arXiv subjects

Idoia Cortes Garcia

Publications and source records attributed to Idoia Cortes Garcia.

At least 19 recordsLinked to original sources

arXiv2026

A mixed Petrov-Galerkin Cosserat rod finite element formulation

This paper presents a total Lagrangian mixed Petrov-Galerkin finite element formulation that provides a computationally efficient approach for analyzing Cosserat rods that is free of singularities and locking. To achieve a singularity-free orientation parametrization of the rod, the nodal kinematical unknowns are defined as the nodal centerline positions and unit quaternions. We apply Lagrange interpolation to all nodal kinematic coordinates, and in combination with a projection of non-unit quaternions, this leads to an interpolation with orthonormal cross-section-fixed bases. To eliminate locking effects such as shear locking, the variational Hellinger-Reissner principle is applied, resulting in a mixed approach with additional fields composed of resultant contact forces and moments. Since the mixed formulation contains the constitutive law in compliance form, it naturally incorporates constrained theories, such as the Kirchhoff-Love theory. This study specifically examines the influence of the additional internal force fields on the numerical performance, including locking mitigation and robustness. Using well-established benchmark examples, the method demonstrates enhanced computational robustness and efficiency, as evidenced by the reduction in required load steps and iterations when applying the standard Newton-Raphson method.

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arXiv2026

A non-intrusive approach to index-aware learning

We present a non-intrusive version of the index-aware learning framework introduced in arXiv:2309.00958. Index-aware learning itself is an approach for learning the time and parameter dependent solutions of differential-algebraic equations (DAEs), in particular those describing electric circuits. A central feature of the approach is that it ensures the learned solutions to fulfill the inherent constraints of the DAE, such as e.g. Kirchhoff's laws in the case of electric circuits. This is achieved by leveraging a decoupling of the DAE into its differential and algebraic parts, with the non-intrusive version of the approach additionally relying on results from arXiv:2604.20475 and arXiv:2107.07755. We illustrate the approach using a filtered buck converter as an example and compare both the intrusive and non-intrusive versions. The code for the example is openly available.

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arXiv2026

A Comparison of Multirate Co-Simulation Techniques for Field-Circuit Coupled Problems

This paper compares three different multirate splitting approaches for the application on field-circuit coupled magnetoquasistatic simulations. For these methods, again three different variants for exchanging values between the field and circuit are tested, namely voltages, currents and flux correction terms. All scenarios are applied on two different benchmark problems, i.e. a coil inductor and transformer model coupled to different circuits. The convergence behavior of different time steppers (Implicit Euler and Trapezoidal Rule) is determined for all possible settings, and guidelines for practical applications are derived.

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arXiv2026

Data-driven moving-window Bayesian inference for transient CO2-temperature network models of buildings

In this work, we proposes a CO2-temperature network model that links multi-zone mass transport and thermal dynamics through shared latent drivers, airflow and occupancy. The thermal component is formulated as a resistance-capacitance (RC) network augmented with airflow-driven convective exchange, while the CO2 component is governed by inter-zonal convective transport. To calibrate the model and track time-varying operating conditions based on sparse sensing, we introduce a moving-window Bayesian inference procedure that jointly estimates thermal parameters, airflow and occupancy trajectories. The estimation also provides room-specific sensor noise levels, yielding posterior predictive forecasts with credible intervals. The framework is assessed using a controlled synthetic benchmark, and a scaled physical validation experiment using CO2 and temperature sensing. In both settings, the posterior accurately reconstructs trajectories within windows and delivers low forecast errors. When inference windows overlap abrupt regime transitions, the widened uncertainty bands and increased inferred noise levels provide an interpretable diagnostic of model-data mismatch, followed by rapid recovery once the new regime is observed. Overall, coupling CO2-informed airflow with thermal dynamics yields a robust approach for conductive and advective temperature prediction, supporting practical monitoring and energy-performance assessment under limited sensing.

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arXiv2026

Waveform Relaxation for Field/Circuit Coupled DAEs with Generalized Capacitances

Field/circuit coupling is a common approach when a lumped representation of a certain electrotechnical device is not accurate enough. To exploit existing code and underlying properties of the coupled systems, cosimulation techniques such as waveform relaxation can be used. The coupled system is of differential-algebraic type, which can potentially lead to divergence. This paper presents a novel, sufficient topological convergence criterion for field/circuit coupled systems of higher index containing a generalized capacitance. Hereby, the criterion holds for a full range of field systems whose structure can be classified as a generalized capacitance. Finally, the theoretical results are supported by numerical simulations.

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arXiv2026

A topological decoupling of modified nodal analysis including controlled sources

We derive a topological decoupling of the equations of modified nodal analysis (MNA) to a semi-explicit index one differential-algebraic equation. The decoupling explicitly allows for controlled sources, which play a crucial role in engineering design workflows. Furthermore, the proof is constructive and provides a graph-based algorithmic framework for the computation of the decoupling, enabling its application to a variety of industry problems. These include the generation of consistent initial conditions, model order reduction, (scientific) machine learning, as well as speeding up conventional circuit simulation. In addition, the decoupling preserves the structure of MNA, i.e. the resulting systems remain sparse and key parts remain positive definite. We illustrate the decoupling using multiple examples, including some of the most common subcircuits containing controlled sources. Lastly, we also provide a first software implementation of the decoupling.

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arXiv2026

Energy-based modeling for field-circuit coupling

This paper presents a generalized energy-based modeling framework extending recent formulations tailored for differential-algebraic equations. The proposed structure, inspired by the port-Hamiltonian formalism, ensures passivity, preserves the power balance, and facilitates the consistent interconnection of subsystems. A particular focus is put on low-frequency power applications in electrical engineering. Stranded, solid, and foil conductor models are investigated in the context of the eddy current problem. Each conductor model is shown to fit into the generalized energy-based structure, which allows their structure-preserving coupling with electrical circuits described by modified nodal analysis. Theoretical developments are validated through a numerical simulation of an oscillator circuit, demonstrating energy conservation in lossless scenarios and controlled dissipation when eddy currents are present. The applicability of the methodology towards engineering applications is studied through a numerical simulation of a nonlinear three-phase transformer.

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arXiv2025

Learning solutions of parameterized stiff ODEs using Gaussian processes

Stiff ordinary differential equations (ODEs) play an important role in many scientific and engineering applications. Often, the dependence of the solution of the ODE on additional parameters is of interest, e.g.\ when dealing with uncertainty quantification or design optimization. Directly studying this dependence can quickly become too computationally expensive, such that cheaper surrogate models approximating the solution are of interest. One popular class of surrogate models are Gaussian processes (GPs). They perform well when approximating stationary functions, functions which have a similar level of variation along any given parameter direction, however solutions to stiff ODEs are often characterized by a mixture of regions of rapid and slow variation along the time axis and when dealing with such nonstationary functions, GP performance frequently degrades drastically. We therefore aim to reparameterize stiff ODE solutions based on the available data, to make them appear more stationary and hence recover good GP performance. This approach comes with minimal computational overhead and requires no internal changes to the GP implementation, as it can be seen as a separate preprocessing step. We illustrate the achieved benefits using multiple examples.

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arXiv2025

Combined Parameter and Shape Optimization of Electric Machines with Isogeometric Analysis

In structural optimization, both parameters and shape are relevant for the model performance. Yet, conventional optimization techniques usually consider either parameters or the shape separately. This work addresses this problem by proposing a simple yet powerful approach to combine parameter and shape optimization in a framework using Isogeometric Analysis (IGA). The optimization employs sensitivity analysis by determining the gradients of an objective function with respect to parameters and control points that represent the geometry. The gradients with respect to the control points are calculated in an analytical way using the adjoint method, which enables straightforward shape optimization by altering of these control points. Given that a change in a single geometry parameter corresponds to modifications in multiple control points, the chain rule is employed to obtain the gradient with respect to the parameters in an efficient semi-analytical way. The presented method is exemplarily applied to nonlinear 2D magnetostatic simulations featuring a permanent magnet synchronous motor and compared to designs, which were optimized using parameter and shape optimization separately. It is numerically shown that the permanent magnet mass can be reduced and the torque ripple can be eliminated almost completely by simultaneously adjusting rotor parameters and shape. The approach allows for novel designs to be created with the potential to reduce the optimization time substantially.

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arXiv2024

A magnetic oriented approach to the systematic coupling of field and circuit equations

A novel strategy is proposed for the coupling of field and circuit equations when modeling power devices in the low-frequency regime. The resulting systems of differential-algebraic equations have a particular geometric structure which explicitly encodes the energy storage, dissipation, and transfer mechanisms. This implies a power balance on the continuous level which can be preserved under appropriate discretization in space and time. The models and main results are presented in detail for linear constitutive models, but the extension to nonlinear elements and more general coupling mechanisms is possible. The theoretical findings are demonstrated by numerical results.

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arXiv2024

Parallel-in-Time Integration of Transient Phenomena in No-Insulation Superconducting Coils Using Parareal

High-temperature superconductors (HTS) have the potential to enable magnetic fields beyond the current limits of low-temperature superconductors in applications like accelerator magnets. However, the design of HTS-based magnets requires computationally demanding transient multi-physics simulations with highly non-linear material properties. To reduce the solution time, we propose using Parareal (PR) for parallel-in-time magneto-thermal simulation of magnets based on HTS, particularly, no-insulation coils without turn-to-turn insulation. We propose extending the classical PR method to automatically find a time partitioning using a first coarse adaptive propagator. The proposed PR method is shown to reduce the computing time when fine engineering tolerances are required despite the highly nonlinear character of the problem. The full software stack used is open-source.

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arXiv2024

Index-aware learning of circuits

Electrical circuits are present in a variety of technologies, making their design an important part of computer aided engineering. The growing number of parameters that affect the final design leads to a need for new approaches to quantify their impact. Machine learning may play a key role in this regard, however current approaches often make suboptimal use of existing knowledge about the system at hand. In terms of circuits, their description via modified nodal analysis is well-understood. This particular formulation leads to systems of differential-algebraic equations (DAEs) which bring with them a number of peculiarities, e.g. hidden constraints that the solution needs to fulfill. We use the recently introduced dissection index that can decouple a given system of DAEs into ordinary differential equations, only depending on differential variables, and purely algebraic equations, that describe the relations between differential and algebraic variables. The idea is to then only learn the differential variables and reconstruct the algebraic ones using the relations from the decoupling. This approach guarantees that the algebraic constraints are fulfilled up to the accuracy of the nonlinear system solver, and it may also reduce the learning effort as only the differential variables need to be learned.

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arXiv2024

Spline-Based Rotor and Stator Optimization of a Permanent Magnet Synchronous Motor

This work features the optimization of a Permanent Magnet Synchronous Motor using 2D nonlinear simulations in an Isogeometric Analysis framework. The rotor and stator designs are optimized for both geometric parameters and surface shapes via modifications of control points. The scaling laws for magnetism are employed to allow for axial and radial scaling, enabling a thorough optimization of all critical machine parameters for multiple operating points. The process is carried out in a gradient-based fashion with the objectives of lowering motor material cost, torque ripple and losses. It is shown that the optimization can be efficiently conducted for many optimization variables and all objective values can be reduced.

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arXiv2023

A Stabilized Circuit-Consistent Foil Conductor Model

The magnetoquasistatic simulation of large power converters, in particular transformers, requires efficient models for their foils windings by means of homogenization techniques. In this article, the classical foil conductor model is derived and an inconsistency in terms of circuit theory is observed, which may lead to time-stepping instability. This can be related to the differential-algebraic nature of the resulting system of equations. It is shown how the foil conductor model can be adapted to mitigate this problem by a modified definition of the turn-by-turn conductance matrix. Numerical results are presented to demonstrate the instability and to verify the effectiveness of the new adapted foil conductor model.

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arXiv2023

How to Build the Optimal Magnet Assembly for Magnetocaloric Cooling: Structural Optimization with Isogeometric Analysis

In the search for more efficient and less environmentally harmful cooling technologies, the field of magnetocalorics is considered a promising alternative. To generate cooling spans, rotating permanent magnet assemblies are used to cyclically magnetize and demagnetize magnetocaloric materials, which change their temperature under the application of a magnetic field. In this work, an axial rotary permanent magnet assembly, aimed for commercialization, is computationally designed using topology and shape optimization. This is efficiently facilitated in an isogeometric analysis framework, where harmonic mortaring is applied to couple the rotating rotor-stator system of the multipatch model. Inner, outer and co-rotating assemblies are compared and optimized designs for different magnet masses are determined. These simulations are used to homogenize the magnetic flux density in the magnetocaloric material. The resulting torque is analyzed for different geometric parameters. Additionally, the influence of anisotropy in the active magnetic regenerators is studied in order to guide the magnetic flux. Different examples are analyzed and classified to find an optimal magnet assembly for magnetocaloric cooling.

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arXiv2021

MONA -- A magnetic oriented nodal analysis for electric circuits

The modified nodal analysis (MNA) is probably the most widely used formulation for the modeling and simulation of electric circuits. Its conventional form uses electric node potentials and currents across inductors and voltage sources as unknowns, thus taking an electric viewpoint. In this paper, we propose a magnetic oriented nodal analysis (MONA) for electric circuits, which is based on magnetic node potentials and charges across capacitors and voltage sources as the primary degrees of freedom, thus giving direct access to these quantities. The resulting system has the structure of a generalized gradient system which immediately ensures passivity in the absence of sources. A complete index analysis is presented showing regularity of the magnetic oriented formulation under standard topological conditions on the network interconnection. In comparison to conventional MNA, the differential-algebraic index is reduced by one in most cases which facilitates the numerical solution. Some preliminary numerical experiments are presented for illustration of the feasibility and stability of the new approach.

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arXiv2021

Parareal for Higher Index Differential Algebraic Equations

This article proposes modifications of the Parareal algorithm for its application to higher index differential algebraic equations (DAEs). It is based on the idea of applying the algorithm to only the differential components of the equation and the computation of corresponding consistent initial conditions later on. For differential algebraic equations with a special structure as e.g. given in flux-charge modified nodal analysis, it is shown that the usage of the implicit Euler method as a time integrator suffices for the Parareal algorithm to converge. Both versions of the Parareal method are applied to numerical examples of nonlinear index 2 differential algebraic equations.

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arXiv2021

Parallel-in-Time Solution of Eddy Current Problems Using Implicit and Explicit Time-stepping Methods

The time domain analysis of eddy current problems often requires the simulation of long time intervals, e.g. until a steady state is reached. Fast-switching excitations e.g. in pulsedwidth modulated signals require in addition very small time step sizes that significantly increase computation time. To speed up the simulation, parallel-in-time methods can be used. In this paper, we investigate the combination of explicit and implicit time integration methods in the context of the parallel-in-time method Parareal and using a simplified model for the coarse propagator.

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