arXiv subjects

Fernando L. Teixeira

Publications and source records attributed to Fernando L. Teixeira.

At least 19 recordsLinked to original sources

arXiv2026

Rapidly Convergent Finite-Element Domain Decomposition Method With Two-Channel Transmission Conditions

A novel dual-primal finite element tearing and interconnecting (FETI-DP) domain decomposition method (DDM) is introduced for solving Maxwell's equations. The proposed method is built upon a two-channel transmission condition (TC) enforcing both tangential-field and normal-flux continuity across subdomain interfaces. Two interface channels are separately constructed from the Faraday and Ampere-Maxwell equations. Simultaneously enforcing tangential-field and normal-flux continuity reduces interface jumps by several orders of magnitude relative to the widely used Robin TC. The resulting global interface equation exhibits markedly improved iterative convergence. Numerical experiments across different partitioning strategies, subdomain counts and volumes, mesh resolutions, and geometries demonstrate drastic reductions in iteration counts, while accuracy, massive parallelism, and scalability are preserved.

physics.comp-ph↗

arXiv2026

Parametric Interpolation of Dynamic Mode Decomposition for Predicting Nonlinear Systems

We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods which interpolate modes, eigenvalues, or reduced operators and can be fragile with sparse training data or multi-dimensional parameter spaces, piDMD learns a single parameter-affine Koopman surrogate reduced order model (ROM) across multiple training parameter samples and predicts at unseen parameter values without retraining. We validate piDMD on fluid flow past a cylinder, electron beam oscillations in transverse magnetic fields, and virtual cathode oscillations -- the latter two being simulated using an electromagnetic particle-in-cell (EMPIC) method. Across all benchmarks, piDMD achieves accurate long-horizon predictions and improved robustness over state-of-the-art interpolation-based parametric DMD baselines, with less training samples and with multi-dimensional parameter spaces.

eess.SY↗

arXiv2024

An Unstructured Body-of-Revolution Electromagnetic Particle-in-Cell Algorithm with Radial Perfectly Matched Layers and Dual Polarizations

A novel electromagnetic particle-in-cell algorithm has been developed for fully kinetic plasma simulations on unstructured (irregular) meshes in complex body-of-revolution geometries. The algorithm, implemented in the BORPIC++ code, utilizes a set of field scalings and a coordinate mapping, reducing the Maxwell field problem in a cylindrical system to a Cartesian finite element Maxwell solver in the meridian plane. The latter obviates the cylindrical coordinate singularity in the symmetry axis. The choice of an unstructured finite element discretization enhances the geometrical flexibility of the BORPIC++ solver compared to the more traditional finite difference solvers. Symmetries in Maxwell's equations are explored to decompose the problem into two dual polarization states with isomorphic representations that enable code reuse. The particle-in-cell scatter and gather steps preserve charge-conservation at the discrete level. Our previous algorithm (BORPIC+) discretized the E and B field components of TE-phi and TM-phi polarizations on the finite element (primal) mesh. A cylindrical perfectly matched layer is implemented as a boundary condition in the radial direction to simulate open space problems, with periodic boundary conditions in the axial direction. We investigate effects of charged particles moving next to the cylindrical perfectly matched layer. We model azimuthal currents arising from rotational motion of charged rings, which produce TM-phi polarized fields. Several numerical examples are provided to illustrate the first application of the algorithm.

math.NA↗

arXiv2024

Accelerating Particle-in-Cell Kinetic Plasma Simulations via Reduced-Order Modeling of Space-Charge Dynamics using Dynamic Mode Decomposition

We present a data-driven reduced-order modeling of the space-charge dynamics for electromagnetic particle-in-cell (EMPIC) plasma simulations based on dynamic mode decomposition (DMD). The dynamics of the charged particles in kinetic plasma simulations such as EMPIC is manifested through the plasma current density defined along the edges of the spatial mesh. We showcase the efficacy of DMD in modeling the time evolution of current density through a low-dimensional feature space. Not only do such DMD-based predictive reduced-order models help accelerate EMPIC simulations, they also have the potential to facilitate investigative analysis and control applications. We demonstrate the proposed DMD-EMPIC scheme for reduced-order modeling of current density, and speed-up in EMPIC simulations involving electron beam under the influence of magnetic field, virtual cathode oscillations, and backward wave oscillator.

physics.plasm-ph↗

arXiv2021

Detection and Prediction of Equilibrium States in Kinetic Plasma Simulations via Mode Tracking using Reduced-Order Dynamic Mode Decomposition

A dynamic mode decomposition (DMD) based reduced-order model (ROM) is developed for tracking, detection, and prediction of kinetic plasma behavior. DMD is applied to the high-fidelity kinetic plasma model based on the electromagnetic particle-in-cell (EMPIC) algorithm to extract the underlying dynamics and key features of the model. In particular, the ability of DMD to reconstruct the spatial pattern of the self electric field from high-fidelity data and the effect of DMD extrapolated self-fields on charged particle dynamics are investigated. An in-line sliding-window DMD method is presented for identifying the transition from transient to equilibrium state based on the loci of DMD eigenvalues in the complex plane. The in-line detection of equilibrium state combined with time extrapolation ability of DMD has the potential to effectively expedite the simulation. Case studies involving electron beams and plasma ball are presented to assess the strengths and limitations of the proposed method.

physics.plasm-ph↗

arXiv2019

Quantum Information Propagation Preserving Computational Electromagnetics

We propose a new methodology, called numerical canonical quantization, to solve quantum Maxwell's equations useful for mathematical modeling of quantum optics physics, and numerical experiments on arbitrary passive and lossless quantum-optical systems. It is based on: (1) the macroscopic (phenomenological) electromagnetic theory on quantum electrodynamics (QED), and (2) concepts borrowed from computational electromagnetics. It was shown that canonical quantization in inhomogeneous dielectric media required definite and proper normal modes. Here, instead of ad-hoc analytic normal modes, we numerically construct complete and time-reversible normal modes in the form of traveling waves to diagonalize the Hamiltonian. Specifically, we directly solve the Helmholtz wave equations for a general linear, reciprocal, isotropic, non-dispersive, and inhomogeneous dielectric media by using either finite-element or finite-difference methods. To convert a scattering problem with infinite number of modes into one with a finite number of modes, we impose Bloch-periodic boundary conditions. This will sparsely sample the normal modes with numerical Bloch-Floquet-like normal modes. Subsequent procedure of numerical canonical quantization is straightforward using linear algebra. We provide relevant numerical recipes in detail and show an important numerical example of indistinguishable two-photon interference in quantum beam splitters, exhibiting Hong-Ou-Mandel effect, which is purely a quantum effect. Also, the present methodology provides a way of numerically investigating existing or new macroscopic QED theories. It will eventually allow quantum-optical numerical experiments of high fidelity to replace many real experiments as in classical electromagnetics.

quant-ph↗

arXiv2019

Beamforming Algorithm for Multiuser Wideband Millimeter-Wave Systems with Hybrid and Subarray Architectures

We present a beamforming algorithm for multiuser wideband millimeter wave (mmWave) communication systems where one access point uses hybrid analog/digital beamforming while multiple user stations have phased-arrays with a single RF chain. The algorithm operates in a more general mode than others available in literature and has lower computational complexity and training overhead. Throughout the paper, we describe: i) the construction of novel beamformer sets (codebooks) with wide sector beams and narrow beams based on the orthogonality property of beamformer vectors, ii) a beamforming algorithm that uses training transmissions over the codebooks to select the beamformers that maximize the received sumpower along the bandwidth, and iii) a numerical validation of the algorithm in standard indoor scenarios for mmWave WLANs using channels obtained with both statistical and raytracing models. Our algorithm is designed to serve multiple users in a wideband OFDM system and does not require channel matrix knowledge or a particular channel structure. Moreover, we incorporate antenna-specific aspects in the analysis, such as antenna coupling, element radiation pattern, and beam squint. Although there are no other solutions for the general system studied in this paper, we characterize the algorithm's achievable rate and show that it attains more than 70 percent of the spectral efficiency (between 1.5 and 3 dB SNR loss) with respect to ideal fully-digital beamforming in the analyzed scenarios. We also show that our algorithm has similar sum-rate performance as other solutions in the literature for some special cases, while providing significantly lower computational complexity (with a linear dependence on the number of antennas) and shorter training overhead.

eess.SP↗

arXiv2019

Performance Analysis and Dynamic Evolution of Deep Convolutional Neural Network for Nonlinear Inverse Scattering

The solution of nonlinear electromagnetic (EM) inverse scattering problems is typically hindered by several challenges such as ill-posedness, strong nonlinearity, and high computational costs. Recently, deep learning has been demonstrated to be a promising tool in addressing these challenges. In particular, it is possible to establish a connection between a deep convolutional neural network (CNN) and iterative solution methods of nonlinear EM inverse scattering. This has led to the development of an efficient CNN-based solution to nonlinear EM inverse problems, termed DeepNIS. It has been shown that DeepNIS can outperform conventional nonlinear inverse scattering methods in terms of both image quality and computational time. In this work, we quantitatively evaluate the performance of DeepNIS as a function of the number of layers using structure similarity measure (SSIM) and mean-square error (MSE) metrics. In addition, we probe the dynamic evolution behavior of DeepNIS by examining its near-isometry property. It is shown that after a proper training stage the proposed CNN is near optimal in terms of the stability and generalization ability.

physics.comp-ph↗

arXiv2018

DeepNIS: Deep Neural Network for Nonlinear Electromagnetic Inverse Scattering

Nonlinear electromagnetic (EM) inverse scattering is a quantitative and super-resolution imaging technique, in which more realistic interactions between the internal structure of scene and EM wavefield are taken into account in the imaging procedure, in contrast to conventional tomography. However, it poses important challenges arising from its intrinsic strong nonlinearity, ill-posedness, and expensive computation costs. To tackle these difficulties, we, for the first time to our best knowledge, exploit a connection between the deep neural network (DNN) architecture and the iterative method of nonlinear EM inverse scattering. This enables the development of a novel DNN-based methodology for nonlinear EM inverse problems (termed here DeepNIS). The proposed DeepNIS consists of a cascade of multi-layer complexvalued residual convolutional neural network (CNN) modules. We numerically and experimentally demonstrate that the DeepNIS outperforms remarkably conventional nonlinear inverse scattering methods in terms of both the image quality and computational time. We show that DeepNIS can learn a general model approximating the underlying EM inverse scattering system. It is expected that the DeepNIS will serve as powerful tool in treating highly nonlinear EM inverse scattering problems over different frequency bands, involving large-scale and high-contrast objects, which are extremely hard and impractical to solve using conventional inverse scattering methods.

cs.IR↗

arXiv2018

Finite Element Time-Domain Body-of-Revolution Maxwell Solver based on Discrete Exterior Calculus

We present a finite-element time-domain (FETD) Maxwell solver for the analysis of body-of-revolution (BOR) geometries based on discrete exterior calculus (DEC) of differential forms and transformation optics (TO) concepts. We explore TO principles to map the original 3-D BOR problem to a 2-D one in the meridian plane based on a Cartesian coordinate system where the cylindrical metric is fully embedded into the constitutive properties of an effective inhomogeneous and anisotropic medium that fills the domain. The proposed solver uses a TE/TM field decomposition and an appropriate set of DEC-based basis functions on an irregular grid discretizing the meridian plane. A symplectic time discretization based on a leap-frog scheme is applied to obtain the full-discrete marching-on-time algorithm. We validate the algorithm by comparing the numerical results against analytical solutions for resonant fields in cylindrical cavities and against pseudo-analytical solutions for fields radiated by cylindrically symmetric antennas in layered media. We also illustrate the application of the algorithm for a particle-in-cell (PIC) simulation of beam-wave interactions inside a high-power backward-wave oscillator.

physics.comp-ph↗

arXiv2018

Launching and Controlling Gaussian Beams from Point Sources via Planar Transformation Media

Based on operations prescribed under the paradigm of Complex Transformation Optics (CTO) [1-5], it was recently shown in [5] that a complex source point (CSP) can be mimicked by a parity-time ($\mathcal{PT}$) transformation media. Such coordinate transformation has a mirror symmetry for the imaginary part, and results in a balanced loss/gain metamaterial slab. A CSP produces a Gaussian beam and, consequently, a point source placed at the center of such metamaterial slab produces a Gaussian beam propagating away from the slab. Here, we extend the CTO analysis to non-symmetric complex coordinate transformations as put forth in [6] and verify that, by using simply a (homogeneous) doubly anisotropic gain-media metamaterial slab, one can still mimic a CSP and produce Gaussian beam. In addition, we show that a Gaussian-like beams can be produced by point sources placed {\it outside} the slab as well [6]. By making use of the extra degrees of freedom (real and imaginary part of the coordinate transformation) provided by CTO, the near-zero requirement on the real part of the resulting constitutive parameters can be relaxed to facilitate potential realization of Gaussian-like beams. We illustrate how beam properties such as peak amplitude and waist location can be controlled by a proper choice of (complex-valued) CTO Jacobian elements. In particular, the beam waist location may be moved bidirectionally by allowing for negative entries in the Jacobian (equivalent to inducing negative refraction effects). These results are then interpreted in light of the ensuing CSP location.

physics.optics↗

arXiv2017

Application of time-reversal-based processing techniques to enhance detection of GPR targets

In this paper we analyze the performance of time-reversal (TR) techniques in conjunction with various Ground Penetrating Radar (GPR) pre-processing methods aimed at improving detection of subsurface targets. TR techniques were first developed for ultrasound applications and, by exploiting the invariance of the wave equation under time reversal, can yield features such as superresolution and statistical stability. The TR method was examined here using both synthetic and actual GPR field data under four different pre-processing strategies on the raw data, namely: mean background removal, eigenvalue background removal, a sliding-window space-frequency technique, and a noise-robust spatial differentiator along the scan direction. Depending on the acquisition mode, it was possible to determine with good precision the position and depth of the studied targets as well as, in some cases, to differentiate the targets from nearby clutter such as localized geological anomalies. The proposed methodology has the potential to be useful when applied to GPR data for the detection of buried targets.

physics.geo-ph↗

arXiv2017

Axisymmetric Charge-Conservative Electromagnetic Particle Simulation Algorithm on Unstructured Grids: Application to Microwave Vacuum Electronic Devices

We present a 2.5-dimensional charge-conservative electromagnetic particle-in-cell (EM-PIC) algorithm optimized for the analysis of vacuum electronic devices (VED) with cylindrical symmetry (axisymmetry). We explore the axisymmetry present in the device geometry, fields, and sources to reduce the dimensionality of the problem from 3D to 2D. Further, we explore `transformation optics' principles to map the original problem in polar coordinates to an equivalent problem on Cartesian coordinates with an effective (artificial) inhomogeneous medium introduced. The resulting problem in the meridian plane is discretized using an unstructured 2D mesh considering TE-polarized fields and properly scaled charges. EM field and source variables (node-based charges and edge-based currents) are expressed as differential forms of various degrees, and discretized using Whitney forms. Using leapfrog time integration, we obtain a mixed finite-element time-domain scheme for the full-discrete Maxwell's equations. We achieve a local and explicit time-update for the field equations by employing the sparse approximate inverse (SPAI) algorithm. Interpolating field values to particles' positions for solving Newton-Lorentz equations of motion is also done via Whitney forms. Particles are advanced using the Boris algorithm with a relativistic correction. In the scatter step, we apply a radial scaling factor on top of a charge-conserving scatter scheme tailored for 2-dimensional unstructured grids. As validation examples, we demonstrate simulations that investigate the physical performance of VEDs designed to harness particle bunching effects arising from the coherent (resonance) Cerenkov electron beam interactions within micromachined slow-wave structures.

physics.plasm-ph↗

arXiv2017

Equalized Time Reversal Beamforming for Indoor Wireless Communications

Time-reversal (TR) is a beamforming technique for frequency-selective channels, which has received increasing attention due to its high energy efficiency and low computational complexity for wireless communications. In this paper, we present two contributions on time-reversal (TR) wireless beamforming for single-user indoor wideband MISO systems. First, we provide novel analyses of a baseband TR system using two commonly used indoor propagation channel models. We derive closed-form approximations for the inter-symbol interference (ISI) with these channel models in order to characterize the influence of propagation conditions (such as the power-delay profile, delay spread, and bandwidth) on TR performance metrics. In particular, we analyze spatial focusing and time compression performance of TR beamforming, and their impact on the bit error rate (BER). As a second contribution, we introduce an equalized TR (ETR) technique that mitigates the ISI of conventional TR. The proposed ETR utilizes a zero-forcing pre-equalizer at the transmitter in a cascade configuration with the TR pre-filter. Unlike previous approaches to ISI mitigation in TR systems, we derive theoretical performance bounds for ETR and show that it greatly enhances the BER performance of conventional TR with minimal impact to its beamforming capabilities. By means of numerical simulations, we verify our closed-form approximations and show that the proposed ETR technique outperforms conventional TR with respect to the BER under any SNR.

cs.NI↗

arXiv2016

Space-Time Block Diagonalization for Frequency-Selective MIMO Broadcast Channels

The most relevant linear precoding method for frequency-flat MIMO broadcast channels is block diagonalization (BD) which, under certain conditions, attains the same nonlinear dirty paper coding channel capacity. However, BD is not easily translated to frequency-selective channels, since space-time information is required for transceiver design. In this paper, we demonstrate that BD is feasible in frequency-selective MIMO broadcast channels to eliminate inter-user interference (IUI) if the transmit block length is sufficiently large, and if the number of transmit antennas is greater than the number of users. We also propose three different approaches to mitigate/eliminate inter-symbol interference (ISI) in block transmissions: i) time-reversal-based BD (TRBD) which maximizes spatial focusing around the receivers using transmitter processing only, ii) equalized BD (EBD) which minimizes the ISI using transmitter processing only, and iii) joint processing BD (JPBD), which uses linear processing at the transmitter and the receiver to suppress ISI. We analyze the theoretical diversity and multiplexing gains of these techniques, and we demonstrate that JPBD approximates full multiplexing gain for a sufficiently large transmit block length. Extensive numerical simulations show that the achievable rate and probability of error performance of all the proposed methods improve those of conventional time-reversal beamforming. Moreover, JPBD provides the highest achievable rate region for frequency-selective MIMO broadcast channels.

cs.IT↗

arXiv2016

Exact Charge-Conserving Scatter-Gather Algorithm for Particle-in-Cell Simulations on Unstructured Grids: A Geometric Perspective

We describe a charge-conserving scatter-gather algorithm for particle-in-cell simulations on unstructured grids. Charge conservation is obtained from first principles, i.e., without the need for any post-processing or correction steps. This algorithm recovers, at a fundamental level, the scatter-gather algorithms presented recently by Campos-Pinto et al. [1] (to first-order) and by Squire et al. [2], but it is derived here in a streamlined fashion from a geometric viewpoint. Some ingredients reflecting this viewpoint are (1) the use of (discrete) differential forms of various degrees to represent fields, currents, and charged particles and provide localization rules for the degrees of freedom thereof on the various grid elements (nodes, edges, facets), (2) use of Whitney forms as basic interpolants from discrete differential forms to continuum space, and (3) use of a Galerkin formula for the discrete Hodge star operators (i.e., "mass matrices" incorporating the metric datum of the grid) applicable to generally irregular, unstructured grids. The expressions obtained for the scatter charges and scatter currents are very concise and do not involve numerical quadrature rules. Appropriate fractional areas within each grid element are identified that represent scatter charges and scatter currents within the element, and a simple geometric representation for the (exact) charge conservation mechanism is obtained by such identification. The field update is based on the coupled first-order Maxwell's curl equations to avoid spurious modes with secular growth (otherwise present in formulations that discretize the second-order wave equation). Examples are provided to verify preservation of discrete Gauss' law for all times.

math.NA↗

arXiv2016

Tensor Green's Function Evaluation in Arbitrarily Anisotropic, Layered Media using Complex-Plane Gauss-Laguerre Quadrature

We discuss the application of Complex-Plane Gauss-Laguerre Quadrature (CGLQ) to efficiently evaluate two-dimensional Fourier integrals arising as the solution to electromagnetic fields radiated by elementary dipole antennas embedded within planar-layered media with arbitrary material parameters. More specifically, we apply CGLQ to the long-standing problem of rapidly and efficiently evaluating the semi-infinite length "tails" of the Fourier integral path while simultaneously and robustly guaranteeing absolute, exponential convergence of the field solution despite diversity in the doubly anisotropic layer parameters, source type (i.e., electric or equivalent magnetic dipole), source orientation, observed field type (magnetic or electric), (non-zero) frequency, and (non-zero) source-observer separation geometry. The proposed algorithm exhibits robustness despite unique challenges arising for the fast evaluation of such two-dimensional integrals. Herein, we develop the mathematical treatment to rigorously evaluate the tail integrals using CGLQ and discuss and address the specific issues posed to the CGLQ method when anisotropic, layered media are present. To empirically demonstrate the CGLQ algorithm's computational efficiency, versatility, and accuracy, we perform a convergence analysis along with two case studies related to modeling of electromagnetic resistivity tools employed in geophysical prospection of layered, anisotropic Earth media and validating the ability of isoimpedance substrates to enhance the radiation performance of planar antennas placed in close proximity to metallic ground planes.

physics.comp-ph↗

arXiv2016

Spectral-Domain-Based Scattering Analysis of Fields Radiated by Distributed Sources in Planar-Stratified Environments with Arbitrarily Anisotropic Layers

We discuss the numerically stable, spectral-domain computation and extraction of the scattered electromagnetic field excited by distributed sources embedded in planar-layered environments, where each layer may exhibit arbitrary and independent electrical and magnetic anisotropic response and loss profiles. This stands in contrast to many standard spectral-domain algorithms that are restricted to computing the fields radiated by Hertzian dipole sources in planar-layered environments where the media possess azimuthal-symmetric material tensors (i.e., isotropic, and certain classes of uniaxial, media). Although computing the scattered field, particularly when due to distributed sources, appears (from the analytical perspective, at least) relatively straightforward, different procedures within the computation chain, if not treated carefully, are inherently susceptible to numerical instabilities and (or) accuracy limitations due to the potential manifestation of numerically overflown and (or) numerically unbalanced terms entering the chain. Therefore, primary emphasis herein is given to effecting these tasks in a numerically stable and robust manner for all ranges of physical parameters. After discussing the causes behind, and means to mitigate, these sources of numerical instability, we validate the algorithm's performance against closed-form solutions. Finally, we validate and illustrate the applicability of the proposed algorithm in case studies concerning active remote sensing of marine hydrocarbon reserves embedded deep within lossy, planar-layered media.

physics.comp-ph↗