hp-Finite element simulation of three-dimensional eddy current problems on multiply connected domains

Ledger, P.D.; Zaglmayr, Sabine

doi:10.1016/j.cma.2010.07.010

Cited by 54 publications

(106 citation statements)

References 74 publications

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“…The second test problem is the classical benchmark problem number 7 in the TEAM workshop (see Fujiwara and Nakata [14]; for more recent numerical results about this problem, with different formulations, see, e.g., Alonso Rodríguez and Vázquez Hernández [17], Ledger and Zaglmayr [18]). It consists of a thick aluminum plate with an eccentrically placed hole, subjected to an asymmetric magnetic field.…”

Section: Benchmark Problem 7 In the Team Workhopmentioning

confidence: 99%

Finite element simulation of eddy current problems using magnetic scalar potentials

Rodríguez

Bertolazzi

Ghiloni

et al. 2015

Journal of Computational Physics

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We propose a new implementation of the finite element approximation of eddy current problems using as principal unknown the magnetic field. In the non-conducting region a scalar magnetic potential is introduced. The method can deal automatically with any topological configuration of the conducting region and, being based on the search of a scalar magnetic potential in the non-conducting region, has the advantage of making use of a reduced number of unknowns. Several numerical tests are presented for illustrating the performance of the proposed method; in particular, the numerical simulation of a new type of transformer of complicated topological shape is shown.

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Section: Benchmark Problem 7 In the Team Workhopmentioning

confidence: 99%

Finite element simulation of eddy current problems using magnetic scalar potentials

Rodríguez

Bertolazzi

Ghiloni

et al. 2015

Journal of Computational Physics

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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%

“…High order finite elements are important in electromagnetics for resolving small skin depths in eddy current problems [153,217]. They are needed to avoid problems with pollution (dispersion) error in wave propagation 3 [16] (This will be revisited in Approaches for Acoustics).…”

Section: Approaches For Electromagneticsmentioning

confidence: 99%

“…For 3D problems this will, however, require the use of iterative solvers and an efficient pre-conditioner to compute the matrix system, for examples of such solvers see [77,153].…”

Section: Chapter Summarymentioning

confidence: 99%

“…In the absence of the surface current density j s the transmission conditions become 19) where [·] ∂Ωc denotes the jump 8 on the conductor-non-conductor interface and n is a unit outward normal vector to ∂Ω c . 7 The temporal gauge has been applied in Ω c and the Coulomb gauge in R 3 \ Ω c [153]. 8 The jump describes the continuity of a field across an interface between two mediums [w] ∂Ωc = w| + − w| − , see Appendix B for more details.…”

Section: Interface Conditionsmentioning

confidence: 99%

See 2 more Smart Citations

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

Bagwell¹

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Accelerating magnetic induction tomography‐based imaging through heterogeneous parallel computing

Walker

Kramer

Biebl

et al. 2019

Concurrency and Computation

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Magnetic Induction Tomography (MIT) is a non-invasive imaging technique, which has applications in both industrial and clinical settings. In essence, it is capable of reconstructing the electromagnetic parameters of an object from measurements made on its surface. With the exploitation of parallelism, it is possible to achieve high quality inexpensive MIT images for biomedical applications on clinically relevant time scales. In this paper we investigate the performance of different parallel implementations of the forward eddy current problem, which is the main computational component of the inverse problem through which measured voltages are converted into images. We show that a heterogeneous parallel method that exploits multiple CPUs and GPUs can provide a high level of parallel scaling, leading to considerably improved runtimes. We also show how multiple GPUs can be used in conjunction with deal.II, awidely-used open source finite element library. KEYWORDScomputational electromagnetics, magnetic induction tomography, parallel applications INTRODUCTIONMagnetic Induction Tomography (MIT) is a non-invasive imaging technique, which has applications in both industrial and clinical settings. In essence, it is capable of reconstructing the electromagnetic parameters of an object from measurements made on its surface. These parameters are the permittivity, , the permeability, , and the conductivity, . An MIT device consists of two sets of coils placed around the boundary of the object to be imaged. The first set of coils is used for the purpose of excitation, and by passing a current through each coil in turn, a primary magnetic field is created. The second set of coils is then used for measurement. This procedure causes an eddy current when each of the primary magnetic fields interacts with a conducting body inducing secondary magnetic fields, and hence voltages, that are measured in the second set of coils. In order to estimate the electromagnetic properties of the material, ( , , ), from the induced currents and measured voltage, an inverse problem must be solved. In many practical applications, the distribution of one or more of these material parameters is assumed to be constant throughout the medium of interest.Conventional imaging techniques for imaging cerebral stroke, such as Magnetic Resonance Imaging (MRI) and Computer Tomography (CT), are expensive. Although MRI may be used for real-time image reconstruction, 1 it has been proposed that MIT can offer a low cost alternative in the first stages of diagnosis. 2 However, the low conductivity contrast between biomedical tissues presents significant challenges to MIT, and there are considerable difficulties in employing current computational techniques to solve the associated inverse problem. 3,4 Enabling MIT to take the step from being an experimental technique, which has already received some clinical interest, to become a viable imaging technique for the detection and monitoring of conditions, such as cerebral stroke, requires a step change in the quality of ...

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hp-Finite element simulation of three-dimensional eddy current problems on multiply connected domains

Cited by 54 publications

References 74 publications

Finite element simulation of eddy current problems using magnetic scalar potentials

Finite element simulation of eddy current problems using magnetic scalar potentials

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

Accelerating magnetic induction tomography‐based imaging through heterogeneous parallel computing

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