A novel formulation for 3D eddy current problems with moving bodies using a Lagrangian description and BEM-FEM coupling

Kurz, Stefan; Fetzer, John C.; Lehner, G.; Rucker, W.M.

doi:10.1109/20.717718

Cited by 68 publications

(44 citation statements)

References 15 publications

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“…the term γ v × (∇ × A) becomes dominant and causes instabilities in the numerical solution process [24]. In (2.16), h denotes the discretization parameter in direction of the velocity v. However, if due to mechanical movements/deformations the overall magnetic field is changed (e.g., movement of the armature in a magnetic valve), we have to consider the formulation of the magnetic problem on the deformed geometry [24].…”

Section: The Magnetic System and The Coupling Termsmentioning

confidence: 99%

“…In (2.16), h denotes the discretization parameter in direction of the velocity v. However, if due to mechanical movements/deformations the overall magnetic field is changed (e.g., movement of the armature in a magnetic valve), we have to consider the formulation of the magnetic problem on the deformed geometry [24]. Observing some point P in a fixed reference frame Γ (x, y, z) (see Fig.…”

Section: The Magnetic System and The Coupling Termsmentioning

confidence: 99%

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A Survey in Mathematics for Industry An efficient method for the numerical simulation of magneto-mechanical sensors and actuators

et al. 2007

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The dynamic behaviour of magneto-mechanical sensors and actuators can be completely described by Maxwell's and Navier-Lamé's partial differential equations (PDEs) with appropriate coupling terms reflecting the interactions of these fields and with the corresponding initial, boundary and interface conditions. Neglecting the displacement currents, which can be done for the classes of problems considered in this paper, and introducing the vector potential for the magnetic field, we arrive at a system of degenerate parabolic PDEs for the vector potential coupled with the hyperbolic PDEs for the displacements.Usually the computational domain, the finite element discretization, the time integration, and the solver are different for the magnetic and mechanical parts. For instance, the vector potential is approximated by edge elements whereas the finite element discretization of the displacements is based on nodal elements on different meshes. The most time consuming modules in the solution procedure are the solvers for both, the magnetical and the mechanical finite element equations arising at each step of the time integration procedure. We use geometrical multigrid solvers which are different for both parts. These multigrid solvers enable us to solve quite efficiently not only academic test problems, but also transient 3D technical magneto-mechanical systems of high complexity such as solenoid valves and electro-magnetic-acoustic transducers. The results of the computer simulation are in very good agreement with the experimental data.

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Section: The Magnetic System and The Coupling Termsmentioning

confidence: 99%

Section: The Magnetic System and The Coupling Termsmentioning

confidence: 99%

A Survey in Mathematics for Industry An efficient method for the numerical simulation of magneto-mechanical sensors and actuators

et al. 2007

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“…In the case of moving bodies the equations (2) and (3) change accordingly to the movement law (see [19] for a short presentation) and we consider the formulation in term of Lagrangian variables.…”

Section: Problem Equations In the Case Of Moving Geometriesmentioning

confidence: 99%

A Slideing Mesh-Mortar Method for a two Dimensional Currents Model of Electric Engines

Buffa

2001

ESAIM: M2AN

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Abstract. The paper deals with the application of a non-conforming domain decomposition method to the problem of the computation of induced currents in electric engines with moving conductors. The eddy currents model is considered as a quasi-static approximation of Maxwell equations and we study its two-dimensional formulation with either the modified magnetic vector potential or the magnetic field as primary variable. Two discretizations are proposed, the first one based on curved finite elements and the second one based on iso-parametric finite elements in both the static and moving parts. The coupling is obtained by means of the mortar element method (see [7]) and the approximation on the whole domain turns out to be non-conforming. In both cases optimal error estimates are provided. Numerical tests are then proposed in the case of standard first order finite elements to test the reliability and precision of the method. An application of the method to study the influence of the free part movement on the currents distribution is also provided.Mathematics Subject Classification. 35Q60, 65N15, 65M55, 68U20, 78A30.

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“…In electromagnetic scattering, a major challenge is overcoming problems with pollution (dispersion) error in wave propagation. In terms of low frequency electromagnetics, such as electromagnetic radiation in low frequency devices such as MRI scanners, the eddy current approximation of the full Maxwell system can be adopted [216,113,37,141,206], which requires special treatment through gauging conditions on the equations [153]. In the eddy current approximation, a major challenge lies in the accurate resolution of the small skin depths in conductors due to higher frequency excitations.…”

Section: Approaches For Electromagneticsmentioning

confidence: 99%

“…The simulation of MRI scanners also builds on the expanding literature devoted to magneto-mechanics and coupled problems including FEM-BEM coupling [125,141], magneto-mechanical damping machines [40], magneto-mechanical effects on material parameters [133], enhanced basis functions for magneto-mechanical coupling [107] and strongly coupled systems [204]. More specifically, attempts to analyse the magneto-mechanical coupling in MRI systems have been considered; with the modelling of axisymmetric superconducting solenoids in self magnetic fields [101] and efficient low order FE solvers for magneto-mechanical coupling in [202], based on the FEM-BEM program CAPA [126], with extensions also to include acoustic effects [203].…”

Section: Applications To Mri Scannersmentioning

confidence: 99%

A High Order Finite Element Coupled Multi-Physics Approach To MRI Scanner Design

Bagwell¹

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A novel formulation for 3D eddy current problems with moving bodies using a Lagrangian description and BEM-FEM coupling

Cited by 68 publications

References 15 publications

A Survey in Mathematics for Industry An efficient method for the numerical simulation of magneto-mechanical sensors and actuators

A Survey in Mathematics for Industry An efficient method for the numerical simulation of magneto-mechanical sensors and actuators

A Slideing Mesh-Mortar Method for a two Dimensional Currents Model of Electric Engines

A High Order Finite Element Coupled Multi-Physics Approach To MRI Scanner Design

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