Magnetodynamic H–$\phi$ Formulation for Improving the Convergence and Speed of Numerical Simulations of Superconducting Materials
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Bibliographic record
Abstract
The growing interest in fast and accurate simulation methods of the electromagnetic behavior of high-temperature superconducting materials has led to many exciting developments in the last decade. Although the H formulation implemented in the finite-element method has proven to be very robust for electromagnetic calculations, the dummy resistivity and vector-dependent variables required in air domains lead to long computation times and spurious currents in certain applications. Thus, the H– <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\phi$</tex-math></inline-formula> formulation has recently gained significant traction in order to speed up simulations. In our previous work, we implemented the H– <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\phi$</tex-math></inline-formula> formulation in COMSOL Multiphysics using the divergence-free condition in air domains and showed that the computation times were reduced by two and three in 2-D and 3-D, respectively. However, high-order shape functions were required in order to obtain sufficient accuracy when compared to the full H formulation. In this article, we implemented a magnetodynamic H– <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\phi$</tex-math></inline-formula> formulation in COMSOL by using Faraday's law in air domains to improve the coupling between the H and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\phi$</tex-math></inline-formula> physics and correctly represent time-varying phenomena in superconducting materials. We show that this formulation leads to better convergence, more accurate solutions, and a slight speed advantage compared to the previously used H– <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\phi$</tex-math></inline-formula> formulation. The magnetodynamic H– <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\phi$</tex-math></inline-formula> formulation results are shown to be nearly identical to the full H formulation even with linear shape functions, while reducing the computation times by a factor of up to four for a given mesh.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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