6 research outputs found
Numerical bifurcation study of superconducting patterns on a square
This paper considers the extreme type-II Ginzburg-Landau equations that model
vortex patterns in superconductors. The nonlinear PDEs are solved using
Newton's method, and properties of the Jacobian operator are highlighted.
Specifically, it is illustrated how the operator can be regularized using an
appropriate phase condition. For a two-dimensional square sample, the numerical
results are based on a finite-difference discretization with link variables
that preserves the gauge invariance. For two exemplary sample sizes, a thorough
bifurcation analysis is performed using the strength of the applied magnetic
field as a bifurcation parameter and focusing on the symmetries of this system.
The analysis gives new insight in the transitions between stable and unstable
states, as well as the connections between stable solution branches.Comment: 31 page
Numerical bifurcation study of superconducting patterns on a square
This paper considers the extreme type-II Ginzburg-Landau equations that model
vortex patterns in superconductors. The nonlinear PDEs are solved using
Newton's method, and properties of the Jacobian operator are highlighted.
Specifically, it is illustrated how the operator can be regularized using an
appropriate phase condition. For a two-dimensional square sample, the numerical
results are based on a finite-difference discretization with link variables
that preserves the gauge invariance. For two exemplary sample sizes, a thorough
bifurcation analysis is performed using the strength of the applied magnetic
field as a bifurcation parameter and focusing on the symmetries of this system.
The analysis gives new insight in the transitions between stable and unstable
states, as well as the connections between stable solution branches.Comment: 31 page
An optimal linear solver for the Jacobian system of the extreme type-II Ginzburg--Landau problem
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
of the solution space, yielding an overall solver complexity of O(n)
Numerical bifurcation~study of superconducting~patterns on a square
This paper considers the extreme type--II Ginzburg--Landau~equations that model vortex patterns in superconductors. The nonlinear PDEs are solved using Newton's method, and properties of the Jacobian operator are highlighted. Specifically, it is illustrated how the operator can be regularized using an appropriate phase condition. For a two-dimensional square sample, the numerical results are based on a finite-difference discretization with link variables that preserves the gauge invariance. For two exemplary sample sizes, a thorough bifurcation analysis is performed in the strength of the applied magnetic field with focus on the symmetries of this particular system. The analysis gives new insight in the transitions between stable and unstable states, as well as the connections between stable solution branches