3D Stochastic Spectral Finite Element Method in static electromagnetism using vector potential formulation

Beddek, K.; Menach, Yvonnick Le; Clénet, S.; Moreau, O.

doi:10.1109/cefc.2010.5481525

Cited by 6 publications

(17 citation statements)

References 2 publications

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“…The non intrusive method consists in adding just an additional "layer" to a deterministic model to take into account the random dimensions. For the intrusive method, a new code has to be developed [3,4,6,7]. The equation (4) can be solved by using the finite element method.…”

Section: Uncertainties On the Behavior Lawmentioning

confidence: 99%

“…In computational electromagnetics, there are generally three kinds of uncertainties: those on the source terms, those on the material behavior and those on the dimensions of the apparatus under study. In [3,4,5,6,7,8,9], some methods using polynomial chaos expansions were proposed to quantify the effect of uncertainties on the behavior laws on the outputs of the model. For problems with random domains (the dimensions are uncertain), discontinuities can appear on the field distribution in the "random dimension"…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Comparison of two approaches to compute magnetic field in problems with random domains

Mac¹,

Clénet²,

Mipo³

2012

IET Sci. Meas. Technol.

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractMethods are now available to solve numerically electromagnetic problems with uncertain input data (behaviour law or geometry). The stochastic approach consists in modelling uncertain data using random variables. Discontinuities on the magnetic field distribution in the stochastic dimension can arise in a problem with uncertainties on the geometry.The basis functions (polynomial chaos) usually used to approximate the unknown fields in the random dimensions are no longer suited. One possibility proposed in the literature is to introduce additional functions (enrichment function) to tackle the problem of discontinuity. In this paper, we focus on the method of random mappings and we show that in this case the discontinuity are naturally taken into account and that no enrichment function needs to be added.

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Section: Uncertainties On the Behavior Lawmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparison of two approaches to compute magnetic field in problems with random domains

Mac¹,

Clénet²,

Mipo³

2012

IET Sci. Meas. Technol.

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show abstract

“…In engineering, this approach was introduced by Ghanem [1] in mechanics and widely developed in this area. In computational electromagnetic, this approach was introduced in [2] and [3].…”

Section: Introductionmentioning

confidence: 99%

“…The estimator is applied to some non-linear problems where the adjoint problem becomes linear and the solution of the adjoint problem needs then less time than the initial one. The error estimation in [6] is also global and can be applied only for the numerical solution obtained by the Spectral Stochastic Finite Element Method (SSFEM) [2], [3]. In [7], an error estimator enabling us to evaluate the error due the stochastic discretization (only due to PCE), the so-called stochastic error, has been proposed.…”

Section: Introductionmentioning

confidence: 99%

A Posteriori Error Estimation for Stochastic Static Problems

Mac

Clénet

2014

IEEE Trans. Magn.

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Abstract-To solve stochastic static field problems, a discretization by the Finite Element Method can be used. A system of equations is obtained with the unknowns (scalar potential at nodes for example) being random variables. To solve this stochastic system, the random variables can be approximated in a finite dimension functional space -a truncated polynomial chaos expansion. The error between the exact solution and the approximated one depends not only on the spatial mesh but also on the discretization along the stochastic dimension. In this paper, we propose an a posteriori estimation of the error due to the discretization along the stochastic dimension.

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“…In the reference problem, the uncertainties are borne by the material behavior laws that become stochastic. Numerical tools are available to solve this kind of problem [5], [6].…”

Section: Introductionmentioning

confidence: 99%

A Priori Error Indicator in the Transformation Method for Problems With Geometric Uncertainties

Mac¹,

Clénet²,

Mipo³

et al. 2013

IEEE Trans. Magn.

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Abstract-To solve stochastic problems with geometric uncertainties, one can transform the original problem in a domain with stochastic boundaries and interfaces to a problem defined in a deterministic domain with uncertainties in the material behavior. The latter problem is then discretized. There exist infinitely many random mappings that lead to identical results in the continuous domain but not in the discretized domain. In this paper, an a priori error indicator is proposed for electromagnetic problems with scalar and vector potential formulations. This leads to criteria for selecting random mappings that reduce the numerical error. In an illustrative numerical example, the proposed a priori error indicator is compared with an a posteriori estimator for both potential formulations Index Terms-Stochastic problem, random domain, transformation method, random mapping, a priori error indicator, static fields.

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3D Stochastic Spectral Finite Element Method in static electromagnetism using vector potential formulation

Cited by 6 publications

References 2 publications

Comparison of two approaches to compute magnetic field in problems with random domains

Comparison of two approaches to compute magnetic field in problems with random domains

A Posteriori Error Estimation for Stochastic Static Problems

A Priori Error Indicator in the Transformation Method for Problems With Geometric Uncertainties

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