations, both in the time and in the frequency domain.
Practical implications
Based on this formulation a new current sensing technique is proposed for realization of low cost current sensors based on magnetic sensor arrays.
Originality/value
The inverse problem addressed in the paper has been solved for the first time.
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Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community…
Abstract
Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.
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Carlo de Falco, Luca Di Rienzo, Nathan Ida and Sergey Yuferev
The purpose of this paper is the derivation and efficient implementation of surface impedance boundary conditions (SIBCs) for nonlinear magnetic conductors.
Abstract
Purpose
The purpose of this paper is the derivation and efficient implementation of surface impedance boundary conditions (SIBCs) for nonlinear magnetic conductors.
Design/methodology/approach
An approach based on perturbation theory is proposed, which expands to nonlinear problems the methods already developed by the authors for linear problems. Differently from the linear case, for which the analytical solution of the diffusion equation in the semi-infinite space for the magnetic field is available, in the nonlinear case the corresponding nonlinear diffusion equation must be solved numerically. To this aim, a suitable smooth map is defined to reduce the semi-infinite computational domain to a finite one; then the diffusion equation is solved by a Galerkin method relying on basis functions constructed via the push-forward of a Lagrangian polynomial basis whose degrees of freedom are collocated at Gauss–Lobatto nodes. The use of such basis in connection with a suitable under-integration naturally leads to mass-lumping without impacting the order of the method. The solution of the diffusion equation is coupled with a boundary element method formulation for the case of parallel magnetic conductors in terms of E and B fields.
Findings
The results are validated by comparison with full nonlinear finite element method simulations showing very good accordance at a much lower computational cost.
Research limitations/implications
Limitations of the method are those arising from perturbation theory: the introduced small parameter must be much less than one. This implies that the penetration depth of the magnetic field into the magnetic and conductive media must be much smaller than the characteristic size of the conductor.
Originality/value
The efficient implementation of a nonlinear SIBC based on a perturbation approach is proposed for an electric and magnetic field formulation of the two-dimensional problem of current driven parallel solid conductors.
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Introduces the fourth and final chapter of the ISEF 1999 Proceedings by stating electric and magnetic fields are influenced, in a reciprocal way, by thermal and mechanical fields…
Abstract
Introduces the fourth and final chapter of the ISEF 1999 Proceedings by stating electric and magnetic fields are influenced, in a reciprocal way, by thermal and mechanical fields. Looks at the coupling of fields in a device or a system as a prescribed effect. Points out that there are 12 contributions included ‐ covering magnetic levitation or induction heating, superconducting devices and possible effects to the human body due to electric impressed fields.
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Introduces papers from this area of expertise from the ISEF 1999 Proceedings. States the goal herein is one of identifying devices or systems able to provide prescribed…
Abstract
Introduces papers from this area of expertise from the ISEF 1999 Proceedings. States the goal herein is one of identifying devices or systems able to provide prescribed performance. Notes that 18 papers from the Symposium are grouped in the area of automated optimal design. Describes the main challenges that condition computational electromagnetism’s future development. Concludes by itemizing the range of applications from small activators to optimization of induction heating systems in this third chapter.
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P. Alotto, A. De Cian, G. Molinari and M. Rossi
To show a possible implementation of surface impedance boundary conditions (SIBCs) in a time domain formulation based on the cell method (CM).
Abstract
Purpose
To show a possible implementation of surface impedance boundary conditions (SIBCs) in a time domain formulation based on the cell method (CM).
Design/methodology/approach
The implementation is based on vector fitting (VF), a technique which allows a time domain representation of a rational approximation of the surface impedance to be found.
Findings
It is shown that very little computational effort is needed to find a very good VF approximation of simple SIBCs and that such approximation is easily fitted into existing CM codes.
Research limitations/implications
The extension to higher order SIBCs has not been taken into account.
Practical implications
The proposed approach avoids the use of convolution integrals, is accurate and easy to implement.
Originality/value
This paper introduces the use of VF for the approximate time domain representation of SIBCs.