2022/10/21 by Limin Ma, Zhonghua Qiao, Ma, Limin +1 · 3 citations
Mathematics · Physics and Astronomy · #68Q25 #68R10 #68U05 #FOS: Mathematics #Magnetic confinement fusion research #Numerical Analysis (math.NA) #Numerical methods for differential equations #Physics of Superconductivity and Magnetism
paper · pdf · doi:10.48550/arxiv.2210.11678
openalex publication_date 2022/10/21 · openalex created_date 2022/10/30 · openalex updated_date 2026/07/28
This paper proposes a decoupled numerical scheme of the time-dependent Ginzburg--Landau equations under the temporal gauge. For the magnetic potential and the order parameter, the discrete scheme adopts the second type Ned\rm \acuteelec element and the linear element for spatial discretization, respectively; and a linearized backward Euler method and the first order exponential time differencing method for time discretization, respectively. The maximum bound principle (MBP) of the order parameter and the energy dissipation law in the discrete sense are proved. The discrete energy stability and MBP-preservation can guarantee the stability and validity of the numerical simulations, and further facilitate the adoption of an adaptive time-stepping strategy, which often plays an important role in long-time simulations of vortex dynamics, especially when the applied magnetic field is strong. An optimal error estimate of the proposed scheme is also given. Numerical examples verify the theoretical results of the proposed scheme and demonstrate the vortex motions of superconductors in an external magnetic field.