Sebastian Schöps

Technische Universität Darmstadt | TU · Department of Electrical Engineering and Information Technology (Dept.18)

This paper addresses different aspects of "coupled" model descriptions in computational electromagnetics. This includes domain decomposition, multiscale problems, multiple or hybrid discrete field formulation and multi-physics problems. Theoretical issues of accuracy, stability and numerical efficiency of the resulting formulations are addressed al...

Superconducting electromagnets commonly exhibit thin layers with high aspect ratio such as insulation layers or turn-to-turn contacts. A finite element analysis of these devices can lead to unfavorable meshes in these thin layers, either because of a high number of degrees of freedom or mesh elements of poor quality which decrease the accuracy of t...

When simulating resistive-capacitive circuits or electroquasistatic problems where conductors and insulators coexist, one observes that large time steps or low frequencies lead to numerical instabilities, which are related to the condition number of the system matrix. Here, we propose several stable formulations by scaling the equation systems. Thi...

In electrical engineering, for example during the design of superconducting radio-frequency cavities, eigenmodes must be identified based on their field patterns. This allows to understand the working principle, optimize the performance of a device and distinguish desired from parasitic modes. For cavities with simple shapes, the eigenmodes are eas...

When simulating no-insulation high-temperature superconducting pancake coils with the finite element (FE) method, the high aspect ratio of the thin turn-to-turn contact layer (T2TCL) leads to unfavorable meshes in these thin layers as manifested by a high number of degrees of freedom (DoF) or mesh elements of poor quality which decrease the accurac...

The eigenmodes of resonating structures, e.g., electromagnetic cavities, are sensitive to deformations of their shape. In order to compute the sensitivities of the eigenpair with respect to a scalar parameter, we state the Laplacian and Maxwellian eigenvalue problems and discretize the models using isogeometric analysis. Since we require the deriva...

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...

The use of trigonometric polynomials as Lagrange multipliers in the harmonic mortar method enables an efficient and elegant treatment of relative motion in the stator-rotor coupling of electric machine simulation. Explicit formulas for the torque computation are derived by energetic considerations, and their realization by harmonic mortar finite el...

An efficient strategy for yield optimization with uncertain and deterministic optimization variables is presented. The gradient based adaptive Newton-Monte Carlo method is modified, such that it can handle variables with (uncertain parameters) and without (deterministic parameters) analytical gradient information. This mixed strategy is numerically...

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 equat...

Conventional magneto-static finite element (FE) analysis of electrical machine design is time-consuming and computationally expensive. Since each machine topology has a distinct set of parameters, design optimization is commonly performed independently. This article presents a novel method for predicting key performance indicators (KPIs) of differe...

Electromagneto-quasistatic (EMQS) field models exhibit capacitive, resistive, and inductive effects, in the absence of wave propagation, while the associated initial boundary value problems are ill-posed. A framework that is based on penalizing a Coulomb-type differential constraint that recovers well-posedness is proposed here. The advocated strat...

In this work, isogeometric mortaring is used for the simulation of a six-pole permanent magnet synchronous machine. Isogeometric mortaring is especially well suited for the efficient computation of rotating electric machines, as it allows for an exact geometry representation for arbitrary rotation angles without the need for remeshing. The appropri...

We describe a modelling approach for the simulation of droplet dynamics in strong electric fields. The model accounts for electroquasistatic fields, convective and conductive currents, contact angle dynamics and charging effects associated with droplet breakup processes. Two classes of applications are considered. The first refers to the problem of...

This contribution investigates the connection between Isogeometric Analysis (IgA) and the Partial Element Equivalent Circuit (PEEC) method for electrostatic problems. We demonstrate that using the spline-based geometry concepts from IgA allows for extracting circuit elements without a meshing step. Moreover, the proposed IgA-PEEC method converges f...

Electromagnetic quasistatic field models, which take into consideration resistive, inductive, and capacitive effects, have been introduced for electrical engineering applications whose geometrical characteristics, combined with the operational frequencies, suggest negligible radiation phenomena. Here, a monolithic variant of a previously proposed t...

When applying isogeometric analysis to engineering problems, one often deals with multi-patch spline spaces that have incompatible discretisations, e.g. in the case of moving objects. In such cases mortaring has been shown to be advantageous. This contribution discusses the appropriate B-spline spaces needed for the solution of Maxwell’s equations...

Electromagnetic quasistatic (EMQS) fields, where radiation effects are neglected, while Ohmic losses and electric and magnetic field energies are considered, can be modeled using Darwin-type field models as an approximation to the full Maxwell equations. Commonly formulated in terms of magnetic vector and electric scalar potentials, these EMQS form...

This work deals with the design optimization of electrical machines under the consideration of manufacturing uncertainties. In order to efficiently quantify the uncertainty, blackbox machine learning methods are employed. A multi-objective optimization problem is formulated, maximizing simultaneously the reliability, i.e., the yield, and further pe...

In this work we propose two Hermite-type optimization methods, Hermite least squares and Hermite BOBYQA, specialized for the case that some partial derivatives of the objective function are available and others are not. The main objective is to reduce the number of objective function calls by maintaining the convergence properties. Both methods are...

Compact dc high-voltage photoelectron guns are able to meet the sophisticated demands of high-current applications such as energy recovery linacs. A main design parameter for such sources is the electric field strength, which depends on the electrode geometry and is limited by the field emission threshold of the electrode material. In order to mini...

In electrical engineering, for example during the design of superconducting radio-frequency cavities, eigenmodes must be identified based on their field patterns. This allows to understand the working principle, optimize the performance of a device and distinguish desired from parasitic modes. For cavities with simple shapes, the eigenmodes are eas...

In this work isogeometric mortaring is used for the simulation of a six pole permanent magnet synchronous machine. Isogeometric mortaring is especially well suited for the efficient computation of rotating electric machines as it allows for an exact geometry representation for arbitrary rotation angles without the need of remeshing. The appropriate...

In the design phase of an electrical machine, finite element (FE) simulation are commonly used to numerically optimize the performance. The output of the magneto-static FE simulation characterizes the electromagnetic behavior of the electrical machine. It usually includes intermediate measures such as nonlinear iron losses, electromagnetic torque,...

Conventional magneto-static finite element analysis of electrical machine models is time-consuming and computationally expensive. Since each machine topology has a distinct set of parameters, design optimization is commonly performed independently. This paper presents a novel method for predicting Key Performance Indicators (KPIs) of differently pa...

In the design phase of an electrical machine, finite element (FE) simulations are commonly used to numerically optimize the performance. The output of the FE simulation is used to characterize the electromagnetic behavior of the machine. The simulation workflow involves intermediate measures such as nonlinear iron losses, electromagnetic torque, an...

This work deals with the design optimization of electrical machines under the consideration of manufacturing uncertainties. In order to efficiently quantify the uncertainty, a hybrid Gauss-Process regression (GPR) model is employed. In contrast to classic Kriging or Bayesian optimization approaches, we train a GPR surrogate for the performance feat...

This contribution investigates the connection between Isogeometric Analysis (IgA) and the Partial Element Equivalent Circuit (PEEC) method for electrostatic problems. We demonstrate that using the spline-based geometry concepts from IgA allows for extracting circuit elements without an explicit meshing step. Moreover, the proposed IgA-PEEC method c...

Quantification and minimization of uncertainty is an important task in the design of electromagnetic devices, which comes with high computational effort. We propose a hybrid approach combining the reliability and accuracy of a Monte Carlo analysis with the efficiency of a surrogate model based on Gaussian Process Regression. We present two optimiza...

The use of trigonometric polynomials as Lagrange multipliers in the harmonic mortar method enables an efficient and elegant treatment of relative motion in the stator-rotor coupling of electric machine simulation. Explicit formulas for the torque computation are derived by energetic considerations, and their realization by harmonic mortar finite el...

Purpose A transient magneto-quasistatic vector potential formulation involving nonlinear material is spatially discretized using the finite element method of first and second polynomial order. By applying a generalized Schur complement the resulting system of differential algebraic equations is reformulated into a system of ordinary differential eq...

When applying isogeometric analysis to engineering problems, one often deals with multi-patch spline spaces that have incompatible discretisations, e.g. in the case of moving objects. In such cases mortaring has been shown to be advantageous. This contribution discusses the appropriate B-spline spaces needed for the solution of Maxwell's equations...

We solve Maxwell's eigenvalue problem via isogeometric boundary elements and a contour integral method. We discuss the analytic properties of the discretization, outline the implementation, and showcase numerical examples.

Accelerators magnets must have minimal magnetic field imperfections to reduce particle-beam instabilities. In the case of coils made of high-temperature superconducting (HTS) tapes, the magnetization due to persistent currents adds an undesired field contribution, potentially degrading the magnetic field quality. In this paper we study the use of s...

In this article, we present and analyze the numerical stability of two coupled finite element formulations. The first one is the $h$ - $a$ -formulation and is well suited for modeling systems with superconductors and ferromagnetic materials. The second one, the so-called $t$ - $a$ -formulation with thin-shell approximation, applies for system...

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 equat...

This paper presents a novel parallel-in-time algorithm able to compute time-periodic solutions of problems where the period is not given. Exploiting the idea of the multiple shooting method, the proposed approach calculates the initial values at each subinterval as well as the corresponding period iteratively. As in the Parareal method, paralleliza...

In this paper a general approach to reconstruct three dimensional field solutions in particle accelerator magnets from distributed magnetic measurements is presented. To exploit the locality of the measurement operation a special discretization of the Laplace equation is used. Extracting the coefficients of the field representations yields an inver...

In this work, we present and analyze the numerical stability of two coupled finite element formulations. The first one is the h-a-formulation and is well suited for modeling systems with superconductors and ferromagnetic materials. The second one, the so-called t-a-formulation with thin-shell approximation, applies for systems with thin superconduc...

In this paper a general approach to reconstruct three dimensional field solutions in particle accelerator magnets from distributed magnetic measurements is presented. To exploit the locality of the measurement operation a special discretization of the Laplace equation is used. Extracting the coefficients of the field representations yields an inver...

In this work an efficient strategy for yield optimization with uncertain and deterministic optimization variables is presented. The gradient based adaptive Newton-Monte Carlo method is modified, such that it can handle variables with (uncertain parameters) and without (deterministic parameters) analytical gradient information. This mixed strategy i...

Accelerators magnets must have minimal magnetic field imperfections for reducing particle-beam instabilities. In the case of coils made of high-temperature superconducting (HTS) tapes, the field imperfections from persistent currents need to be carefully evaluated. In this paper we study the use of superconducting screens based on HTS tapes for red...

This work deals with shape optimization of electric machines using isogeometric analysis. Isogeometric analysis is particularly well suited for shape optimization as it allows to easily modify the geometry without remeshing the domain. A 6-pole interior permanent magnet synchronous machine (IPMSM) is modeled using a multipatch isogeometric approach...

The design of an electrical machine can be quantified and evaluated by Key Performance Indicators (KPIs) such as maximum torque, critical field strength, costs of active parts, sound power, etc. Generally, cross-domain tool-chains are used to optimize all the KPIs from different domains (multi-objective optimization) by varying the given input para...

Motivated by the task to design quench protection systems for superconducting magnets in particle accelerators we address a coupled field/circuit simulation based on a magneto-quasistatic field modeling. We investigate how a waveform relaxation of Gauß-Seidel type performs for a coupled simulation when circuit solving packages are used that describ...

This paper presents a numerical algorithm for the simulation of pulse-width modulated power converters via parallelization in time domain. The method applies the multirate partial differential equation approach on the coarse grid of the (two-grid) parallel-in-time algorithm Parareal. Performance of the proposed approach is illustrated via its appli...

Harmonic stator-rotor coupling offers a promising approach for the interconnection of rotating subsystems in the simulation of electric machines. This paper studies the stability of discretization schemes based on harmonic coupling in the framework of mortar methods for Poisson-like problems. A general criterion is derived that allows to ensure the...

Superconducting magnets are used to generate high magnetic fields and are employed in several applications, such as in particle accelerators to control the beam of particles that is travelling through them. The superconducting material can, under certain circumstances, quench, that is, lose its superconductivity and as a consequence get potentially...

Digital twins are used in industry to understand the life cycle of engineering products. Particularly during product design, simulations are important, e.g., to optimize the geometry or to investigate possible sources of uncertainties. The mathematical model behind the twin is typically a set of partial differential equations.

The design of an electrical machine can be quantified and evaluated by Key Performance Indicators (KPIs) such as maximum torque, critical field strength, costs of active parts, sound power, etc. Generally, cross-domain tool-chains are used to optimize all the KPIs from different domains (multi-objective optimization) by varying the given input para...

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 metho...

Compact DC high-voltage photo-electron guns are able to meet the challenging demands of high-current applications such as energy-recovery linacs. A main design parameter for such sources is the electric field strength, which depends on the electrode geometry and is limited by the field-emission threshold of the electrode material. In order to minim...

Screening currents are field-induced dynamic phenomena which occur in superconducting materials, leading to persistent magnetization. Such currents are of importance in ReBCO tapes, where the large size of the superconducting filaments gives rise to strong magnetization phenomena. In consequence, superconducting accelerator magnets based on ReBCO t...

We apply the multigrid-reduction-in-time (MGRIT) algorithm to an eddy current simulation of a two-dimensional induction machine supplied by a pulse-width-modulation signal. To resolve the fast-switching excitations, small time steps are needed, such that parallelization in time becomes highly relevant for reducing the simulation time. The MGRIT alg...

A transient magneto-quasistatic vector potential formulation involving nonlinear material is spatially discretized using the finite element method of first and second polynomial order. By applying a generalized Schur complement the resulting system of differential algebraic equations is reformulated into a system of ordinary differential equations...

Quantification and minimization of uncertainty is an important task in the design of electromagnetic devices, which comes with high computational effort. We propose a hybrid approach combining the reliability and accuracy of a Monte Carlo analysis with the efficiency of a surrogate model based on Gaussian Process Regression. We present two optimiza...

In this paper an efficient and reliable method for stochastic yield estimation is presented. Since one main challenge of uncertainty quantification is the computational feasibility, we propose a hybrid approach where most of the Monte Carlo sample points are evaluated with a surrogate model, and only a few sample points are reevaluated with the ori...

Time-periodic problems appear naturally in engineering applications. For instance,the time-periodic steady-state behavior of an electromagnetic device is often the main interest in electrical engineering, because devices are operated most of their life-time in this state.

The structural analysis, i.e., the investigation of the differential-algebraic nature, of circuits containing simple elements, i.e., resistances, inductances and capacitances is well established. However, nowadays circuits contain all sorts of elements, e.g. behavioral models or partial differential equations stemming from refined device modelling....

Switch‐mode power converters are used in various applications to convert between different voltage (or current) levels. They use transistors to switch on and off the input voltage to generate a pulsed voltage whose arithmetic average is the desired output voltage of the converter. After smoothening by filters, the converter output is used to supply...

We propose a numerical method for the solution of electromagnetic problems on axisymmetric domains, based on a combination of a spectral Fourier approximation in the azimuthal direction with an IsoGeometric Analysis (IGA) approach in the radial and axial directions. This combination allows to blend the flexibility and accuracy of IGA approaches wit...

This note describes an extended exercise on the finite-element (FE) simulation of an accelerator magnet. The students construct and simulate a magnet model using the FEMM freeware. They get the opportunity to exercise on the theory of FEs, including Maxwell equations, magnetoquasistatic formulation, weighted residual approach, choice of appropriate...

This lecture note describes how to set up and what is behind a magnetodynamic field simulation for an accelerator magnet. The relevant formulation of Maxwell's equations is derived. The formulation is discretized in space by the finite-element method and in time by a standard time integration method. The steps for setting up the accelerator-magnet...

This paper presents an efficient numerical algorithm for the simulation of pulse-width modulated power converters via parallelization in time domain. The method applies the multirate partial differential equation approach on the coarse grid of the (two-grid) parallel-in-time algorithm Parareal. Performance of the proposed approach is illustrated vi...

Motivated by the task to design quench protection systems for superconducting magnets in particle accelerators we address a coupled field/circuit simulation based on a magneto-quasistatic field modeling. We investigate how a waveform relaxation of Gau{\ss}-Seidel type performs for a coupled simulation when circuit solving packages are used that des...

Harmonic stator-rotor coupling offers a promising approach for the interconnection of rotating subsystems in the simulation of electric machines. This paper studies the stability of discretization schemes based on harmonic coupling in the framework of mortar methods for Poisson-like problems. A general criterion is derived that allows to ensure the...

Screening currents are field-induced dynamic phenomena which occur in superconducting materials, leading to persistent magnetization. Such currents are of importance in ReBCO tapes, where the large size of the superconducting filaments gives rise to strong magnetization phenomena. In consequence, superconducting accelerator magnets based on ReBCO t...

This paper reports on comprehensive efforts on uncertainty quantification and global sensitivity analysis for accelerator cavity design. As a case study object the TESLA shaped superconducting cavities, as produced for the European X-ray Free Electron Laser (EXFEL), are selected. The choice for these cavities is explained by the available measureme...

This paper presents a novel parallel-in-time algorithm able to compute time-periodic solutions of problems where the period is not given. Exploiting the idea of the multiple shooting method, the proposed approach calculates the initial values at each subinterval as well as the corresponding period iteratively. As in the Parareal method, paralleliza...

In this paper an efficient and reliable method for stochastic yield estimation is presented. Since one main challenge of uncertainty quantification is the computational feasibility, we propose a hybrid approach where most of the Monte Carlo sample points are evaluated with a surrogate model, and only a few sample points are reevaluated with the ori...

This work addresses the simulation of heat flow and electric currents in thin wires. An important application is the use of bond wires in microelectronic chip packaging. The heat distribution is modeled by an electrothermal coupled problem, which poses numerical challenges due to the presence of different geometric scales. The necessity of very fin...

We solve Maxwell's eigenvalue problem via isogeometric boundary elements and a contour integral method. We discuss the analytic properties of the discretisation, outline the implementation, and showcase numerical examples.

The application of high-temperature superconductors to accelerator magnets for future particle colliders is under study. Numerical methods are crucial for an accurate evaluation of the complex dynamical behavior of the magnets, especially concerning the magnetic field quality and thermal behavior. We present a coupled A-H field formulation for the...

This paper proposes an efficient parallelised computation of field/circuit coupled systems co-simulated with the Waveform Relaxation (WR) technique. The main idea of the introduced approach lies in application of the parallel-in-time method parareal to the WR framework. Acceleration obtained by the time-parallelisation is further increased in the c...

The numerical simulation of electrohydrodynamic atomization of a conductive liquid in the cone-jet electrospray mode is considered. The numerical approach is based on the solution of the multiphase flow equations coupled with an electroquasistatic problem including capacitive, resistive and convective electric currents. The formulation allows for t...

This paper focuses on efficient steady-state computations of induction machines. In particular, the periodic Parareal algorithm with initial-value coarse problem (PP-IC) is considered for acceleration of classical time-stepping simulations via non-intrusive parallelization in time domain, i.e., existing implementations can be reused. Superiority of...