FastFourier2DSolver¶

class FastFourier2DSolver(boundary_conditions=None, order=None)¶

The Hybrid FFT2D + Finite-Difference-1D Poisson solver.

Parameters:

boundary_conditions (list of DirichletBoundaryCondition | NeumannBoundaryCondition | PeriodicBoundaryCondition | MultipoleBoundaryCondition) –
A list of shape (3,2) specifying the boundary conditions on the 6 surfaces of the unit cell for the configuration.
Default:
- MoleculeConfiguration: [[PeriodicBoundaryCondition()] * 2] * 3
- BulkConfiguration: [[PeriodicBoundaryCondition()] * 2] * 3
- SurfaceConfiguration:
```
[[PeriodicBoundaryCondition()] * 2,
 [PeriodicBoundaryCondition()] * 2,
 [DirichletBoundaryCondition(), NeumannBoundaryCondition()]]
```
- DeviceConfiguration:
```
[[PeriodicBoundaryCondition()] * 2,
 [PeriodicBoundaryCondition()] * 2,
 [DirichletBoundaryCondition()] * 2]
```
order (int) – The order of the finite difference kernel used for solving in the C-direction. Must be either 1 or 2.
Default: 2

boundaryConditions()¶

Returns:	The boundary conditions for the solver.
Return type:	list of `DirichletBoundaryCondition` \| `NeumannBoundaryCondition` \| `PeriodicBoundaryCondition` \| `MultipoleBoundaryCondition`

order()¶

Returns:	The order.
Return type:	int

Usage Examples¶

Define a FastFourier2DSolver with periodic boundary conditions:

poisson_solver = FastFourier2DSolver(
    boundary_conditions=[
        [PeriodicBoundaryCondition(), PeriodicBoundaryCondition()],
        [PeriodicBoundaryCondition(), PeriodicBoundaryCondition()],
        [PeriodicBoundaryCondition(), PeriodicBoundaryCondition()]
    ]
)

calculator = LCAOCalculator(
    poisson_solver=poisson_solver
)

Define a FastFourier2DSolver with Dirichlet boundary conditions in the C-direction:

poisson_solver = FastFourier2DSolver(
    boundary_conditions=[
        [PeriodicBoundaryCondition(), PeriodicBoundaryCondition()],
        [PeriodicBoundaryCondition(), PeriodicBoundaryCondition()],
        [DirichletBoundaryCondition(), DirichletBoundaryCondition()]
    ]
)

calculator = LCAOCalculator(
    poisson_solver=poisson_solver
)

Notes¶

The FastFourier2DSolver uses a FFT in the A, B directions and a finite difference operator in the C direction to solve Poisson’s equation [ONK10].

The FastFourier2DSolver is the default solver for a DeviceConfiguration that has no metallic and dielectric regions.

Reference¶

[ONK10]

T. Ozaki, K. Nishio, and H. Kino. Efficient implementation of the nonequilibrium green function method for electronic transport calculations. Phys. Rev. B, 81:035116, 2010. doi:10.1103/PhysRevB.81.035116.