arXiv subjects

D. Gómez

Publications and source records attributed to D. Gómez.

5 recordsLinked to original sources

arXiv2026

Numerical approximation of a transient thermo-electromagnetic problem in axisymmetric geometries

This paper analyzes a transient thermo-electromagnetic problem arising in the modeling of induction heating processes. Unlike previous studies that focused on steady-state scenarios, we consider a time-dependent thermal problem coupled with a nonlinear time-harmonic electromagnetic problem through temperature-dependent electrical conductivity and Joule effect. Exploiting cylindrical symmetry and assuming a purely azimuthal current density, we formulate the problem on a two-dimensional meridional section. We introduce a variational formulation in appropriately weighted Sobolev spaces and prove existence of a solution by a fixed-point argument. Under reasonable assumptions on the physical parameters, we also prove uniqueness. A finite element discretization combined with implicit time stepping is used to compute the numerical solution. To evaluate the accuracy of the approximation, a priori error estimates are derived and validated by numerical experiments. Finally, numerical simulations illustrate the effectiveness of the proposed approach in an industrially relevant configuration.

math.NA↗

arXiv2025

Relax-and-round strategies for solving the Unit Commitment problem with AC Power Flow constraints

The Unit Commitment problem with AC power flow constraints (UC-ACOPF) is a non-convex mixed-integer nonlinear programming (MINLP) problem encountered in power systems. Its combination of combinatorial complexity and non-convex nonlinear constraints makes it particularly challenging. A common approach to tackle this issue is to relax the integrality condition, but this often results in infeasible solutions. Consequently, rounding heuristics are frequently employed to restore integer feasibility. This paper addresses recent advancements in heuristics aimed at quickly obtaining feasible solutions for the UC-ACOPF problem, focusing specifically on direct relax-and-round strategies. We propose a model-based heuristic that rescales the solution of the integer-relaxed problem before rounding. Furthermore, we introduce rounding formulas designed to enforce combinatorial constraints and aim to maintain AC feasibility in the resulting solutions. These methodologies are compared against standard direct rounding techniques in the literature, applied to a 6-bus and a 118-bus test systems. Additionally, we integrate the proposed heuristics into an implementation of the Feasibility Pump (FP) method, demonstrating their utility and potential to enhance existing rounding strategies.

math.OC↗

arXiv2024

Numerical simulation of resistance furnaces by using distributed and lumped models

This work proposes a methodology combining distributed and lumped models to simulate the current distribution in an indirect heat resistance furnace and, in particular, to compute the current to be supplied in order to obtain a desired power. The distributed model is a time-harmonic eddy current problem which has been numerically solved by using a finite element method. The lumped model is based on the computation of a reduced impedance associated to an equivalent circuit model. The effectiveness of the method has been assessed by numerical simulations and plant measurements. The good correlation between the results reveals this approximation is well-suited in order to aid the design and improve the efficiency of the furnace in a short-time.

math.AP↗

arXiv2019

Mathematical analysis and numerical solution of models with dynamic Preisach hysteresis

Hysteresis is a phenomenon that is observed in a great variety of physical systems, which leads to a nonlinear and multivalued behavior, making their modeling and control difficult. Even though the analysis and mathematical properties of classical or rate-independent hysteresis models are known, this is not the case for dynamic models where current approaches lack a proper functional analytic framework which is essential to formulate optimization problems and develop stable numerics, both being crucial in practice. This paper deals with the description and mathematical analysis of the dynamic Preisach hysteresis model. Toward that end, we complete a widely accepted definition of the dynamic model commonly used to describe the constitutive relation between the magnetic field H and the magnetic induction B, in which, the values of B not only depends on the present values of H but also on the past history and its velocity. We first analyze mathematically some important properties of the model and compare them with known results for the static Preisach model. Then, we consider a parabolic problem with dynamic hysteresis motivated by electromagnetic field equations. Under suitable assumptions, we show the well posedness of a weak formulation of the problem and solve it numerically. Finally, we report a numerical test in order to assess the order of convergence and to illustrate the behavior of the numerical solution for different configurations of the dynamic Preisach model

math.AP↗

arXiv2014

Effects of electron inertia in collisionless magnetic reconnection

We present a study of collisionless magnetic reconnection within the framework of full two-fluid MHD for a completely ionized hydrogen plasma, retaining the effects of the Hall current, electron pressure and electron inertia. We performed 2.5D simulations using a pseudo-spectral code with no dissipative effects. We check that the ideal invariants of the problem are conserved down to round-off errors. Our results show that the change in the topology of the magnetic field lines is exclusively due to the presence of electron inertia. The computed reconnection rates remain a fair fraction of the Alfvén velocity, which therefore qualifies as fast reconnection.

physics.plasm-ph↗