Systems of Differential Algebraic Equations in Computational Electromagnetics

Garcia, Idoia Cortes; Schöps, Sebastian; Gersem, Herbert De; Baumanns, Sascha

doi:10.1007/11221_2018_8

Cited by 12 publications

(3 citation statements)

References 75 publications

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“…It should be noted that while there is freedom to choose the initial condition for x and u (as long as the initial condition for x and u satisfies the constraint), the initial condition for z must be 0. Therefore, a geometric result that is similar to lemma 3.1 can not be obtained by directly applying the lemma to equation (8). However, as the solution exists, it satisfies the constraint h(x, z, u) = 0.…”

Section: Necessary Conditionmentioning

confidence: 99%

“…From the application point of view, DAE is often used in control of physical/engineering systems such as in robotics [4,11,12], power engineering [20,9], aerodynamics [24], satellite applications [7] etc. Other than control, DAE also finds application in areas such as biochemistry [23,25], ecological sciences [10], astronomy and astrophysics [2], electromagnetism [8] etc. There is abundant literature on both theoretical and numerical aspects of DAEs.…”

Section: Introductionmentioning

confidence: 99%

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On Explicit Stochastic Differential Algebraic Equations

Suthar¹,

Raha²

2021

Preprint

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Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such systems results in solving path constrained SDEs. Broadly, these problems fall under the category of Stochastic Differential-Algebraic Equations (SDAEs). In this article, the focus is on combining ideas from the local theory of Differential-Algebraic Equations with that of Stochastic Differential Equations. The question of existence and uniqueness of the solution for SDAEs is addressed by using contraction mapping theorem in an appropriate Banach space to arrive at a sufficient condition. From the geometric point of view, a necessary condition is derived for the existence of the solution. It is observed that there exists a class of high index SDAEs for which there is no solution. Hence, computational methods to find approximate solution of high index equations are presented. The techniques are illustrated in form of algorithms with examples and numerical computations.

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Section: Necessary Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Explicit Stochastic Differential Algebraic Equations

Suthar¹,

Raha²

2021

Preprint

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“…By the Helmholtz decomposition, the electric field E can be split into two parts: an irrotational part E irr , which is curl free, and a solenoidal part E sol , which is divergence free [17] E…”

Section: Darwin Modelmentioning

confidence: 99%

Numerical Simulation-Based Investigation of the Limits of Different Quasistatic Models

et al. 2021

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The modeling of the capacitive phenomena, including the inductive effects becomes critical, especially in the case of a power converter with high switching frequencies, supplying an electrical device. At a low frequency, the electro-quasistatic (EQS) model is widely used to study the coupled resistive-capacitive effects, while the magneto-quasistatic (MQS) model is used to describe the coupled resistive-inductive effects. When the frequency increases, the Darwin model is preferred, which is able to capture the coupled resistive-capacitive-inductive effects by neglecting the radiation effects. In this work, we are interested in specifying the limits of these models, by investigating the influence of the frequency on the electromagnetic field distributions and the impedance of electromagnetic devices. Two different examples are carried out. For the first one, to validate the Darwin model, the measurement results are provided for comparison with the simulation results, which shows a good agreement. For the second one, the simulation results from three different models are compared, for both the local field distributions and the global impedances. It is shown that the EQS model can be used as an indicator to know at which frequency the Darwin model should be applied.

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