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 - <p style="text-align: justify;">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.</p>