arXiv subjects

Jaime Mora-Paz

Publications and source records attributed to Jaime Mora-Paz.

4 recordsLinked to original sources

arXiv2026

Bent optical waveguide finite element analysis with a 3D envelope Maxwell model

With the goal of accurately extracting the optical field losses in a three-dimensional (3D), circularly coiled waveguide (e.g., bent optical fiber), this effort presents the numerical methodologies that are implemented for an envelope Maxwell model that propagates electromagnetic fields as an entirely boundary value problem. Our unique modeling approach includes an ultraweak variational formulation of the envelope Maxwell model in the curved geometry of the bending, which is discretized by the discontinuous Petrov-Galerkin (DPG) method, which permits residual-driven mesh and polynomial-order adaptivity. This also, then, requires a unique approach for constructing perfectly matched layers (PMLs) as absorbing boundary conditions in both the direction of optical field propagation and in the tangential directions, where unguided energy escapes the waveguide. Our coiled waveguide modeling technology extracts the mode confinement losses from the propagation of the coherent optical field through the bent waveguide. We verify our simulations against the semi-analytical results from the analogous bent slab waveguide problem, and we successfully demonstrate stable convergence to loss values for the 3D coiled optical fiber problem, which has never been done previously for our specific modeling approach.

physics.optics↗

arXiv2025

Bessel Functions and Analysis of Circular Waveguides

The paper is devoted to the study of circularly coiled optical slab waveguides, which is also applicable to acoustical waveguides. We use a change of variables and the classical Frobenius method to compute Bessel functions of complex order and complex argument, and combine it with a perfectly matched layer technique to solve the relevant Bessel eigenvalue problem and deliver accurate loss factors for eigensolutions to the three-layer optical slab waveguide problem. The solutions provide a benchmark for verifying model implementations of this problem and allow for a numerical verification of the Glazman criterion that provides a foundation for the well-posedness and stability analysis of homogeneous circular waveguides with impedance boundary conditions.

physics.comp-ph↗

arXiv2024

Formulation and analysis of a DPG discretization for a simplified electrochemical model

We present a simplified model consisting on two linear elliptic boundary-value problems that represent a single step and single fixed-point iteration in an electrochemical battery model. The main variables are the concentration and the electric potential, whose equation is assigned a Robin BC with a very important physical interpretation. The solvability of both equations is studied in different funcional settings, to finally prove the well-posedness of a broken mixed variational formulation. The latter formulation opens the opportunity of performing discretization and numerical solution via the Discontinuous Petrov-Galerkin (DPG) method, which guarantees discrete stability thanks to optimal test functions. With only the usual assumptions on the data and the discretization, we show that the method herein proposed is convergent. This analytical effort complements other recent works on batttery multiphysics, that have been more modeling and computing oriented, and establishes the DPG approach as a valuable tool to contribute toward an efficient analysis and design of batteries.

math.NA↗

arXiv2024

High-order transient multidimensional simulation of a thermo-electro-chemo-mechanical model for Lithium-ion batteries

We build a transient multidimensional multiphysical model based on continuum theories, involving the coupled mechanical, thermal and electrochemical phenomena occurring simultaneously in the discharge or charge of lithium-ion batteries. The process delivers a system of coupled nonlinear partial differential equations. Besides initial and boundary conditions, we highlight the treatment of the electrode-electrolyte interface condition, which corresponds to a Butler-Volmer reaction kinetics equation. We present the derivation of the strong and weak forms of the model, as well as the discretization procedure in space and in time. The discretized model is computationally solved in two dimensions by means of a finite element method that employs $hp$ layered meshes, along with staggered second order semi-implicit time integration. The expected error estimate is of higher order than any other similar work, both in space and in time. A representative battery cell geometry, under distinct operating scenarios, is simulated. The numerical results show that the full model allows for important additional insights to be drawn than when caring only for the electrochemical coupling. Considering the multiphysics becomes more important as the applied current is increased, whether for discharge or for charge. Our full model provides battery design professionals with a valuable tool to optimize designs and advance the energy storage industry.

math.NA↗