Model reduction for linear and nonlinear magneto‐quasistatic equations

Kerler-Back, Johanna; Stykel, Tatjana

doi:10.1002/nme.5507

Cited by 13 publications

(15 citation statements)

References 52 publications

(106 reference statements)

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“…Reduced order models (ROMs) based on POD have been successfully applied to efficiently generate solutions for new problem parameters using a small number representative full order model solutions (often called snapshots, e.g., References 21,22) in a range of engineering applications including mechanics, 28,29 thermal problems, 30,31 fluid flow 32,33 as well as electromagnetic problems with application to integrated circuits 34 and recently to coupled magnetomechanical problems. 22 However, ROMs have not been applied to the computation of MPT spectral signatures.…”

Section: Introductionmentioning

confidence: 99%

Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition

Wilson

Ledger

2021

Numerical Meth Engineering

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The identification of hidden conducting permeable objects from measurements of the perturbed magnetic field taken over a range of low frequencies is important in metal detection. Applications include identifying threat items in security screening at transport hubs, location of unexploded ordnance, and antipersonnel landmines in areas of former conflict, searching for items of archeological significance and recycling of valuable metals. The solution of the inverse problem, or more generally locating and classifying objects, has attracted considerable attention recently using polarizability tensors. The magnetic polarizability tensor (MPT) provides a characterization of a conducting permeable object using a small number of coefficients, has an explicit formula for the calculation of their coefficients, and a well understood frequency behavior, which we call its spectral signature. However, to compute such signatures, and build a library of them for object classification, requires the repeated solution of a transmission problem, which is typically accomplished approximately using a finite element discretization. To reduce the computational cost, we propose an efficient reduced order model (ROM) that further reduces the problem using a proper orthogonal decomposition for the rapid computation of MPT spectral signatures. Our ROM benefits from a posteriori error estimates of the accuracy of the predicted MPT coefficients with respect to those obtained with finite element solutions. These estimates can be computed cheaply during the online stage of the ROM allowing the ROM prediction to be certified. To further increase the efficiency of the computation of the MPT spectral signature, we provide scaling results, which enable an immediate calculation of the signature under changes in the object size or conductivity. We illustrate our approach by application to a range of homogenous and inhomogeneous conducting permeable objects.

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Section: Introductionmentioning

confidence: 99%

Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition

Wilson

Ledger

2021

Numerical Meth Engineering

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“…We prove that the POD reduced model is passive and present a passivity enforcing method for the POD-DEIM reduced model. Some parts of Sections 4.4 and 4.5 have been published in [KBS17]. In Section 4.6, we report some results of numerical experiments for a single-phase 2D transformer model.…”

Section: Outline Of the Thesismentioning

confidence: 99%

Dynamic iteration and model order reduction for magneto-quasistatic systems

Kerler-Back¹

2019

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“…Therefore, there is a demand for reduced order models (see, e.g. [13]) of this quasilinear PDE, which can be further used as surrogates in the optimization procedure. Our approach is applicable to the 2D magnetoquasistatic problem as well, and we present according numerical results.…”

Section: Introductionmentioning

confidence: 99%

“…This allows us to consider a pure parabolic problem instead of a parabolicelliptic system with differential-algebraic structure (see, e.g. [13]). We set μ := σ 1 and define the parameter set D = [5 • 10 6 , 10 7 ] and the time interval I = (0, 0.02].…”

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confidence: 99%

A space-time certified reduced basis method for quasilinear parabolic partial differential equations

Hinze

Korolev

2021

Adv Comput Math

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In this paper, we propose a certified reduced basis (RB) method for quasilinear parabolic problems with strongly monotone spatial differential operator. We provide a residual-based a posteriori error estimate for a space-time formulation and the corresponding efficiently computable bound for the certification of the method. We introduce a Petrov-Galerkin finite element discretization of the continuous space-time problem and use it as our reference in a posteriori error control. The Petrov-Galerkin discretization is further approximated by the Crank-Nicolson time-marching problem. It allows to use a POD-Greedy approach to construct the reduced-basis spaces of small dimensions and to apply the Empirical Interpolation Method (EIM) to guarantee the efficient offline-online computational procedure. In our approach, we compute the reduced basis solution in a time-marching framework while the RB approximation error in a space-time norm is controlled by our computable bound. Therefore, we combine a POD-Greedy approximation with a space-time Galerkin method.

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Model reduction for linear and nonlinear magneto‐quasistatic equations

Cited by 13 publications

References 52 publications

Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition

Efficient computation of the magnetic polarizabiltiy tensor spectral signature using proper orthogonal decomposition

Dynamic iteration and model order reduction for magneto-quasistatic systems

A space-time certified reduced basis method for quasilinear parabolic partial differential equations

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