fenicsx package

Subpackages

• fenicsx.fluid_dynamics package
  • Submodules
  • fenicsx.fluid_dynamics.steady_ns module
    • fixedValueVelocity
    • lid()
    • lid_velocity_expression()
    • noslip_boundary()
    • ns_steady_nl
      • ns_steady_nl.F_fun()
      • ns_steady_nl.J_fun()
      • ns_steady_nl.assemble()
      • ns_steady_nl.create_snes_solution()
      • ns_steady_nl.obj_fun()
      • ns_steady_nl.parameters()
      • ns_steady_nl.set_bc()
      • ns_steady_nl.set_cavity_bc()
      • ns_steady_nl.solve()
      • ns_steady_nl.update_solution()
  • fenicsx.fluid_dynamics.transient_ns module
    • drag_lift
      • drag_lift.compute()
    • pressure_projection
      • pressure_projection.advance()
      • pressure_projection.assembleForm()
    • tentative_velocity
      • tentative_velocity.advance()
      • tentative_velocity.assembleForm()
    • update_velocity
      • update_velocity.advance()
      • update_velocity.assembleForm()
  • Module contents
• fenicsx.neutronics package
  • Submodules
  • fenicsx.neutronics.neutr_diff module
    • steady_neutron_diff
      • steady_neutron_diff.assembleForm()
      • steady_neutron_diff.solve()
      • steady_neutron_diff.update_xs()
    • transient_neutron_diff
      • transient_neutron_diff.advance()
      • transient_neutron_diff.assembleForm()
      • transient_neutron_diff.update_xs()
  • fenicsx.neutronics.thermal module
    • steady_thermal_diffusion
      • steady_thermal_diffusion.assembleForm()
      • steady_thermal_diffusion.solve()
      • steady_thermal_diffusion.update_xs()
    • transient_thermal_diffusion
      • transient_thermal_diffusion.advance()
      • transient_thermal_diffusion.assembleForm()
      • transient_thermal_diffusion.update_xs()
  • Module contents

Submodules

fenicsx.backends module

class fenicsx.backends.LoopProgress(msg: str, final: float = 100)

Bases: object

A class to make progress bar.

Parameters:

• msg (str) – Message to be displayed

• final (float, optional (Default = 100)) – Maximum value for the iterations

update(step: float, percentage: bool = True)

Update message to display and clears the previous one.

Parameters:

• step (float) – Interger or float value to add at the counter.

• percentage (boolean, optional (Default = True)) – Indicates if the bar should be displayed in %.

class fenicsx.backends.norms(V: dolfinx.fem.FunctionSpace, is_H1=False, metadata_degree=4)

Bases: object

A class to compute norms and inner products. \(L^2\) and \(H^1\) (semi and full are implemented for both scalar and vector fields), whereas the average and the integral are available for scalar only.

Parameters:

• V (FunctionSpace) – Functional Space onto which the Function are defined.

• is_H1 (boolean, optional (Default = False)) – If the function belongs to \(H^1\), the forms for the inner products and norms are computed.

H1innerProd(u: dolfinx.fem.Function, v: dolfinx.fem.Function, semi=True)

Computes the \(H^1\) semi or full inner product of the functions u and v over the domain

\[\langle u, v \,\rangle_{H^1} = \int_\Omega \nabla u \cdot \nabla v\,d\Omega\]

\[(u,v)_{H^1} = \int_\Omega u\cdot v \,d\Omega + \int_\Omega \nabla u\cdot \nabla v \,d\Omega\]

Parameters:

• u (Function) – Function belonging to the same functional space V

• v (Function) – Function belonging to the same functional space V

• semi (boolean, optional (Default = True)) – Indicates if the semi norm must be computed.

Returns:

value – \(H^1\) inner product of the functions

Return type:

float

H1norm(u: dolfinx.fem.Function, semi=True)

Computes the \(H^1\) semi or full norm of the function u over the domain

\[| u |_{H^1} = \sqrt{\int_\Omega \nabla u \cdot \nabla u\,d\Omega}\]

\[\| u \|_{H^1} = \sqrt{\int_\Omega \nabla u \cdot \nabla u\,d\Omega + \int_\Omega u \cdot u\,d\Omega}\]

Parameters:

• u (Function) – Function belonging to the same functional space V

• semi (boolean, optional (Default = True)) – Indicates if the semi norm must be computed.

Returns:

value – \(H^1\) norm of the function

Return type:

float

L2innerProd(u: dolfinx.fem.Function, v: dolfinx.fem.Function)

Computes the \(L^2\) inner product of the functions u and v over the domain

\[(u,v)_{L^2}=\int_\Omega u\cdot v \,d\Omega\]

Parameters:

• u (Function) – Function belonging to the same functional space V

• v (Function) – Function belonging to the same functional space V

Returns:

value – \(L^2\) inner product between the functions

Return type:

float

L2norm(u: dolfinx.fem.Function)

Computes the \(L^2\) norm of the function u over the domain

\[\| u\|_{L^2} = \sqrt{\int_\Omega u \cdot u\,d\Omega}\]

Parameters:

u (Function) – Function belonging to the same functional space V

Returns:

value – \(L^2\) norm of the function

Return type:

float

Linftynorm(u: dolfinx.fem.Function)

Computes the \(L^\infty\) norm of a given function u over the domain

\[\| u \|_{L^\infty}=\max\limits_\Omega |u|\]

Parameters:

u (Function) – Function belonging to the same functional space V

Returns:

value – \(L^\infty\) norm of the function

Return type:

float

average(u: dolfinx.fem.Function)

Computes the integral average of a given scalar function u over the domain

\[\langle u \rangle = \frac{1}{|\Omega|}\int_\Omega u \,d\Omega\]

Parameters:

u (Function) – Function belonging to the same functional space V (it must be a scalar!)

Returns:

ave_value – Average over the domain

Return type:

float

integral(u: dolfinx.fem.Function)

Computes the integral of a given scalar function u over the domain

\[\int_\Omega u \,d\Omega\]

Parameters:

u (Function) – Function belonging to the same functional space V (it must be a scalar!)

Returns:

val – Integral over the domain

Return type:

float

fenicsx.plotting module

fenicsx.plotting.PlotScalar(fun: dolfinx.fem.Function, filename: str | None = None, format: str = 'png', varname: str | None = None, clim=None, colormap=<matplotlib.colors.LinearSegmentedColormap object>, resolution=[1080, 720], show=False)

Python function to plot a scalar field.

Parameters:

• fun (Function) – Field to plot.

• varname (str) – Name of the variable.

• filename (str) – Name of the file to save.

• clim (optional (Default = None)) – Colorbar limit, if None the mininum and maximum of fun are computed

• colormap (optional (Default = jet)) – Colormap for the plot

• resolution (list, optional (Default = [1080, 720])) – Resolution of the image

fenicsx.plotting.extract_cells(domain: dolfinx.mesh.Mesh, points: ndarray)

This function can be used to extract data along a line defined by the variables points, crossing the domain.

Parameters:

• domain (dolfinx.mesh.Mesh) – Domain to extract data from.

• points (np.ndarray) – Points listing the line from which data are extracted.

Returns:

• xPlot (np.ndarray) – Coordinate denoting the cell from which data are extracted.

• cells (list) – List of cells of the mesh.

fenicsx.plotting.get_scalar_grid(fun: dolfinx.fem.Function, varname: str, real=True)

This function extracts the dofs of a scalar function for the plot using pyvista.

Parameters:

• fun (Function) – Function from which the dofs are extracted.

• varname (str) – Name of the variable.

• real (boolean, optional (Default = True)) – Real dofs are considered, if False imaginary dofs are used.

Returns:

u_grid – Unstructured grid of values for the selected function.

Return type:

pyvista.UnstructuredGrid

Module contents

models/fenicsx.

OFELIA: FEniCSx models for MultiPhysics.