Modeling and analysis of a periodic Ginzburg-Landau model for type-II superconductors
SIAM Journal on Applied Mathematics
Vortex configurations in type-II superconducting films
Journal of Computational Physics
Ginzburg-Landau vortices: dynamics, pinning, and hysteresis
SIAM Journal on Mathematical Analysis
SIAM Journal on Matrix Analysis and Applications
Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
Journal of Computational Physics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Algebraic Multigrid Solvers for Complex-Valued Matrices
SIAM Journal on Scientific Computing
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This paper considers the extreme type-II Ginzburg-Landau equations, a nonlinear PDE model for describing the states of a wide range of superconductors. Based on properties of the Jacobian operator and an AMG strategy, a preconditioned Newton-Krylov method is constructed. After a finite-volume-type discretization, numerical experiments are done for representative two- and three-dimensional domains. Strong numerical evidence is provided that the number of Krylov iterations is independent of the dimension n of the solution space, yielding an overall solver complexity of O(n).