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A Shape Function Order Approach to Accelerate the Computation Time of the J-A Formulation
  • Gabriel dos Santos,
  • Bárbara Maria Oliveira
Gabriel dos Santos

Corresponding Author:[email protected]

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Bárbara Maria Oliveira


The J-A formulation has been proposed as a way to model the electromagnetic behavior of superconducting devices in finite element simulations. It is based on the current density, J, and the magnetic vector potential, A. It has been found that, to ensure better stability of simulations results, the shape functions of J should be discontinuous Lagrange of constant order, whereas for A second order continuous Lagrange functions should be used. However, applying second order shape functions increase the computational complexity of the simulation, both of degrees of freedom and computation time. In this paper, an approach to solve this issue is proposed. The finite element domain is divided into two parts, superconducting and non-superconducting. For the superconducting parts, the shape function of A is second order continuous Lagrange to ensure numerical stability. For the non-superconducting parts, a first order continuous Lagrange is used for A. To couple the two types of domains, Dirichlet Boundary Conditions are used. Three case scenarios are investigated and their results are compared to those of the common J-A formulation. Full agreement is obtained.
15 Jan 2024Submitted to TechRxiv
26 Jan 2024Published in TechRxiv