Chair of Electromagnetic Theory

EMQS Field Formulations of Darwin-Type

Principal researchers
Prof. Dr. Markus Clemens
Marvin-Lucas Henkel, M.Sc.
Dr. Fotios Kasolis            
Bernhard Kähne, M.Sc.
Prof. Michael Günther
Prof. Dr. Sebastian Schöps
Prof. Dr. Herbert De Gersem

Project duration
Since 2019

Quasistatic fields, resistive-inductive-capacitive fields, electromagneto-quasistatic fields, Darwin field model, Kirchhoff model, Maxwell equations, numerical linear algebra

Project description

The regime of quasistatic electromagnetic field models is applicable, if the structures under consideration are small w.r.t. to the wave lengths of the highest operational frequency for a given problem, i.e., if radiation affects can be neglected.

This model regime includes the limit case of static field configurations, where merely capacitive, resistive or inductive effects need to be considered in electrostatic or stationary direct current and corresponding magnetostatic field configurations. More generally, it also covers slowly varying electric or magnetic fields: the electro-quasistatic (EQS) field model covers problems governed by capacitive and resistive effects, whereas magneto-quasistatic (MQS) field models describe resistive-inductive field problems. The majority of these established submodels of Maxwell’s equations are based on mathematical formulations in terms of electric and/or magnetic scalar and vector potentials.

Electromagneto-quasistatic (EMQS) field problems, where resistive, inductive and capacitive effects need to be considered simultaneously, have recently gained interest related to the modeling of high-frequency coils e.g. in transformer or in inductive wireless power transfer systems and also w.r.t. electromagnetic compatibility issues of power electronic systems.

Geometric multiscale aspect ratios of such systems often result in lumped parameter circuit formulations (RLC circuit descriptions based on the Kirchhoff model), hybridized field-circuit formulations or circuit-type formulations as e.g. the partial-element equivalent circuit (PEEC) methods to be the preferred method of modelling.

Rather recently, electromagneto-quasistatic (EMQS) field formulations of such application problems have come into the focus of interest: these field-oriented formulations are developed to consider local nonlinear material behavior and a fine grained description of local inductive and capacitive coupling effects combined with the ability to model transient effects.

Based on the original electromagneto-quasistatic (EMQS) field model of Darwin which was originally devised to describe the electromagnetic field of moving charged particles in free space without wave propagation effects, the development, analysis and extension of electromagneto-quasistatic (EMQS) field formulations of Darwin-type which are capable of including electrically conductive, dielectric and ferromagnetic material behavior simultaneously is a topic of ongoing research efforts in electromagnetic field theory and computational electromagnetics.

Project-related publications

M. Henkel, F. Kasolis and M. Clemens, "A Grad-Div Regularized Electromagneto-Quasistatic Field Formulation", IEEE Transactions on Magnetics, vol. 60, pp. 1-4, 03 2024.
M. Clemens, M. Henkel and M. Günther, "Structural Aspects of Electromagneto-Quasistatic Field Formulations of Darwin-Type Derived in the Port-Hamiltonian System Framework", 21st Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2024), Jeju, South Korea., 02.-05.06.2024, Dec. 2023.
M. Henkel, F. Kasolis, M. Clemens, M. Günther and S. Schöps, "Implicit Gauging of Electromagneto-Quasistatic Field Formulations", IEEE Transactions on Magnetics, vol. 58, no. 9, 09 2022. IEEE.
M. Henkel, F. Kasolis, S. Schöps and M. Clemens, "A comparative study on electromagnetic quasistatic time-domain field calculations", International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, pp. e3049, 07 2022. John Wiley & Sons, Ltd.
M. Clemens, M. Henkel, F. Kasolis, M. Günther, H. De Gersem and S. Schöps, "Electromagnetic Quasistatic Field Formulations of Darwin Type", International Compumag Society (ICS) Newsletter, vol. 29, no. 1, 2022.
M. Henkel, F. Kasolis and M. Clemens, "Design Principles of Electromagneto-Quasistatic Field Formulations", URSI e.V. Deutschland 2021 Kleinheubacher Tagung (KHB 2021), Miltenberg, Germany, 28.-30.09.2021, Sep. 2021.
M. Clemens, F. Kasolis, M. Henkel, B. Kähne and M. Günther, "A Two-Step Darwin Time Domain Formulation for Quasistatic Electromagnetic Field Calculations", IEEE Transactions on Magnetics, vol. 57, no. 6, pp. 1-4, Jun. 2021. IEEE.
M. Clemens, M. Henkel, F. Kasolis and S. Schöps, "A Class of Electromagnetic Quasistatic Darwin Field Formulations Based on Semi-Discrete Full Maxwell Continuity Gauge Equations", The 12th International Symposium on Electric and Magnetic Fields (EMF 2021), Online Conference, 06.-08.07.2021, Abstract, 2021.
M. Henkel, F. Kasolis and M. Clemens, "A Two-Step Darwin Model in Frequency-Domain for Quasistatic Electromagnetic Field Simulations", 21st ECMI Conference on Industrial and Applied Mathematics (ECMI 2021), Wuppertal, Germany, 13.-15.04.2021, 2021.
M. Clemens, C. Magele and M. Pantelyat, "Quasistatic Electromagnetic Field Problems Including Capacitive, Inductive and Resistive Effects: Applications and Models", ICS Newsletter (International Compumag Society), vol. 27, no. 3, pp. 15-18, Nov. 2020.
M. Clemens, B. Kähne and S. Schöps, "A Darwin Time Domain Scheme for the Simulation of Transient Quasistatic Fields Including Resistive, Capacitive and Inductive Effects", 2019 Kleinheubach Conference, Miltenberg, Germany, 23.-25.09.2019, IEEE, Oct. 2019, pp. 1-4.

ISBN: 978-3-948571-00-9

M. Clemens and S. Schöps, "Quasistatic Darwin Model Field Formulations in Time Domain", 21st Edition of the International Conference on Electromagnetics in Advanced Applications and 9th edition of the IEEE-APS Topical Conference on Antennas and Propagation in Wireless Communications (ICEAA-IEEE APWC 2019),, Granada, Spain, 09.-13.09.2019, IEEE, Sep. 2019.

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