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Date of Publication:2022-10-10

Journal:Transactions of China Electrotechnical Society

Volume:33

Issue:5

Page Number:1167-1176

ISSN No.:1000-6753

Key Words:"Magnetostatics; mixed finite element method; Coulomb gauge; Lagrange multiplier method; Uzawa method"

CN No.:11-2188/TM

Abstract:This paper proposes to adopt mixed finite element method to eliminate spurious solution in simulating magnetostatic problems. By introducing a scalar Lagrange multiplier, Coulomb gauge is incorporated into magnetic vector potential formulation based on constrained variational principle, leading to A-lambda mixed formulation. Furthermore, the gradient of the scalar Lagrange multiplier is identified as the incompatible component of exciting current source. By means of Newton-Raphson method, iterative strategy is established for material nonlinearity problems. Edge elements are employed to discretize magnetic vector potential, and nodal elements are employed to discretize Lagrange multiplier. By augmented Lagrange multiplier technique, the saddle point problem arising from mixed finite element discretization can be transferred to an equivalent problem which can be iteratively solved by Uzawa method. Compared with conventional nodal element and edge element, the mixed element can suppress potential spurious solutions, and obtain a more accurate solution.

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