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Volume 38, Issue 5
An Efficient Numerical Algorithm for Solving Coupled Time-Dependent Ginzburg-Landau Equation for Superconductivity and Elasticity

Qingguo Hong, Limin Ma, Daniel Fortino, Long-Qing Chen & Jinchao Xu

DOI: 10.4208/cicp.OA-2023-0239

Commun. Comput. Phys., 38 (2025), pp. 1498-1514.

Published online: 2025-09

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  • Abstract

A decoupled finite element algorithm is developed for simulating the vortex dynamics on an elastic superconductor which couples the time-dependent Ginzburg-Landau equation with the complex-valued superconducting order parameter and the vector-valued magnetic potential, and the elasticity equation. We present an iterative algorithm for the decoupled system arising from the time and spatial discretization using a combination of preconditioner, algebraic multigrid method (AMG) and preconditioned conjugate gradient method (PCG). The iterative algorithm allows us to perform large-scale three-dimensional simulations of mesoscale pattern formation during superconducting phase transitions with arbitrary elastic boundary conditions. The performance and efficiency of the algorithm are numerically verified by several benchmark problems, exhibiting up to two orders of magnitude improvement depending on the scale of discrete system compared to the exact solver.

  • Keywords

Efficiency, preconditioner, Ginzburg-Landau equation, elasticity.

  • AMS Subject Headings

65F08, 65M55, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-38-1498, author = {Hong , QingguoMa , LiminFortino , DanielChen , Long-Qing and Xu , Jinchao}, title = {An Efficient Numerical Algorithm for Solving Coupled Time-Dependent Ginzburg-Landau Equation for Superconductivity and Elasticity}, journal = {Communications in Computational Physics}, year = {2025}, volume = {38}, number = {5}, pages = {1498--1514}, abstract = {

A decoupled finite element algorithm is developed for simulating the vortex dynamics on an elastic superconductor which couples the time-dependent Ginzburg-Landau equation with the complex-valued superconducting order parameter and the vector-valued magnetic potential, and the elasticity equation. We present an iterative algorithm for the decoupled system arising from the time and spatial discretization using a combination of preconditioner, algebraic multigrid method (AMG) and preconditioned conjugate gradient method (PCG). The iterative algorithm allows us to perform large-scale three-dimensional simulations of mesoscale pattern formation during superconducting phase transitions with arbitrary elastic boundary conditions. The performance and efficiency of the algorithm are numerically verified by several benchmark problems, exhibiting up to two orders of magnitude improvement depending on the scale of discrete system compared to the exact solver.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0239}, url = {http://global-sci.org/intro/article_detail/cicp/24464.html} }
TY - JOUR T1 - An Efficient Numerical Algorithm for Solving Coupled Time-Dependent Ginzburg-Landau Equation for Superconductivity and Elasticity AU - Hong , Qingguo AU - Ma , Limin AU - Fortino , Daniel AU - Chen , Long-Qing AU - Xu , Jinchao JO - Communications in Computational Physics VL - 5 SP - 1498 EP - 1514 PY - 2025 DA - 2025/09 SN - 38 DO - http://doi.org/10.4208/cicp.OA-2023-0239 UR - https://global-sci.org/intro/article_detail/cicp/24464.html KW - Efficiency, preconditioner, Ginzburg-Landau equation, elasticity. AB -

A decoupled finite element algorithm is developed for simulating the vortex dynamics on an elastic superconductor which couples the time-dependent Ginzburg-Landau equation with the complex-valued superconducting order parameter and the vector-valued magnetic potential, and the elasticity equation. We present an iterative algorithm for the decoupled system arising from the time and spatial discretization using a combination of preconditioner, algebraic multigrid method (AMG) and preconditioned conjugate gradient method (PCG). The iterative algorithm allows us to perform large-scale three-dimensional simulations of mesoscale pattern formation during superconducting phase transitions with arbitrary elastic boundary conditions. The performance and efficiency of the algorithm are numerically verified by several benchmark problems, exhibiting up to two orders of magnitude improvement depending on the scale of discrete system compared to the exact solver.

Hong , QingguoMa , LiminFortino , DanielChen , Long-Qing and Xu , Jinchao. (2025). An Efficient Numerical Algorithm for Solving Coupled Time-Dependent Ginzburg-Landau Equation for Superconductivity and Elasticity. Communications in Computational Physics. 38 (5). 1498-1514. doi:10.4208/cicp.OA-2023-0239
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