Implementation of the H-$\varphi$ formulation in COMSOL Multiphysics for simulating the magnetization of bulk superconductors and comparison with the H-formulation

Abstract

The H-formulation, used abundantly for the simulation of high temperature superconductors, has shown to be a very versatile and easily implementable way of modeling electromagnetic phenomena involving superconducting materials. However, the simulation of a full vector field in current-free domains unnecessarily adds degrees of freedom to the model, thereby increasing computation times. In this contribution, we implement the well known H-$\varphi$ formulation in COMSOL Multiphysics in order to compare the numerical performance of the H and H-$\varphi$ formulations in the context of computing the magnetization of bulk superconductors. We show that the H-$\varphi$ formulation can reduce the number of degrees of freedom and computation times by nearly a factor of two for a given relative error. The accuracy of the magnetic fields obtained with both formulations are demonstrated to be similar. The computational benefits of the H-$\varphi$ formulation are shown to far outweigh the added complexity of its implementation, especially in 3-D. Finally, we identify the ideal element orders for both H and H-$\varphi$ formulations to be quartic in 2-D and cubic in 3-D, corresponding to the highest element orders implementable in COMSOL.

References in corpus (6)

• Calculation of AC losses in stacks and coils made of second generation high temperature superconducting tapes for large scale applications
• Review of the AC Loss Computation for HTS using the H-formulation
• Superconducting Magnetic Bearings Simulation using an H-formulation Finite Element Model
• Dynamic modeling of levitation of a superconducting bulk by coupled $H$-magnetic field and Arbitrary Lagrangian-Eulerian formulations
• Composite stacks for reliable > 17 T trapped fields in bulk superconductor magnets
• Demagnetization of cubic Gd-Ba-Cu-O bulk superconductor by cross-fields: measurements and 3D modelling

Cited by in corpus (5)

• COMSOL implementation of the H-$\varphi$-formulation with thin cuts for modeling superconductors with transport currents
• $H$-$\varphi$ formulation in Sparselizard combined with domain decomposition methods for modeling superconducting tapes, stacks, and twisted wires
• Fully-staggered-array bulk Re-Ba-Cu-O short-period undulator: large-scale 3D electromagnetic modelling and design optimization using A-V and H-formulation methods
• Proposal for the search for exotic spin-spin interactions at the micrometer scale using functionalized cantilever force sensors
• Observation of Uniform Supercurrent Flow in Polycrystalline K-doped Ba122 by Combined Magneto-optical Imaging and Finite-element Modeling