arXiv subjects

F. L. Teixeira

Publications and source records attributed to F. L. Teixeira.

14 recordsLinked to original sources

arXiv2026

Hierarchical Finite-Element Analysis of Multiscale Electromagnetic Problems via Sparse Operator-Adapted Wavelet Decomposition

In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches, while capable of achieving the desired accuracy without requiring a complete re-meshing of the computational domain, inherently couple different resolution levels. This coupling requires recomputation of coarser-level solutions whenever finer details are added to improve accuracy, resulting in substantial computational overhead. Our proposed method addresses this issue by decoupling resolution levels. This feature enables independent computations at each scale that can be incorporated into the solutions to improve accuracy whenever needed, without requiring re-computation of coarser-level solutions. The main algorithm is hierarchical, constructing solutions from finest to coarser levels through a series of sparse matrix-vector multiplications. Due to its sparse nature, the overall computational complexity of the algorithm is nearly linear. Moreover, Krylov subspace iterative solvers are employed to solve the final linear equations, with ILU preconditioners that enhance solver convergence and maintain overall computational efficiency. The numerical experiments presented in this article verify the high precision and nearly linear computational complexity of the proposed algorithm.

physics.comp-ph↗

arXiv2025

Sparse Operator-Adapted Wavelet Decomposition Using Polygonal Elements for Multiscale FEM Problems

We develop a sparse multiscale operator-adapted wavelet decomposition-based finite element method (FEM) on unstructured polygonal mesh hierarchies obtained via a coarsening procedure. Our approach decouples different resolution levels, allowing each scale to be solved independently and added to the entire solution without the need to recompute coarser levels. At the finest level, the meshes consist of triangular elements which are geometrically coarsened at each step to form convex polygonal elements. Smooth field regions of the domain are solved with fewer, larger, polygonal elements, whereas high-gradient regions are represented by smaller elements, thereby improving memory efficiency through adaptivity. The proposed algorithm computes solutions via sequences of hierarchical sparse linear-algebra operations with nearly linear computational complexity.

physics.comp-ph↗

arXiv2024

Electrical capacitance volume sensor for microgravity mass gauging: Advancements in sensor calibration for microgravity fluid configurations and propellant management devices

Microgravity mass gauging has gained increasing importance in recent years due to the acceleration in planning for long-term space missions as well as in-space refueling and transfer operations. It is of particular importance with cryogenic propellants where periodic tank venting maneuvers and leak detection place a special emphasis on accurate mass gauging. Several competing technologies have arisen, but capacitance mass gauging has several distinct advantages due to its low mass, non-intrusiveness, and whole volume interrogation technique. Capacitance based measurement has also seen recent success in measuring cryogenic liquid nitrogen and hydrogen volume fraction and flow rate, showing its compatibility with cryogenic propellants. However, the effects of gravity on fluid behavior make the calibration and testing of these sensors difficult on the ground. In this paper a prototype sensor is constructed that can emulate fluid positions in microgravity and earth gravity configurations. Experimental propellant fills and drains are conducted using a simulant fluid with similar electrical properties to cryogenic propellants. This expanded dataset is compared with previous simulation results and used to construct a machine learning model capable of calculating the fluid mass in tanks both with and without propellant management devices.

physics.ins-det↗

arXiv2024

Toward Microgravity Mass Gauging with Electrical Capacitance Volume Sensing: Sensor Design and Experiment

The use of capacitance sensors for fuel mass gauging has been in consideration since the early days of manned space flight. However, certain difficulties arise when considering tanks in microgravity environments. Surface tension effects lead to fluid wetting of the interior surface of the tank, leaving large interior voids, while thrust/settling effects can lead to dispersed two-phase mixtures. With the exception of capacitance-based sensing, few sensing technologies are well suited for measuring annular, stratified, and dispersed fluid configurations. Two modalities of capacitance measurement are compared: Electrical Capacitance Volume Tomography (ECVT) and Electrical Capacitance Volume Sensing (ECVS). ECVT is a non-invasive imaging modality first introduced in 2006. ECVS is a measurement modality introduced in this paper that is derived from ECVT technology but does not reconstruct an image as part of the mass measurement. To optimize the design of future capacitance-based spherical tank mass gauging sensors, different electrode plate layouts are evaluated in a mass gauging context. Prototype sensors are constructed, and experiments are conducted with fluid fills in various orientations. The plate layouts and their effect on the performance of the sensor as a fuel mass gauge are analyzed through the use of imaging and averaging techniques.

eess.SY↗

arXiv2019

Diagnosing numerical Cherenkov instabilities in relativistic plasma simulations based on general meshes

Numerical Cherenkov radiation (NCR) or instability is a detrimental effect frequently found in electromagnetic particle-in-cell (EM-PIC) simulations involving relativistic plasma beams. NCR is caused by spurious coupling between electromagnetic-field modes and multiple beam resonances. This coupling may result from the slow down of poorly-resolved waves due to numerical (grid) dispersion and from aliasing mechanisms. NCR has been studied in the past for finite-difference-based EM-PIC algorithms on regular (structured) meshes with rectangular elements. In this work, we extend the analysis of NCR to finite-element-based EM-PIC algorithms implemented on unstructured meshes. The influence of different mesh element shapes and mesh layouts on NCR is studied. Analytic predictions are compared against results from finite-element-based EM-PIC simulations of relativistic plasma beams on various mesh types.

physics.comp-ph↗

arXiv2018

Relativistic Extension of a Charge-Conservative Finite Element Solver for Time-Dependent Maxwell-Vlasov Equations

In many problems involving particle accelerators and relativistic plasmas, the accurate modeling of relativistic particle motion is essential for accurate physical predictions. Here, we extend a charge-conserving finite element time-domain (FETD) particle-in-cell (PIC) algorithm for the time-dependent Maxwell-Vlasov equations on irregular (unstructured) meshes to the relativistic regime by implementing and comparing three particle pushers: (relativistic) Boris, Vay, and Higuera-Cary. We illustrate the application of the proposed relativistic FETD-PIC algorithm for the analysis of particle cyclotron motion at relativistic speeds, harmonic particle oscillation in the Lorentz-boosted frame, and relativistic Bernstein modes in magnetized charge-neutral (pair) plasmas.

physics.comp-ph↗

arXiv2016

Stable evaluation of Green's functions in cylindrically stratified regions with uniaxial anisotropic layers

We present a robust algorithm for the computation of electromagnetic fields radiated by point sources (Hertzian dipoles) in cylindrically stratified media where each layer may exhibit material properties (permittivity, permeability, and conductivity) with uniaxial anisotropy. Analytical expressions are obtained based on the spectral representation of the tensor Green's function based on cylindrical Bessel and Hankel eigenfunctions, and extended for layered uniaxial media. Due to the poor scaling of these eigenfunctions for extreme arguments and/or orders, direct numerical evaluation of such expressions can produce numerical instability, i.e., underflow, overflow, and/or round-off errors under finite precision arithmetics. To circumvent these problems, we develop a numerically stable formulation through suitable rescaling of various expressions involved in the computational chain, to yield a robust algorithm for all parameter ranges. Numerical results are presented to illustrate the robustness of the formulation including cases of practical interest to geophysical exploration.

math.NA↗

arXiv2014

Stable pseudoanalytical computation of electromagnetic fields from arbitrarily-oriented dipoles in cylindrically stratified media

Computation of electromagnetic fields due to point sources (Hertzian dipoles) in cylindrically stratified media is a classical problem for which analytical expressions of the associated tensor Green's function have been long known. However, under finite-precision arithmetic, direct numerical computations based on the application of such analytical (canonical) expressions invariably lead to underflow and overflow problems related to the poor scaling of the eigenfunctions (cylindrical Bessel and Hankel functions) for extreme arguments and/or high-order, as well as convergence problems related to the numerical integration over the spectral wavenumber and to the truncation of the infinite series over the azimuth mode number. These problems are exacerbated when a disparate range of values is to be considered for the layers' thicknesses and material properties (resistivities, permittivities, and permeabilities), the transverse and longitudinal distances between source and observation points, as well as the source frequency. To overcome these challenges in a systematic fashion, we introduce herein different sets of range-conditioned, modified cylindrical functions (in lieu of standard cylindrical eigenfunctions), each associated with non-overlapped subdomains of (numerical) evaluation to allow for stable computations under any range of physical parameters. In addition adaptively-chosen integration contours are employed in the complex spectral wavenumber plane to ensure convergent numerical integration in all cases. We illustrate the application of the algorithm to problems of geophysical interest involving layer resistivities ranging from 1000 $Ω\cdot$m to 10$^{-8} Ω\cdot$m, frequencies of operation ranging from 10 MHz down to the low magnetotelluric range of 0.01 Hz, and for various combinations of layer thicknesses.

math-ph↗

arXiv2013

Bayesian compressive sensing for ultrawideband inverse scattering in random media

We develop an ultrawideband (UWB) inverse scattering technique for reconstructing continuous random media based on Bayesian compressive sensing. In addition to providing maximum a posteriori estimates of the unknown weights, Bayesian inversion provides estimate of the confidence level of the solution, as well as a systematic approach for optimizing subsequent measurement(s) to maximize information gain. We impose sparsity priors directly on spatial harmonics to exploit the spatial correlation exhibited by continuous media, and solve for their posterior probability density functions efficiently using a fast relevance vector machine. We linearize the problem using the first-order Born approximation which enables us to combine, in a single inversion, measurements from multiple transmitters and ultrawideband frequencies. We extend the method to high-contrast media using the distorted-Born iterative method. We apply time-reversal strategies to adaptively focus the inversion effort onto subdomains of interest, and hence reduce the overall inversion cost. The proposed techniques are illustrated in a number of canonical scenarios including crosshole and borehole sensing.

physics.data-an↗

arXiv2013

Robust Computation of Dipole Electromagnetic Fields in Arbitrarily-Anisotropic, Planar-Stratified Environments

We develop a general-purpose formulation, based on two-dimensional spectral integrals, for computing electromagnetic fields produced by arbitrarily-oriented dipoles in planar-stratified environments, where each layer may exhibit arbitrary and independent anisotropy in both the (complex) permittivity and permeability. Among the salient features of our formulation are (1) computation of eigenmodes (characteristic plane waves) supported in arbitrarily anisotropic media in a numerically robust fashion, (2) implementation of an hp-adaptive refinement for the numerical integration to evaluate the radiation and weakly-evanescent spectra contributions, and (3) development of an adaptive extension of an integral convergence acceleration technique to compute the strongly-evanescent spectrum contribution. While other semianalytic techniques exist to solve this problem, none have full applicability to media exhibiting arbitrary double anisotropies in each layer, where one must account for the whole range of possible phenomena such as mode coupling at interfaces and non-reciprocal mode propagation. Brute-force numerical methods can tackle this problem but only at a much higher computational cost. The present formulation provides an efficient and robust technique for field computation in arbitrary planar-stratified environments. We demonstrate the formulation for a number of problems related to geophysical exploration.

physics.comp-ph↗

arXiv2013

Random Lattice Gauge Theories and Differential Forms

We provide a brief overview on the application of the exterior calculus of differential forms to the ab initio formulation of field theories on random simplicial lattices. In this framework, discrete analogues of the exterior derivative and the Hodge star operator are employed for the factorization of discrete field equations into a purely combinatorial (metric-free) part and a metric-dependent part. The Hodge star duality (isomorphism) is invoked to motivate the use of primal and dual lattices (a dual cell complex). The natural role of Whitney forms in the construction of discrete Hodge star operators is stressed.

math-ph↗

arXiv2013

Metamaterial Loadings for Waveguide Miniaturization

We show that a rectangular metallic waveguide loaded with metamaterial elements consisting of electric-field coupled (ELC) resonators placed at the side walls can operate well below the cutoff frequency of the respective unloaded waveguide. The dispersion diagrams indicate that propagating modes in ELC-loaded waveguides are of forward-type for both TE and TM modes. We also study the dispersion diagram and transmission characteristics of rectangular metallic waveguides simultaneously loaded with ELCs and split ring resonators (SRRs). Such doubly-loaded waveguides can support both forward wave and backward waves, and provide independent control of the propagation characteristics for the respective modes.

physics.class-ph↗

arXiv2005

Geometric Finite Element Discretization of Maxwell Equations in Primal and Dual Spaces

Based on a geometric discretization scheme for Maxwell equations, we unveil a mathematical\textit{\}transformation between the electric field intensity $E$ and the magnetic field intensity $H$, denoted as Galerkin duality. Using Galerkin duality and discrete Hodge operators, we construct two system matrices, $[ X_{E}] $ (primal formulation) and $[ X_{H} % ] $ (dual formulation) respectively, that discretize the second-order vector wave equations. We show that the primal formulation recovers the conventional (edge-element) finite element method (FEM) and suggests a geometric foundation for it. On the other hand, the dual formulation suggests a new (dual) type of FEM. Although both formulations give identical dynamical physical solutions, the dimensions of the null spaces are different.

physics.comp-ph↗

arXiv2005

On the degrees of freedom of lattice electrodynamics

Using Euler's formula for a network of polygons for 2D case (or polyhedra for 3D case), we show that the number of dynamic\textit{\}degrees of freedom of the electric field equals the number of dynamic degrees of freedom of the magnetic field for electrodynamics formulated on a lattice. Instrumental to this identity is the use (at least implicitly) of a dual lattice and of a (spatial) geometric discretization scheme based on discrete differential forms. As a by-product, this analysis also unveils a physical interpretation for Euler's formula and a geometric interpretation for the Hodge decomposition.

hep-lat↗