Svirl: A Ginzburg-Landau (GL) solver

Svirl is an open source GPU accelerated solver that solves the two-dimensional time-dependent Ginzburg-Landau (TDGL) equations at both finite and infinite kappa limits for an arbitrary user-defined material tiling. The solver is also capable of minimizing the GL free energy using a modified non-linear conjugate-gradient method (CG). The two solvers, TDGL and CG, can be used interchangeably during the simulation.

The solver can compute the following observables: magnetic field, current and supercurrent densities, and free energy density, and can detect the presence of vortices using algorithms from the literature.

The TDGL solver supports fixing vortices at a particular position.

Main features:

• 2D time-dependent TDGL solver at finite and infinite GL parameter limits
• single and double precision floating point arithmetic
• Modified non-linear conjugate gradient solver to
• user-defined material domain for order parameter
• fixed vortices can be added by using irregular vector potential
• vortex detector (CPU version)
• observables such as GL free energy, current and supercurrent densities, and induced magnetic field

Requires:

• python3
• numpy / scipy
• pycuda (installation)
• Pillow / matplotlib / cmocean (optional)

Example:

import numpy as np
from svirl import GinzburgLandauSolver

gl = GinzburgLandauSolver(
    dx = 0.5, dy = 0.5,
    Lx = 64, Ly = 64,
    order_parameter = 'random',
    gl_parameter = 5.0,  # np.inf
    normal_conductivity = 200.0,
    homogeneous_external_field = 0.1,
    dtype = np.float64,
)

gl.solve.td(dt=0.1, Nt=1000)

gl.solve.cg(n_iter = 1000)

vx, vy, vv = gl.params.fixed_vortices.vortices
print('Order parameter: array of shape', gl.vars.order_parameter.shape)
print('%d vortices detected' % vx.size)

print('Free energy: ', gl.observables.free_energy)

ch, cv = gl.observables.current_density
print('Total current density: two arrays of shape', ch.shape, '[horizontal links] and', cv.shape, '[vertical links]')

ch, cv = gl.observables.supercurrent_density
print('Supercurrent density: two arrays of shape', ch.shape, '[horizontal links] and', cv.shape, '[vertical links]')
print('Magnetic field: array of shape', gl.observables.magnetic_field.shape)

Directory structure

• svirl — main package
  • svirl/solvers — conjugate gradient free energy minimizer and time-dependent solvers
  • svirl/mesh — material tiling and grid coordinates at cells, nodes, and edges
  • svirl/storage — storage on host and device
  • svirl/parallel — reductions and cuda device initialization
  • svirl/variables — parameters and variables
  • svirl/observables — physical observables including vortex detector
  • svirl/cuda — CUDA kernels
• docs — documentation
  • Style guide
• examples — examples and use cases
• tests — automatic and manual tests

Further reading

For details, refer to this [paper] (https://arxiv.org/pdf/1409.8340.pdf).

Code of Conduct

We follow the Microsoft Open Source Code of Conduct