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An efficient electromagnetic inversion scheme for imaging sparse 3-D domains is proposed. The scheme achieves its efficiency and accuracy by integrating two concepts. First, the nonlinear optimization problem is constrained using L0 or L1 -norm of the solution as the penalty term to alleviate the ill-posedness of the inverse problem. The resulting Tikhonov minimization problem is solved using nonlinear Landweber iterations (NLW). Second, the efficiency of the NLW is significantly increased using a steepest descent algorithm. The algorithm uses a projection operator to enforce the sparsity constraint by thresholding the solution at every iteration. Thresholding level and iteration step are selected carefully to increase the efficiency without sacrificing the convergence of the algorithm. Numerical results demonstrate the efficiency and accuracy of the proposed imaging scheme in reconstructing sparse 3-D dielectric profiles. [ABSTRACT FROM PUBLISHER]

An efficient method for statistically characterizing multiconductor transmission line (MTL) networks subject to a large number of manufacturing uncertainties is presented. The proposed method achieves its efficiency by leveraging a high-dimensional model representation (HDMR) technique that approximates observables (quantities of interest in MTL networks, such as voltages/currents on mission-critical circuits) in terms of iteratively constructed component functions of only the most significant random variables (parameters that characterize the uncertainties in MTL networks, such as conductor locations and widths, and lumped element values). The efficiency of the proposed scheme is further increased using a multielement probabilistic collocation (ME-PC) method to compute the component functions of the HDMR. The ME-PC method makes use of generalized polynomial chaos (gPC) expansions to approximate the component functions, where the expansion coefficients are expressed in terms of integrals of the observable over the random domain. These integrals are numerically evaluated and the observable values at the quadrature/collocation points are computed using a fast deterministic simulator. The proposed method is capable of producing accurate statistical information pertinent to an observable that is rapidly varying across a high-dimensional random domain at a computational cost that is significantly lower than that of gPC or Monte Carlo methods. The applicability, efficiency, and accuracy of the method are demonstrated via statistical characterization of frequency-domain voltages in parallel wire, interconnect, and antenna corporate feed networks. [ABSTRACT FROM PUBLISHER]

A numerical framework that incorporates recently developed iterative shrinkage thresholding (IST) algorithms within the Born iterative method (BIM) is proposed for solving the two-dimensional inverse electromagnetic scattering problem. IST algorithms minimize a cost function weighted between measurement-data misfit and a zeroth/first-norm penalty term and therefore promote “sharpness” in the solution. Consequently, when applied to domains with sharp variations, discontinuities, or sparse content, the proposed framework is more efficient and accurate than the “classical” BIM that minimizes a cost function with a second-norm penalty term. Indeed, numerical results demonstrate the superiority of the IST-BIM over the classical BIM when they are applied to sparse domains: Permittivity and conductivity profiles recovered using the IST-BIM are sharper and more accurate and converge faster. [ABSTRACT FROM PUBLISHER]

An adaptive multi-element probabilistic collocation (ME-PC) method for quantifying uncertainties in electromagnetic compatibility and interference phenomena involving electrically large, multi-scale, and complex platforms is presented. The method permits the efficient and accurate statistical characterization of observables (i.e., quantities of interest such as coupled voltages) that potentially vary rapidly and/or are discontinuous in the random variables (i.e., parameters that characterize uncertainty in a system's geometry, configuration, or excitation). The method achieves its efficiency and accuracy by recursively and adaptively dividing the domain of the random variables into subdomains using as a guide the decay rate of relative error in a polynomial chaos expansion of the observables. While constructing local polynomial expansions on each subdomain, a fast integral-equation-based deterministic field-cable-circuit simulator is used to compute the observable values at the collocation/integration points determined by the adaptive ME-PC scheme. The adaptive ME-PC scheme requires far fewer (computationally costly) deterministic simulations than traditional polynomial chaos collocation and Monte Carlo methods for computing averages, standard deviations, and probability density functions of rapidly varying observables. The efficiency and accuracy of the method are demonstrated via its applications to the statistical characterization of voltages in shielded/unshielded microwave amplifiers and magnetic fields induced on car tire pressure sensors. [ABSTRACT FROM PUBLISHER]

Internal resonant modes are always observed in the marching-on-in-time (MOT) solution of the time domain electric field integral equation (EFIE), although “relaxed initial conditions,” which are enforced at the beginning of time marching, should in theory prevent these spurious modes from appearing. It has been conjectured that, numerical errors built up during time marching establish the necessary initial conditions and induce the internal resonant modes. However, this conjecture has never been proved by systematic numerical experiments. Our numerical results in this communication demonstrate that, the internal resonant modes' amplitudes are indeed dictated by the numerical errors. Additionally, it is shown that in a few cases, the internal resonant modes can be made “invisible” by significantly suppressing the numerical errors. These tests prove the conjecture that the internal resonant modes are induced by numerical errors when the time domain EFIE is solved by the MOT method. [ABSTRACT FROM PUBLISHER]

An explicit marching on-in-time (MOT) scheme for solving the time-domain magnetic field integral equation (TD-MFIE) is presented. The proposed MOT-TD-MFIE solver uses Rao–Wilton–Glisson basis functions for spatial discretization and a \\PE(CE)^m-type linear multistep method for time marching. Unlike previous explicit MOT-TD-MFIE solvers, the time step size can be chosen as large as that of the implicit MOT-TD-MFIE solvers without adversely affecting accuracy or stability. An algebraic stability analysis demonstrates the stability of the proposed explicit solver; its accuracy and efficiency are established via numerical examples. [ABSTRACT FROM PUBLISHER]

A spatially hierarchical current expansion is used to construct a marching-on-in-time based time domain electric field integral equation solver. The formulation gives rise to well-conditioned linear systems and is immune to time domain low-frequency breakdown phenomena. Numerical results that demonstrate the effectiveness of the proposed hierarchical approach in comparison with existing technologies are presented. [ABSTRACT FROM AUTHOR]

A method for constructing explicit marching-on-in-time (MOT) schemes to solve the time-domain magnetic field volume integral equation (TD-MFVIE) on inhomogeneous dielectric scatterers is proposed. The TD-MFVIE is cast in the form of an ordinary differential equation (ODE) and the unknown magnetic field is expanded using curl conforming spatial basis functions. Inserting this expansion into the TD-MFVIE and spatially testing the resulting equation yield an ODE system with a Gram matrix. This system is integrated in time for the unknown time-dependent expansion coefficients using a linear multistep method. The Gram matrix is sparse and well conditioned for Galerkin testing and consists of only four diagonal blocks for point testing. The resulting explicit MOT schemes, which call for the solution of this matrix system at every time step, are more efficient than their implicit counterparts, which call for inversion of a fuller matrix system at lower frequencies. Numerical results compare the efficiency, accuracy, and stability of the explicit MOT schemes and their implicit counterparts for low-frequency excitations. The results show that the explicit MOT scheme with point testing is significantly faster than the other three solvers without sacrificing from accuracy. [ABSTRACT FROM AUTHOR]

It is well known that graphene demonstrates spatial dispersion properties, i.e., its conductivity is nonlocal and a function of spectral wavenumber (momentum operator) $\mathbf {q}$. In this paper, to account for effects of spatial dispersion on transmission of high-speed signals along graphene nanoribbon (GNR) interconnects, a discontinuous Galerkin time-domain (DGTD) algorithm is proposed. The atomically thick GNR is modeled using a nonlocal transparent surface impedance boundary condition (SIBC) incorporated into the DGTD scheme. Since the conductivity is a complicated function of $\mathbf {q}$ (and one cannot find an analytical Fourier transform pair between $\mathbf {q}$ and spatial differential operators), an exact time-domain SIBC model cannot be derived. To overcome this problem, the conductivity is approximated by its Taylor series in spectral domain under low- $\mathbf {q}$ assumption. This approach permits expressing the time-domain SIBC in the form of a second-order partial differential equation (PDE) in current density and electric field intensity. To permit easy incorporation of this PDE with the DGTD algorithm, three auxiliary variables, which degenerate the second-order (temporal and spatial) differential operators to first-order ones, are introduced. Regarding to the temporal dispersion effects, the auxiliary differential equation method is utilized to eliminate the expensive temporal convolutions. To demonstrate the applicability of the proposed scheme, numerical results, which involve characterization of spatial dispersion effects on the transfer-impedance matrix of GNR interconnects, are presented. [ABSTRACT FROM AUTHOR]

A wavelet-enhanced plane-wave time-domain (PWTD) algorithm for efficiently and accurately solving time-domain surface integral equations (TD-SIEs) on electrically large conducting objects is presented. The proposed scheme reduces the memory requirement and computational cost of the PWTD algorithm by representing the PWTD ray data using local cosine wavelet bases (LCBs) and performing PWTD operations in the wavelet domain. The memory requirement and computational cost of the LCB-enhanced PWTD-accelerated TD-SIE solver, when applied to the analysis of transient scattering from smooth quasi-planar objects with near-normal incident pulses, scale nearly as O(Ns \log Ns) and O(Ns^{1.5}) , respectively. Here, Ns denotes the number of spatial unknowns. The efficiency and accuracy of the proposed scheme are demonstrated through its applications to the analysis of transient scattering from a 185-wavelength long NASA almond and a 123-wavelength long Airbus A-320 model. [ABSTRACT FROM PUBLISHER]

In this paper, a discontinuous Galerkin time-domain (DGTD) method is developed to analyze the power-ground planes taking into account the decoupling capacitors. In the presence of decoupling capacitors, the whole physical system can be split into two subsystems: 1) the field subsystem that is governed by Maxwell’s equations that will be solved by the DGTD method, and 2) the circuit subsystem including the capacitor and its parasitic inductor and resistor, which is going to be characterized by the modified nodal analysis algorithm constructed circuit equations. With the aim to couple the two subsystems together, a lumped port is defined over a coaxial surface between the via barrel and the ground plane. To reach the coupling from the field to the circuit subsystem, a lumped voltage source calculated by the integration of electric field along the radial direction is introduced. On the other hand, to facilitate the coupling from the circuit to field subsystem, a lumped port current source calculated from the circuit equation is introduced, which serves as an impressed current source for the field subsystem. With these two auxiliary terms, a hybrid field-circuit matrix equation is established, which enables the field and circuit subsystems are solved in a synchronous scheme. Furthermore, the arbitrarily shaped antipads are considered by enforcing the proper wave port excitation using the magnetic surface current source derived from the antipads supported electric eigenmodes. In this way, the S-parameters corresponding to different modes can be conveniently extracted. To further improve the efficiency of the proposed algorithm in handling multiscale meshes, the local time-stepping marching scheme is applied. The proposed algorithm is verified by several representative examples. [ABSTRACT FROM PUBLISHER]

A discontinuous Galerkin time-domain (DGTD) method analyzing signal/power integrity on multilayered power-ground parallel plate pairs is proposed. The excitation is realized by introducing wave ports on the antipads where electric/magnetic current sources are represented in terms of the eigenmodes of the antipads. Since closed-forms solutions do not exist for the eigenmodes of the arbitrarily shaped antipads, they have to be calculated using numerical schemes. Spatial orthogonality of the eigenmodes permits determination of each mode's temporal expansion coefficient by integrating the product of the electric field and the mode over the wave port. The temporal mode coefficients are then Fourier transformed to accurately calculate the S-parameters corresponding to different modes. Additionally, to generalize the DGTD to manipulate dispersive media, the auxiliary differential equation method is employed. This is done by introducing a time-dependent polarization volume current as an auxiliary unknown and the constitutive relation between this current and the electric field as an auxiliary equation. Consequently, computationally expensive temporal convolution is avoided. Various numerical examples, which demonstrate the applicability, robustness, and accuracy of the proposed method, are presented. [ABSTRACT FROM PUBLISHER]

A multitrace surface integral equation (MT-SIE) solver is proposed to analyze electromagnetic field interactions on composite devices involving magnetized and nonmagnetized graphene sheets. The computation domain is decomposed into two subdomains: an exterior subdomain that represents the unbounded background medium where the device resides in an interior subdomain that represents the dielectric substrate. Resistive Robin transmission conditions (RRTCs) are formulated to describe the infinitesimally thin graphene sheet that partially covers the surface between the two subdomains. On the rest of this surface, traditional Robin transmission conditions (RTCs) are enforced. The electric and magnetic field equations are used as the governing equations in each subdomain. The governing equations of a subdomain are locally coupled to the governing equations of its neighbor using RRTCs and RTCs. The accuracy and the applicability of the proposed MT-SIE solver are demonstrated by various numerical examples. [ABSTRACT FROM AUTHOR]

In this work, to characterize the radiated emission from electronic circuits in shielding enclosure, an improved electric dipole-based source reconstruction method (SRM) is developed. Moreover, by resorting to this reconstructed equivalent source, the estimation of electromagnetic interference (EMI) between different circuit modules in the enclosure can be conveniently and accurately evaluated. Different from the free-space SRM, the equivalent dipoles of the proposed SRM are directly placed over the shielding box enclosed circuit board, and the numerical Green’s function (NGF) is developed to bridge the connection between the equivalent dipoles and the planar scanned magnetic near-field. With the NGF strategy, the effects of surrounding environments (including the presence of substrate, ground plane, and shielding enclosure) are inclusively considered, which makes the proposed SRM valid for any complex EM environments in theory. Since the proposed SRM also has the capability of reproducing the radiated emission inside the shielding enclosure, it is critically helpful to evaluate the EMI between different circuit modules inside the shielding enclosure. To reach this aim, the Rayleigh-Carson Reciprocity theorem is referred, in which the original EM coupling problem is decomposed into the “forward problem” and “reverse problem.” A Huygens box enclosing the victim circuit module is built and the EM fields on the box are obtained using the reconstructed dipoles in both problems. Then the EMI can be calculated accordingly. Therefore, the novelty and merits of the proposed approach are threefold: 1) the physically-based equivalent dipole model considers the interactions between the radiation sources and the surrounding objects, leading to the accurate prediction of radiated emissions both outside and inside the enclosure; 2) due to the utilization of the NGF, there is no approximation involved in the solution of the dipole’s radiation, thus improving the calculation precision; and 3) the near-field coupling between multiple electronic circuit modules inside the shielding enclosure can be identified precisely, which is useful for diagnostics of radiation sources. The effectiveness of this algorithm is verified by representative numerical examples. [ABSTRACT FROM AUTHOR]

A parallel plane-wave time-domain (PWTD)-accelerated explicit marching-on-in-time (MOT) scheme for solving the time-domain electric field volume integral equation (TD-EFVIE) is presented. The proposed scheme leverages pulse functions and Lagrange polynomials to spatially and temporally discretize the electric flux density induced throughout the scatterers, and a finite-difference scheme to compute the electric fields from the Hertz electric vector potentials radiated by the flux density. The flux density is explicitly updated during time marching by a predictor–corrector (PC) scheme and the vector potentials are efficiently computed by a scalar PWTD scheme. The memory requirement and computational complexity of the resulting explicit PWTD-PC-EFVIE solver scale as O(N_s\,\log \,N_s) and O(N_sN_t), respectively. Here, N_s is the number of spatial basis functions and N_t is the number of time steps. A scalable parallelization of the proposed MOT scheme on distributed-memory CPU clusters is described. The efficiency, accuracy, and applicability of the resulting (parallelized) PWTD-PC-EFVIE solver are demonstrated via its application to the analysis of transient electromagnetic wave interactions on canonical and real-life scatterers represented with up to 25 million spatial discretization elements. [ABSTRACT FROM PUBLISHER]

A scalable parallel plane-wave time-domain (PWTD) algorithm for efficient and accurate analysis of transient scattering from electrically large objects is presented. The algorithm produces scalable communication patterns on very large numbers of processors by leveraging two mechanisms: 1) a hierarchical parallelization strategy to evenly distribute the computation and memory loads at all levels of the PWTD tree among processors and 2) a novel asynchronous communication scheme to reduce the cost and memory requirement of the communications between the processors. The efficiency and accuracy of the algorithm are demonstrated through its applications to the analysis of transient scattering from a perfect electrically conducting (PEC) sphere with a diameter of 70 wavelengths and a PEC square plate with a dimension of 160 wavelengths. Furthermore, the proposed algorithm is used to analyze transient fields scattered from realistic airplane and helicopter models under high frequency excitation. [ABSTRACT FROM PUBLISHER]

A numerical scheme, which hybridizes the element-level dual-field time-domain finite-element domain decomposition method (ELDDM) and the time-domain boundary integral (TDBI) method to accurately and efficiently analyze open-region transient electromagnetic scattering problems, is proposed. Element-level decomposition decouples Maxwell equations on a discretization element from those on its neighboring elements using equivalent currents defined on their faces. For any element inside the computation domain, the equivalent currents are obtained from fields in the neighboring elements. For any element on the boundary of the computation domain, the equivalent currents are obtained using the fields generated by TDBI. To generate these fields, TDBI “radiates” equivalent currents on a Huygens surface enclosing the scatterer. This approach when combined with a leapfrog-type time updates results in a fully explicit numerical scheme that allows ELDDM and TDBI to use different time steps. Numerical results that demonstrate the applicability of the proposed method to concave and disconnected scatterers are presented. [ABSTRACT FROM AUTHOR]

A time-domain electric field volume integral equation (TD-EFVIE) solver is proposed for characterizing transient electromagnetic wave interactions on high-contrast dielectric scatterers. The TD-EFVIE is discretized using the Schaubert–Wilton–Glisson (SWG) and approximate prolate spherical wave (APSW) functions in space and time, respectively. The resulting system of equations cannot be solved by a straightforward application of the marching on-in-time (MOT) scheme since the two-sided APSW interpolation functions require the knowledge of unknown “future” field samples during time marching. Causality of the MOT scheme is restored using an extrapolation technique that predicts the future samples from known “past” ones. Unlike the extrapolation techniques developed for MOT schemes that are used in solving time-domain surface integral equations, this scheme trains the extrapolation coefficients using samples of exponentials with exponents on the complex frequency plane. This increases the stability of the MOT-TD-EFVIE solver significantly, since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme. Numerical results demonstrate that the proposed MOT solver maintains its stability even when applied to analyzing wave interactions on high-contrast scatterers. [ABSTRACT FROM PUBLISHER]

In this paper, the electromagnetic (EM) features of graphene are characterized by a discontinuous Galerkin time-domain (DGTD) algorithm with a resistive boundary condition (RBC). The atomically thick graphene is equivalently modeled using an RBC by regarding the graphene as an infinitesimally thin conductive sheet. To incorporate RBC into the DGTD analysis, the surface conductivity of the graphene composed of contributions from both intraband and interband terms is first approximated by rational basis functions using the fast-relaxation vector-fitting (FRVF) method in the Laplace domain. Next, through the inverse Laplace transform, the corresponding time-domain matrix equations in integral can be obtained. Finally, these matrix equations are solved by time-domain finite integral technique (FIT). For elements not touching the graphene sheet, however, the well-known Runge-Kutta (RK) method is employed to solve the two first-order time-derivative Maxwell’s equations. The application of the surface boundary condition significantly alleviates the memory consuming and the limitation of time step size required by Courant–Friedrichs–Lewy (CFL) condition. To validate the proposed algorithm, various numerical examples are presented and compared with available references. [ABSTRACT FROM PUBLISHER]

A hybrid electromagnetics (EM)-circuit simulator exploiting the discontinuous Galerkin time domain (DGTD) method and the modified nodal analysis (MNA) algorithm is developed for analyzing hybrid distributive and nonlinear multiport lumped circuit systems. The computational domain is split into two subsystems. One is the EM subsystem that is analyzed by DGTD, while the other is the circuit subsystem that is solved by the MNA method. The coupling between the EM and circuit subsystems is enforced at the lumped port where related field and circuit unknowns are coupled via the use of numerical flux, port voltages, and current sources. Since the spatial operations of DGTD are localized, thanks to the use of numerical flux, coupling matrices between EM and circuit subsystems are small and are directly inverted. To handle nonlinear devices within the circuit subsystem, the standard Newton-Raphson method is applied to the nonlinear coupling matrix system. In addition, a local time-stepping scheme is applied to improve the efficiency of the hybrid solver. Numerical examples including single and multiport linear/nonlinear circuit networks are presented to validate the proposed solver. [ABSTRACT FROM PUBLISHER]

Single-source time-domain electric- and magnetic-field integral equations for analyzing scattering from homogeneous penetrable objects are presented. Their temporal discretization is effected by using shifted piecewise polynomial temporal basis functions and a collocation testing procedure, thus allowing for a marching-on-in-time (MOT) solution scheme. Unlike dual-source formulations, single-source equations involve space-time domain operator products, for which spatial discretization techniques developed for standalone operators do not apply. Here, the spatial discretization of the single-source time-domain integral equations is achieved by using the high-order divergence-conforming basis functions developed by Graglia alongside the high-order divergence- and quasi curl-conforming (DQCC) basis functions of Valdés The combination of these two sets allows for a well-conditioned mapping from div- to curl-conforming function spaces that fully respects the space-mapping properties of the space-time operators involved. Numerical results corroborate the fact that the proposed procedure guarantees accuracy and stability of the MOT scheme. [ABSTRACT FROM PUBLISHER]

The time domain combined field integral equation (TD-CFIE), which is constructed from a weighted sum of the time domain electric and magnetic field integral equations (TD-EFIE and TD-MFIE) for analyzing transient scattering from closed perfect electrically conducting bodies, is free from spurious resonances. The standard marching-on-in-time technique for discretizing the TD-CFIE uses Galerkin and collocation schemes in space and time, respectively. Unfortunately, the standard scheme is theoretically not well understood: stability and convergence have been proven for only one class of space-time Galerkin discretizations. Moreover, existing discretization schemes are nonconforming, i.e., the TD-MFIE contribution is tested with divergence conforming functions instead of curl conforming functions. We therefore introduce a novel space-time mixed Galerkin discretization for the TD-CFIE. A family of temporal basis and testing functions with arbitrary order is introduced. It is explained how the corresponding interactions can be computed efficiently by existing collocation-in-time codes. The spatial mixed discretization is made fully conforming and consistent by leveraging both Rao–Wilton–Glisson and Buffa–Christiansen basis functions and by applying the appropriate bi-orthogonalization procedures. The combination of both techniques is essential when high accuracy over a broad frequency band is required. [ABSTRACT FROM PUBLISHER]

A scheme that discretizes exact absorbing boundary conditions (EACs) to incorporate them into a time-domain discontinuous Galerkin finite element method (TD-DG-FEM) is described. The proposed TD-DG-FEM with EACs is used for accurately characterizing transient electromagnetic wave interactions on two-dimensional waveguides. Numerical results demonstrate the proposed method's superiority over the TD-DG-FEM that employs approximate boundary conditions and perfectly matched layers. Additionally, it is shown that the proposed method can produce the solution with ten-eleven digit accuracy when high-order spatial basis functions are used to discretize the Maxwell equations as well as the EACs. [ABSTRACT FROM PUBLISHER]

A discontinuous Galerkin finite element method (DG-FEM) with a highly accurate time integration scheme for solving Maxwell equations is presented. The new time integration scheme is in the form of traditional predictor-corrector algorithms, PE(CE)^m, but it uses coefficients that are obtained using a numerical scheme with fully controllable accuracy. Numerical results demonstrate that the proposed DG-FEM uses larger time steps than DG-FEM with classical PE(CE)^m schemes when high accuracy, which could be obtained using high-order spatial discretization, is required. [ABSTRACT FROM PUBLISHER]

Wrapping a computation domain with a perfectly matched layer (PML) is one of the most effective methods of imitating/approximating the radiation boundary condition in the Maxwell and wave equation solvers. Many PML implementations often use a smoothly increasing attenuation coefficient to increase the absorption for a given layer thickness, and, at the same time, to reduce the numerical reflection from the interface between the computation domain and the PML. In discontinuous Galerkin time-domain (DGTD) methods, using a PML coefficient that varies within a mesh element requires a different mass matrix to be stored for every element and therefore significantly increases the memory footprint. In this work, this bottleneck is addressed by applying a weight-adjusted approximation to these mass matrices. The resulting DGTD scheme has the same advantages as the scheme that stores individual mass matrices, namely, higher accuracy (due to reduced numerical reflection) and increased meshing flexibility (since the PML does not have to be defined layer by layer), but it requires significantly less memory. [ABSTRACT FROM AUTHOR]

The development of time-domain integral equation solvers with robust late-time stability properties has been a long-standing quest. Among the many methods that have been investigated, those leveraging quasi-exact integration techniques appear to be most successful. This article presents stable and accurate marching-on-in-time (MOT) solvers for time-domain electric, magnetic, and combined field integral equations (EFIE, MFIE, and CFIE) based on quasi-exact integration techniques. The novel MOT solvers exhibit excellent stability while yielding highly accurate results, as demonstrated by various numerical examples. In addition, the solvers’ excellent stability and accuracy properties are used to examine spurious modes encountered when time-domain integral equations are applied to closed surfaces. It is demonstrated that MOT solutions to the time domain EFIE and MFIE often are polluted by spurious modes at the cavity’s resonant frequencies whereas those of the CFIE solver are devoid of such contamination. [ABSTRACT FROM AUTHOR]

An explicit marching-on-in-time (MOT) scheme to efficiently solve the time-domain magnetic field integral equation (TD-MFIE) with a large time step size (under a low-frequency excitation) is developed. The proposed scheme spatially expands the current using high-order nodal functions defined on curvilinear triangles discretizing the scatterer surface. Applying Nyström discretization, which uses this expansion, to the TD-MFIE, which is written as an ordinary differential equation (ODE) by separating self-term contribution, yields a system of ODEs in unknown time-dependent expansion coefficients. A predictor–corrector method is used to integrate this system for the samples of these coefficients. Since the Gram matrix arising from the Nyström discretization is a block-diagonal, the resulting MOT scheme replaces the matrix “inversion” required at each time step by a product of the inverse block-diagonal Gram matrix and the right-hand side vector. It is shown that, on the convergence of the corrector updates, this explicit MOT scheme produces the same solution as its implicit counterpart and is faster for large time step sizes. [ABSTRACT FROM AUTHOR]

In this article, a local coupling multitrace domain decomposition method (LCMT-DDM) based on surface integral equation (SIE) formulations is proposed to analyze electromagnetic scattering from multilayered dielectric objects. Different from the traditional SIE-DDM, where the interactions between subdomains are accounted for using global radiation coupling, LCMT-DDM uses a local coupling scheme. The original multilayered object is decomposed into several independent domains, i.e., the exterior region (free space) and many homogeneous interior regions (dielectrics). The boundaries of subdomains are all touching faces, where only the Robin transmission conditions (RTCs) are enforced to ensure the field continuity. Hence, each subdomain only couples with its neighboring regions, which makes the DDM system a highly sparse matrix, especially when the number of subdomains is large. In each subdomain, the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE) for dielectrics are used as the governing equations. By imposing RTCs, well-conditioned equations are formed in each subdomain without invoking the combined-field integral equation (CFIE), which usually causes accuracy issues in dielectric modeling. Since the subdomain matrices are diagonally dominant, the flexible generalized minimal residual (FGMRES) technique is used to accelerate the iterative solution of the whole DDM system. Moreover, an effective preconditioner that can be recursively constructed is proposed. [ABSTRACT FROM AUTHOR]

Due to the temperature-dependent resistivity of power distribution network (PDN) interconnects, a wiser and necessary strategy is to proceed the electrical–thermal cosimulation in order to include the thermal effects caused by Joule heating. As a natural domain decomposition method (DDM), in this article, a discontinuous Galerkin (DG) method is proposed to facilitate the steady-state electrical and thermal coanalysis. With the intention to avoid solving a globally coupled steady-state matrix system equations resulted from the implicit numerical flux in DG, the block Thomas method is deployed to solve the entire domain in a subdomain-by-subdomain scheme. As a direct solver, the block Thomas method is free of convergence problem frequently occurring in iterative methods, such as block Gauss–Seidel method. The capability of the proposed DG method in handling multiscale and complex 3-D PDNs is validated by several representative examples. [ABSTRACT FROM AUTHOR]

With the purpose of avoiding very fine mesh cells in the proximity of a thin wire, the modified telegrapher’s equations (MTEs) are employed to describe the thin wire voltage and current distributions, which consequently results in reduced number of unknowns and augmented Courant–Friedrichs–Lewy (CFL) number. As hyperbolic systems, both the MTEs and the Maxwell’s equations are solved by the discontinuous Galerkin time-domain (DGTD) method. In realistic situations, the thin wires could be either driven or loaded by circuit networks. The thin wire–circuit interface performs as a boundary condition for the thin wire solver, where the thin wire voltage and current used for the incoming flux evaluation involved in the DGTD-analyzed MTEs are not available. To obtain this voltage and current, an auxiliary current flowing through the thin wire–circuit interface is introduced at each interface. Corresponding auxiliary equations derived from the invariable property of characteristic variable for hyperbolic systems are developed and solved together with the circuit equations established by the modified nodal analysis (MNA) modality. Furthermore, in order to characterize the field and thin wire interactions, a weighted electric field and a volume current density are added into the MTEs and Maxwell–Ampere’s law equation, respectively. To validate the proposed algorithm, three representative examples are presented. [ABSTRACT FROM PUBLISHER]

To meet the electromagnetic interference regulation, the radiated emission from device under test such as electronic devices must be carefully manipulated and accurately characterized. Instead of resorting to the direct far-field measurement, in this paper, a novel approach is proposed to model the radiated emission from electronic devices placed in shielding enclosures by using the near electric field only. Based on the Schelkkunoff's equivalence principle and Raleigh–Carson reciprocity theorem, only the tangential components of the electric field over the ventilation slots and apertures of the shielding enclosure are sufficient to obtain the radiated emissions outside the shielding box if the inside of the shielding enclosure was filled with perfectly electric conductor (PEC). In order to efficiently model wideband emission, the time-domain sampling scheme is employed. Due to the lack of analytical Green's function for arbitrary PEC boxes, the radiated emission must be obtained via the full-wave numerical methods by considering the total radiated emission as the superposition between the direct radiation from the equivalent magnetic currents in free space and the scattered field generated by the PEC shielding box. In this study, the state-of-the-art discontinuous Galerkin time-domain (DGTD) method is utilized, which has the flexibility to model irregular geometries, keep high-order accuracy, and more importantly involves only local operations. For open-region problems, a hybridized DGTD and time-domain boundary integration method applied to rigorously truncate the computational domain. To validate the proposed approach, several representative examples are presented and compared with both analytical and numerical results. [ABSTRACT FROM PUBLISHER]

To avoid straightforward volumetric discretization, a discontinuous Galerkin time-domain (DGTD) method integrated with the impedance boundary condition (IBC) is presented in this paper to analyze the scattering from objects with finite conductivity. Two situations are considered. 1) The skin depth is smaller than the thickness of the conductive volume. 2) The skin depth is larger than the thickness of a thin conductive sheet. For the first situation, a surface impedance boundary condition (SIBC) is employed, wherein the surface impedance usually exhibits a complex relation with the frequency. To incorporate the SIBC into DGTD, the surface impedance is first approximated by rational functions in the Laplace domain using the fast relaxation vector-fitting (FRVF) technique. Via inverse Laplace transform, the time-domain DGTD matrix equations can be obtained conveniently in integral form with respect to time t. For the second situation, a transmission IBC (TIBC) is used to include the transparent effects of the fields. In the TIBC, the tangential magnetic field jump is related with the tangential electric field via the surface conductivity. In this work, a specifically designed DGTD algorithm with TIBC is developed to model the graphene up to the terahertz (THz) band. In order to incorporate the TIBC into DGTD without involving the time-domain convolution, an auxiliary surface polarization current governed by a first-order differential equation is introduced over the graphene. For open-region scattering problems, the DGTD algorithm is further hybridized with the time-domain boundary integral (TDBI) method to rigorously truncate the computational domain. To demonstrate the accuracy and applicability of the proposed algorithm, several representative examples are provided. [ABSTRACT FROM PUBLISHER]

Stability of time domain integral equation (TDIE) solvers has remained an elusive goal for many years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method's efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples. [ABSTRACT FROM PUBLISHER]

A scheme hybridizing discontinuous Galerkin time-domain (DGTD) and time-domain boundary integral (TDBI) methods for accurately analyzing transient electromagnetic scattering is proposed. Radiation condition is enforced using the numerical flux on the truncation boundary. The fields required by the flux are computed using the TDBI from equivalent currents introduced on a Huygens' surface enclosing the scatterer. The hybrid DGTDBI ensures that the radiation condition is mathematically exact and the resulting computation domain is as small as possible since the truncation boundary conforms to scatterer's shape and is located very close to its surface. Locally truncated domains can also be defined around each disconnected scatterer additionally reducing the size of the overall computation domain. Numerical examples demonstrating the accuracy and versatility of the proposed method are presented. [ABSTRACT FROM PUBLISHER]

The standard and mixed discretizations for the magnetic field integral equation (MFIE) and the Müller integral equation (MUIE) are investigated in the context of low-frequency (LF) scattering problems involving simply connected scatterers. It is proved that, at low frequencies, the frequency scaling of the nonsolenoidal part of the solution current can be incorrect for the standard discretization. In addition, it is proved that the frequency scaling obtained with the mixed discretization is correct. The reason for this problem in the standard discretization scheme is the absence of exact solenoidal currents in the rotated RWG finite element space. The adoption of the mixed discretization scheme eliminates this problem and leads to a well-conditioned system of linear equations that remains accurate at low frequencies. Numerical results confirm these theoretical predictions and also show that, when the frequency is lowered, a finer and finer mesh is required to keep the accuracy constant with the standard discretization. [ABSTRACT FROM PUBLISHER]