ISFvelocity module

class ISFvelocity.computeVelocity(domain: dolfinx.mesh.Mesh, degree_psi=1)

Bases: object

assemble(hbar: float, direct: bool = False)

This function assembles the forms of the weak formulations and creates the linear structures for the solution (matrix, rhs and solver).

The velocity is computed as follows:

\[\mathbf{u} = \hbar\,\Re\{-(\Psi^*)^T\,i\,\nabla\Psi\} = \hbar\,\Re\{-i(\psi_1^*\,\nabla\psi_1+\psi_2^*\,\nabla\psi_2)\}\]

Parameters:

• hbar (float) – Value of \(\hbar\).

• direct (boolean (Default: False)) – Boolean variable to identify if a direct solver must be used.

solve(psi_1: dolfinx.fem.Function, psi_2: dolfinx.fem.Function)

This function computes the velocity given a couple of wave functions.

Parameters:

• psi_1 (dolfinx.fem.Function) – First component of the wave function \(\psi_1\).

• psi_2 (dolfinx.fem.Function) – Second component of the wave function \(\psi_2\).