Fully discrete potential-based finite element methods for a transient eddy current problem

Kang, Tong; Kim, Kwang Ik

doi:10.1007/s00607-009-0049-4

Cited by 21 publications

(5 citation statements)

References 11 publications

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“…. ; u M Þ : u k 2 X; 1 6 k 6 Mg equipped with the norm The following two lemmas are shown to discuss the existence and uniqueness of the solutions of the problem (3.5)-(3.7), whose proofs are easily given by Lemma 2.1 and 2.2 in [7]. …”

Section: A-/ Composite Grid Discretizationmentioning

confidence: 99%

A–ϕ finite element method with composite grids for time-dependent eddy current problem

Kang

Chen

Zhang

et al. 2015

Applied Mathematics and Computation

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Section: A-/ Composite Grid Discretizationmentioning

confidence: 99%

A–ϕ finite element method with composite grids for time-dependent eddy current problem

Kang

Chen

Zhang

et al. 2015

Applied Mathematics and Computation

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“…Similarly in , according to the left‐hand side of the formulations and , we introduce a projection operator

P_{h} MathClass-punc: {\overset{bold H}{false}}_{0}^{1} (Ω_{c}) MathClass-bin\times W MathClass-rel\to {bold-italicV}_{h}^{0} MathClass-bin\times W_{h}

such that, for any

bold-italicQ MathClass-rel\in {\overset{bold H}{false}}_{0}^{1} (Ω_{c})

, φ ∈ W , we have

({, \begin{matrix} falsenonefalsearray \\ array {(μ (MathClass-open(Q - \nabla ϕ MathClass-close) - MathClass-open(P_{h} Q - \nabla P_{h} ϕ MathClass-close)), Q_{h})}_{Ω_{c}} + {(\frac{1}{σ} div MathClass-open(Q - P_{h} Q MathClass-close), div Q_{h})}_{Ω_{c}} \\ array + {(\frac{1}{σ} curl MathClass-open(Q - P_{h} Q MathClass-close), curl Q_{h})}_{Ω_{c}} = 0, \\ array MathClass-open(μ MathClass-open(MathClass-... \end{matrix})

…”

Section: Error Estimatesmentioning

confidence: 99%

A (T,ψ)‐ψ_e decoupled scheme for a time‐dependent multiply‐connected eddy current problem

Chen

Kang

et al. 2013

Math Methods in App Sciences

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Communicated by M. CostabelThe aim of this paper is to develop a fully discrete .T, /-e finite element decoupled scheme to solve time-dependent eddy current problems with multiply-connected conductors. By making 'cuts' and setting jumps of e across the cuts in nonconductive domain, the uniqueness of e is guaranteed. Distinguished from the traditional T-method, our decoupled scheme solves the potentials T and -e separately in two different simple equation systems, which avoids solving a saddle-point equation system and leads to a remarkable reduction in computational efforts. The energy-norm error estimate of the fully discrete decoupled scheme is provided. Finally, the scheme is applied to solve two benchmark problems-TEAM Workshop Problems 7 and IEEJ model.

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“…Besides, it can also be changed into potential formulations by means of decomposition of the field E or H (called the A-φ or T -ψ method) and thus nodal finite elements are used to solve it numerically, cf. [1,[4][5][6][7][8][9][10]16,17]. There are several advantages for the potential method.…”

Section: Introductionmentioning

confidence: 99%

Boundary data identification for an electromagnetic problem by means of the potential field method

Zhang

Kang

Wang

et al. 2017

Computers & Mathematics with Applications

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This paper is devoted to the study of a boundary data identification for an electromagnetic problem by means of the potential field method (the A-φ method). One part of the boundary is over-determined. The other part of the boundary is unreachable and has to be determined as a part of the problem. We design a constructive algorithm by the A-φ formulation to solve this problem. The numerical scheme is based on the steepest descent method (SDM) for the minimization of a regularized cost functional, having its derivative determined via an adjoint method. We analyse the properties of the cost functional and prove the convergence of the minimization process. The method is supported by several numerical experiments.

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Fully discrete potential-based finite element methods for a transient eddy current problem

Cited by 21 publications

References 11 publications

A–ϕ finite element method with composite grids for time-dependent eddy current problem

A–ϕ finite element method with composite grids for time-dependent eddy current problem

A (T,ψ)‐ψ_e decoupled scheme for a time‐dependent multiply‐connected eddy current problem

Boundary data identification for an electromagnetic problem by means of the potential field method

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Fully discrete potential-based finite element methods for a transient eddy current problem

Cited by 21 publications

References 11 publications

A–ϕ finite element method with composite grids for time-dependent eddy current problem

A–ϕ finite element method with composite grids for time-dependent eddy current problem

A (T,ψ)‐ψe decoupled scheme for a time‐dependent multiply‐connected eddy current problem

Boundary data identification for an electromagnetic problem by means of the potential field method

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Product

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A (T,ψ)‐ψ_e decoupled scheme for a time‐dependent multiply‐connected eddy current problem