Showing papers on "Computational electromagnetics published in 2016"

Domain Decomposition Preconditioning for Surface Integral Equations in Solving Challenging Electromagnetic Scattering Problems

Abstract: We propose and study a nonoverlapping and nonconforming domain decomposition method for the integral-equation-based solution of large, complex electromagnetic (EM) scattering problems. The continuity of the electric surface current across the boundary between adjacent subdomains is enforced by a skew-symmetric interior penalty formulation. A nonoverlapping additive Schwarz preconditioner is designed and analyzed for the solution of the linear system of equations resulting from Galerkin boundary-element discretization. We show that the preconditioned system exhibits a uniformly confined eigenspectrum with respect to changing problem and discretization parameters. Numerical examples are presented to demonstrate the fast convergence of iterative solvers and the superior accuracy of the solutions obtained by our method. The proposed work can be viewed as an effective preconditioning scheme that reduces the condition number of very large systems of equations in challenging EM scattering problems. The strength and capability of the proposed method will be illustrated by means of several examples of practical interest.

Simulation of Metasurfaces in Finite Difference Techniques

Abstract: We introduce a rigorous and simple method for analyzing metasurfaces, modeled as zero-thickness electromagnetic sheets, in finite difference (FD) techniques. The method consists in describing the spatial discontinuity induced by the metasurface as a virtual structure, located between nodal rows of the Yee grid, using an FD version of generalized sheet transition conditions. In contrast to previously reported approaches, the proposed method can handle sheets exhibiting both electric and magnetic discontinuities, and represents therefore a fundamental contribution to computational electromagnetics. It is presented here in the framework of the FD frequency domain method, but also applies to the FD time domain scheme. The theory is supported by five illustrative examples.

Fast Electromagnetic Analysis of MRI Transmit RF Coils Based on Accelerated Integral Equation Methods

Abstract: A fast frequency domain full-wave electromagnetic simulation method is introduced for the analysis of MRI coils loaded with the realistic human body models. The approach is based on integral equation methods decomposed into two domains: 1) the RF coil array and shield, and 2) the human body region where the load is placed. The analysis of multiple coil designs is accelerated by introducing the precomputed magnetic resonance Green functions (MRGFs), which describe how the particular body model used responds to the incident fields from external sources. These MRGFs, which are precomputed once for a given body model, can be combined with any integral equation solver and reused for the analysis of many coil designs. This approach provides a fast, yet comprehensive, analysis of coil designs, including the port S-parameters and the electromagnetic field distribution within the inhomogeneous body. The method solves the full-wave electromagnetic problem for a head array in few minutes, achieving a speed up of over 150 folds with root mean square errors in the electromagnetic field maps smaller than 0.4% when compared to the unaccelerated integral equation-based solver. This enables the characterization of a large number of RF coil designs in a reasonable time, which is a first step toward an automatic optimization of multiple parameters in the design of transmit arrays, as illustrated in this paper, but also receive arrays.

Electromagnetic Model Reliably Predicts Radar Scattering Characteristics of Airborne Organisms

Abstract: The radar scattering characteristics of aerial animals are typically obtained from controlled laboratory measurements of a freshly harvested specimen. These measurements are tedious to perform, difficult to replicate, and typically yield only a small subset of the full azimuthal, elevational, and polarimetric radio scattering data. As an alternative, biological applications of radar often assume that the radar cross sections of flying animals are isotropic, since sophisticated computer models are required to estimate the 3D scattering properties of objects having complex shapes. Using the method of moments implemented in the WIPL-D software package, we show for the first time that such electromagnetic modeling techniques (typically applied to man-made objects) can accurately predict organismal radio scattering characteristics from an anatomical model: here the Brazilian free-tailed bat (Tadarida brasiliensis). The simulated scattering properties of the bat agree with controlled measurements and radar observations made during a field study of bats in flight. This numerical technique can produce the full angular set of quantitative polarimetric scattering characteristics, while eliminating many practical difficulties associated with physical measurements. Such a modeling framework can be applied for bird, bat, and insect species, and will help drive a shift in radar biology from a largely qualitative and phenomenological science toward quantitative estimation of animal densities and taxonomic identification.

Large-Scale Characteristic Mode Analysis With Fast Multipole Algorithms

Abstract: Large-scale characteristic mode analysis (CMA) poses challenges in computational electromagnetics as it calls for efficient solutions of large dense generalized eigenvalue problems. In this paper, we consider two applications that involve large-scale CMA, and demonstrate that fast multipole algorithms (FMAs) can be easily incorporated into the implicitly restarted Arnoldi method (IRAM) for eigenanalysis after simple modifications. The first application performs CMA for large platforms made by closed perfectly conducting surfaces. Multilevel FMA (MLFMA) is embedded into a combined field integral equation-based theory of characteristic mode (TCM). The second application addresses multiscale modeling of small but geometrically complicated objects, which possess fine subwavelength structures. An augmented electric field integral equation-based TCM is formulated, and low-frequency (LF-)FMA is adopted to accelerate the required matrix–vector products.

The development of HFSS

Abstract: HFSS was the first general-purpose software product to solve arbitrary three-dimensional electromagnetic field problems. It introduced a number of new technologies in computational electromagnetics including automatic adaptive mesh generation, tangential vector finite elements, transfinite elements, and reduced-order modeling. This talk describes the early development of HFSS, the issues critical to its success, and some of the recent advances that enable HFSS to solve ever more complex problems quickly and accurately.

Robust Estimation of Metal Target Shape Using Time-Domain Electromagnetic Induction Data

Abstract: Discriminating metal parts of buried hazardous targets from ordinary metallic clutter is a very difficult and time-consuming task. For that purpose, electromagnetic induction (EMI) sensors composed of multiple transmitter/receiver coils in multiaxis arrangements are commonly used. In this way, data of high fidelity and spatial diversity are obtained so that the target can be characterized in terms of its geometric and electromagnetic properties. However, this often increases sensor size and reduces its portability, which is a problem for humanitarian demining applications, where compact, robust, and lightweight sensors are needed. If such sensors are to be used for target characterization, robust estimation algorithms are required, capable of coping with limited spatial information content and uncertainties related to sensor positioning and its coil geometry model. In this paper, we present a robust concept for estimating the general shape of magnetic metal targets using time-domain EMI sensors with single-axis coil geometries. We introduce the signature matrix, a parameter derived from time-dependent eigenvalues of the target’s magnetic polarizability tensor, and use it for shape estimation. The proposed method was evaluated both through simulations and experiments, using two different sensor platforms (laboratory-based experimental sensor platform and a commercial metal detector mounted on a mobile robot). The obtained results clearly indicate that the target shape can be estimated from sensor data of limited spatial diversity and under the uncertainties of sensor positioning and coil geometry.

Electromagnetic Resonances of Individual Single-Walled Carbon Nanotubes With Realistic Shapes: A Characteristic Modes Approach

Abstract: In composites, carbon nanotubes (CNTs) are rarely perfectly straight and they usually exhibit complex shapes. In this paper, we employ the method-of-moments formulation for arbitrary thin wires to study the electromagnetic scattering characteristics of CNTs with realistic shapes. More than 800 different CNT shapes were simulated in this work. These shapes were generated using a coarse-grained molecular dynamics model calibrated using realistic CNT shapes encountered experimentally. The analysis shows that the shape and orientation of CNTs has a strong effect on the scattered electromagnetic response. We used the theory of characteristic modes (TCM) to explain this dependence of the scattered electromagnetic waves on the shape of the CNT. Using TCM, we developed simplified but highly accurate formulas that link the shapes of the CNTs to the resonances in their total extinction coefficient spectrum. These formulations have the potential to be the basis for advancing the nondestructive evaluation of CNT composites using electromagnetic waves as well as the development of novel CNT electromagnetic systems and devices.

Near-field thermal electromagnetic transport: An overview

Abstract: A general near-field thermal electromagnetic transport formalism that is independent of the size, shape and number of heat sources is derived. The formalism is based on fluctuational electrodynamics, where fluctuating currents due to thermal agitation are added to Maxwell’s curl equations, and is thus valid for heat sources in local thermodynamic equilibrium. Using a volume integral formulation, it is shown that the proposed formalism is a generalization of the classical electromagnetic scattering framework in which thermal emission is implicitly assumed to be negligible. The near-field thermal electromagnetic transport formalism is afterwards applied to a problem involving three spheres with size comparable to the wavelength, where all multipolar interactions are taken into account. Using the thermal discrete dipole approximation, it is shown that depending on the dielectric function, the presence of a third sphere slightly affects the spatial distribution of power absorbed compared to the two-sphere case. A transient analysis shows that despite a non-uniform spatial distribution of power absorbed, the sphere temperature remains spatially uniform at any instant due to the fact that the thermal resistance by conduction is much smaller than the resistance by radiation. The formalism proposed in this paper is general, and could be used as a starting point for adapting solution methods employed in traditional electromagnetic scattering problems to near-field thermal electromagnetic transport.

Controlling electromagnetic scattering with wire metamaterial resonators

Abstract: Manipulation of radiation is required for enabling a span of electromagnetic applications. Since properties of antennas and scatterers are very sensitive to the surrounding environment, macroscopic artificially created materials are good candidates for shaping their characteristics. In particular, metamaterials enable controlling both dispersion and density of electromagnetic states, available for scattering from an object. As a result, properly designed electromagnetic environments could govern wave phenomena and tailor various characteristics. Here electromagnetic properties of scattering dipoles, situated inside a wire medium (metamaterial), are analyzed both numerically and experimentally. The effect of the metamaterial geometry, dipole arrangement inside the medium, and frequency of the incident radiation on the scattering phenomena is studied in detail. It is shown that the resonance of the dipole hybridizes with Fabry-Perot modes of the metamaterial, giving rise to a complete reshaping of electromagnetic properties. Regimes of controlled scattering suppression and super-scattering are experimentally observed. Numerical analysis is in agreement with the experiment, performed at the GHz spectral range. The reported approach to scattering control with metamaterials could be directly mapped into optical and infrared spectral ranges by employing scalability properties of Maxwell's equations.

Multi-purpose VHP-female version 3.0 cross-platform computational human model

Abstract: Simulation of the electromagnetic response of the human body relies upon efficient computational models. The objective of this paper is to describe a new platform-independent and computationally-efficient full-body electromagnetic model, the Visible Human Project® (VHP)-Female v.3.0 and to outline its distinct features. We also report model performance results using two leading commercial electromagnetic antenna simulation packages: ANSYS HFSS and CST MICROWAVE STUDIO®.

Transient simulation of an electrical rotating machine achieved through model order reduction

Abstract: Model order reduction (MOR) methods are more and more applied on many different fields of physics in order to reduce the number of unknowns and thus the computational time of large-scale systems. However, their application is quite recent in the field of computational electromagnetics. In the case of electrical machine, the numerical model has to take into account the nonlinear behaviour of ferromagnetic materials, motion of the rotor, circuit equations and mechanical coupling. In this context, we propose to apply the proper orthogonal decomposition combined with the (Discrete) empirical interpolation method in order to reduce the computation time required to study the start-up of an electrical machine until it reaches the steady state. An empirical offline/online approach based on electrical engineering is proposed in order to build an efficient reduced model accurate on the whole operating range. Finally, a 2D example of a synchronous machine is studied with a reduced model deduced from the proposed approach.

Full-Wave Computational Model of Electromagnetic Scattering by Arbitrarily Rotated 1-D Periodic Multilayer Structure

Abstract: A full-wave computational model of electromagnetic scattering of conically incident plane waves by arbitrarily rotated 1-D periodic multilayer structure is proposed. Each layer in the structure (overall sandwiched between two half-spaces) consists of a dielectric material within which an infinite chain of periodically arranged and arbitrarily orientated circular cylinders is embedded. The orientations of the cylinder arrays in different layers are arbitrary with respect to one another, offering full generality. The above is a model of fiber-reinforced composite laminates as in industry but also of multilayered photonic crystals. Combining Rayleigh’s method and mode-matching produces scattering matrices for each layer cascaded from the top to the bottom in order to relate the reflection/transmission coefficients to the incident field. Power reflection and transmission coefficients follow from Poynting’s theorem. The mathematical derivation insists on modal representations and building up proper S-matrices. Numerical simulations show that the model is accurate, known results on woodpile structures in photonics are in particular recovered. The model is also versatile in terms of illuminations, geometries, and material parameters. The results could also be used as benchmarks in view of lack of data in present-day literature on such arbitrarily orientated layerings. Calculations of pertinent dyadic Green functions is one of possible extensions in view of the imaging methods of possibly damaged multilayer structures.

A Multisolver Scheme Based on Robin Transmission Conditions for Electromagnetic Modeling of Highly Complex Objects

Abstract: A multisolver scheme based on Robin transmission conditions (RTCs) is proposed for electromagnetic modeling of highly complex objects. Different from the traditional finite element–boundary integral (FE-BI) method that applies BI equations to truncate the FE domain, the proposed multisolver scheme employs both FE and BI equations to model an object along with its background. To be specific, the entire computational domain consisting of the object and its background is first decomposed into multiple nonoverlapping subdomains with each modeled by either an FE or BI equation. The equations in the subdomains are then coupled into a multisolver system by enforcing the RTC at the subdomain interfaces. Finally, the combined system is solved iteratively with the application of an extended preconditioner based on an absorbing boundary condition and the multilevel fast multipole algorithm. To obtain an accurate solution, both the Rao–Wilton–Glisson and the Buffa–Christiansen functions are employed as the testing functions to discretize the BI equations. This scheme is applied to a variety of benchmark problems and the scattering from an aircraft with a launched missile to demonstrate its accuracy, versatility, and capability. The proposed scheme is compared with the multisolver scheme based on combined field integral equations to illustrate the differences between the two schemes.

A Generalized Fabry–Pérot Formulation for Optical Modeling of Organic Light-Emitting Diodes Considering the Dipole Orientation and Light Polarization

Abstract: The Fabry–Perot formulation has been widely used as a simple and intuitive optical modeling method of organic light-emitting diodes (OLEDs). However, because the Fabry–Perot formulation in the optical modeling of OLEDs does not include the effect of the dipole orientation and light polarization on light emission characteristics, rigorous electromagnetic models should be used, in spite of their heavy mathematical and computational complexity. In addition, the validity and the limitation of the Fabry–Perot formulation for OLEDs have yet to be proven. We propose a generalized Fabry–Perot formulation to calculate the dependence of the dipole orientation and light polarization on the angular emission characteristics using a simple analytical equation rather than a complicated electromagnetic model. The generalized Fabry–Perot formulation is derived, together with detailed steps, and becomes equivalent to the current Fabry–Perot formulation in isotropic dipole orientation. In addition, the physical interpretation of the proposed Fabry–Perot formulation is elucidated in comparison with the quantum mechanical model. To demonstrate the applicability and the validity of the generalized Fabry–Perot formulation, the angular emission spectra of a top-emitting OLED are calculated with respect to the horizontal dipole ratio and the light polarization, which can be easily calculated based on a simple analytical equation.

Design of a High-Speed ferrite-based Brushless DC Machine for electric vehicles

Abstract: In the present paper an analytic procedure for the preliminary design of a High-Speed ferrite-based Brushless DC Machine (HS-BLDC) has been proposed. In particular, a mechanical and electromagnetic modeling has been developed in order to take into account their mutual influence in the definition of the geometry of the electrical machine. In addition, suitable design targets have been imposed in accordance with electric vehicle application requirements. Hence, several mechanical and electromagnetic constraints have been introduced in order to comply with high-speed operation, preventing demagnetization issues of ferrite magnets as well. Subsequently, a HS-BLDC characterized by an inner rotor configuration has been designed in accordance with the proposed methodology. The analytical procedure and the corresponding results have been reported and validated by means of Finite Element Analyses (FEAs), highlighting the effectiveness of the proposed configuration and design solutions.

Verification Process of Finite-Element Method Code for Electromagnetics: Using the method of manufactured solutions.

Abstract: Computational electromagnetics (CEM) has become an indispensable tool for the analysis of electromagnetic problems because of the predictive power of Maxwell's equations. If these equations are solved correctly, the solution can predict experimental outcomes and design performances. CEM techniques are being used in many different areas such as electromagnetic compatibility, antenna analysis, radar cross section (RCS), cellular phone?human body interaction, design of electrical and medical devices, target recognition, and lightning strike simulation.

Analysis of magnetically biased graphene-based periodic structures using a transmission-line formulation

Abstract: The surface conductivity of graphene turns to a tensor in the presence of a static magnetic field, which complicates the required tools for computational electromagnetics (EMs). In this paper, a Fourier-based numerical method in the form of a transmission-line formulation (TLF) is generalized to analyze magnetically biased graphene-based multilayer periodic structures. Correct factorization rules, which are required for reducing computational time and improving convergence rate, cannot be applied to the boundary conditions encountered in these structures. Thus, an approximate boundary condition that has recently been proposed for a fast Fourier modal method developed for a periodic array made of graphene is modified for TLF to analyze such structures under a static magnetic field bias. The obtained numerical results for various structures are presented and compared with those generated by commercial EM solvers to verify the computational efficiency and accuracy of the proposed method.

Complete Set of Partial Differential Equations for Direct Localization of a Magnetic Dipole

Abstract: Recently, the use of Euler’s homogeneity equation has been proposed to obtain a direct algorithm for localizing a magnetic dipole in a free space. This is based on the vector-homogeneity of the magnetic field generated by the source. However, the magnetic field generated is also governed by electromagnetic constraints such as divergence-freeness. In order to obtain the methods that consider the full properties of the dipole-induced magnetic field, we develop an additional set of partial differential equations (PDEs), such that the general solution of the combined equations satisfies a complete or subset of the electromagnetic constraints induced and restricted by the magnetic dipole and field. We apply the weighted integral method considering a suitable form of weight functions (observation functions) for each PDE. In them, the magnetic dipole can be localized from line integrals (measurements) or surface integrals of the magnetic field, while Euler’s homogeneity equation requires volume integrals. The methods are verified by numerical simulations and experiments for application in a shorter search and rapid localization of an avalanche beacon.

Electromagnetic modeling of large subwavelength-patterned highly resonant structures

Abstract: The rigorous modeling of large (hundreds of wavelengths) optical resonant components patterned at a subwavelength scale remains a major issue, especially when long range interactions cannot be neglected. In this Letter, we compare the performances of the discrete dipole approximation approach to that of the Fourier modal, the finite element and the finite difference time domain methods, for simulating the spectral behavior of a cavity resonator integrated grating filter (CRIGF). When the component is invariant along one axis (two-dimensional configuration), the four techniques yield similar results, despite the modeling difficulty of such a structure. We also demonstrate, for the first time to the best of our knowledge, the rigorous modeling of a three-dimensional CRIGF.

Stable Electromagnetic Modeling Using a Multigrid Solver on Stretching Grids: The Magnetotelluric Example

Abstract: Electromagnetic (EM) surveys are widely used in geophysical study. Reliable 3-D forward modeling is required for the inversion and interpretation of geophysical data. We have introduced a novel method for 3-D EM modeling using stretching grids, which uses a multigrid iterative solver for solving the formed linear system of equations based on the staggered finite-difference method. The developed algorithm is applied for the simulation of the magnetotelluric fields. We have tested this new algorithm using synthetic geoelectric models. The proposed multigrid method using stretching grids is also compared with the preconditioned Krylov-subspace solvers, the biconjugate gradients stabilized method, and the generalized minimum residual method. The developed multigrid method is proved to be more stable and requires less iterations to converge.

Finite-Difference Time-Domain Solution of Maxwell's Equations

Abstract: For over 100 years after the publication of Maxwell's equations in 1865, essentially all solution techniques for electromagnetic fields and waves were based on Fourier-domain concepts, assuming a priori a time-harmonic (sinusoidal steady-state) field variation and possibly the existence of a particular Green's function or a set of spatial modes. In 1966, Kane Yee's seminal paper introduced a complete paradigm shift in how to solve Maxwell's equations, reporting a field evolution-in-time technique that subsequently evolved into the finite-difference time-domain (FDTD) method. In the decades since the publication of Yee's paper, there has been an explosion of interest in FDTD and related grid-based time-marched solutions of Maxwell's equations among scientists and engineers. During this period, FDTD modeling has evolved to an advanced stage enabling large-scale simulations of full-wave time-domain electromagnetic wave interactions with volumetrically complex structures over large frequency ranges, spatial scales, and timescales. Currently, FDTD modeling spans the electromagnetic spectrum from ultralow frequencies to visible light. FDTD modeling is routinely conducted as an invaluable virtual laboratory bench in scientific inquiry and exploration in electrodynamics; as an integral part of the electromagnetic engineering design and optimization process; and as a powerful forward solver in imaging and sensing inverse problems. This article reviews the technical basis of the key features of FDTD solution techniques for Maxwell's equations and provides 18 modeling examples spanning the electromagnetic spectrum to illustrate the power, flexibility, and robust nature of FDTD computational electrodynamics simulations. Keywords: computational electrodynamics; finite-difference time-domain; FDTD; Maxwell's equations

GPU Accelerated Discontinuous Galerkin Time Domain Algorithm for Electromagnetic Problems of Electrically Large Objects

Abstract: In this paper, an efficient time domain simulation algorithm is proposed to analyze the electromagnetic scattering and radiation problems. The algorithm is based on discontinuous Galerkin time domain (DGTD) method and parallelization acceleration technique using the graphics processing units (GPU), which offers the capability for accelerating the computational electromagnetics analyses. The bottlenecks using the GPU DGTD acceleration for electromagnetic analyses are investigated, and potential strategies to alleviate the bottlenecks are proposed. We first discuss the efficient parallelization strategies handling the local-element differentiation, surface integrals, RK time-integration assembly on the GPU platforms, and then, we explore how to implement the DGTD method on the Compute Unified Device Architecture (CUDA). The accuracy and performance of the DGTD method are analyzed through illustrated benchmarks. We demonstrate that the DGTD method is better suitable for GPUs to achieve significant speedup improvement over modern multi-core CPUs.

Comparison of iterative solvers for electromagnetic analysis of plasmonic nanostructures using multiple surface integral equation formulations

Abstract: The electromagnetic behavior of plasmonic structures can be predicted after discretizing and solving a linear system of equations, derived from a continuous surface integral equation (SIE) and the appropriate boundary conditions, using a method of moments (MoM) methodology. In realistic large-scale optical problems, a direct inversion of the SIE–MoM matrix cannot be performed due to its large size, and an iterative solver must be used instead. This paper investigates the performance of four iterative solvers (GMRES, TFQMR, CGS, and BICGSTAB) for five different SIE–MoM formulations (PMCHWT, JMCFIE, CTF, CNF, and MNMF). Moreover, under this plasmonic context, a set of suggested guidelines are provided to choose a suitable SIE formulation and iterative solver depending on the desired simulation error and available runtime resources.

Simulation of Metasurfaces in Finite Difference Techniques

Abstract: We introduce a rigorous and simple method for analyzing metasurfaces, modeled as zero-thickness electromagnetic sheets, in Finite Difference (FD) techniques. The method consists in describing the spatial discontinuity induced by the metasurface as a virtual structure, located between nodal rows of the Yee grid, using a finite difference version of Generalized Sheet Transition Conditions (GSTCs). In contrast to previously reported approaches, the proposed method can handle sheets exhibiting both electric and magnetic discontinuities, and represents therefore a fundamental contribution in computational electromagnetics. It is presented here in the framework of the FD Frequency Domain (FDFD) method but also applies to the FD Time Domain (FDTD) scheme. The theory is supported by five illustrative examples.

Novel Formulation to Determine the Potential on the Soil Surface Generated by a Lightning Surge

Abstract: This paper presents the development of an analytical formulation for estimating the potential on the soil surface, caused by electric current calculated on a grounding conductor. The formulation has a great significance in its use in conjunction with 1-D numerical methods, which are not able to determine such potentials directly. The proposed study focuses on lightning surges considering the frequency dependence of the soil properties. First, the subject is introduced emphasizing important aspects related to the analysis and representation of grounding systems against lightning. Afterward, the proposed analytical formulation is introduced with a focus on the computational implementation of the transmission line modeling method in 1-D. Simulations were carried out considering a typical horizontal electrode used as grounding in the power electric system. The formulation was validated by comparing the results with the solution based on the electromagnetic model (CDEGS Software), which is considered the most stringent for the solution of full Maxwell equations due to their minimum approaches. The results demonstrate that the generalized formulation presents good accuracy, contributing to an improved representation of grounding systems based on numerical techniques in 1-D.

${A}$ – ${T}$ Volume Integral Formulations for Solving Electromagnetic Problems in the Frequency Domain

Abstract: A volume integral formulation for solving electromagnetic problems in the frequency domain is proposed. First, it is based on a magnetic flux and current density face element interpolation for representing the electromagnetic problem through an equivalent circuit. Second, magnetic vector potentials $A$ and electric vector potential $T$ are considered, thanks to the use of finite element mesh connectivity matrices. The formulation is particularly well adapted to solving electromagnetic problems with large air domains, in the presence of thin electric regions and magnetic materials.

Domain Decomposition Methods for Time-Harmonic Electromagnetic Waves With High-Order Whitney Forms

Abstract: Classically, the domain decomposition methods (DDMs) for time-harmonic electromagnetic wave propagation problems make use of the standard, low-order, Nedelec basis functions. This paper analyzes the convergence rate of DDM when higher order finite elements are used for both volume and interface discretizations, in particular when different orders are used in the volume and on the interfaces.