Functions

Indicator Fields

flatiron_tk.functions.indicator_fields.build_field_scalar_function(domain_mesh, fictitious_mesh, inside_value, outside_value, name=None)

Create a scalar function defined on the domain mesh that is constant inside the fictitious mesh and has a different value outside. :param domain_mesh: The mesh of the domain where the function is defined. :type domain_mesh: flatironx.mesh :param fictitious_mesh: The mesh of the fictitious region where the function takes the inside value. :type fictitious_mesh: flatironx.mesh :param inside_value: The value of the function inside the fictitious region. :type inside_value: float :param outside_value: The value of the function outside the fictitious region. :type outside_value: float :param name: The name of the function. If not provided, name will default to “field_scalar_function”. :type name: str, optional

Returns:

A function defined on the domain mesh, where each local degree of freedom (DOF) is assigned the inside value if it is in the fictitious region, and the outside value otherwise.

Return type:

dolfinx.fem.Function

flatiron_tk.functions.indicator_fields.build_rank_indicator_function(mesh, name=None)

Create a scalar function that indicates the rank of the process on which it is defined. :param mesh: The mesh on which the function is defined. :type mesh: flatironx.mesh :param name: The name of the function. If not provided, name will default to “PID”. :type name: str, optional

Returns:

A function defined on the mesh, where each local degree of freedom (DOF) is assigned the rank ID.

Return type:

dolfinx.fem.Function

Utilities

class flatiron_tk.functions.utils.PointEvaluator(mesh)

Bases: object

Efficiently evaluate finite element functions at user-specified points without rebuilding the bounding box tree each time.

Parameters:

mesh (flatiron_tk.Mesh) – The mesh on which the function is defined.

evaluate_point(function, point, show_warning=True)

Evaluate a Dolfinx Function at a single point in parallel. Returns the value or None if the point is outside the mesh.

Parameters:

• function (dolfinx.fem.Function) – The function to evaluate.

• point (array-like) – Point at which to evaluate.

• show_warning (bool, optional) – Whether to show a warning if the point is outside the mesh. Default is True.

Returns:

value – Function value at the point (as a list) or None if outside the mesh.

Return type:

list or None

evaluate_set(function, points)

Evaluate a Dolfinx Function at multiple points in parallel. Returns the points (as Nx3 array) and a list of values (or None if outside mesh).

Parameters:

• function (dolfinx.fem.Function) – The function to evaluate.

• points (sequence of array-like) – Points at which to evaluate.

Returns:

• points_3d (np.ndarray) – Nx3 array of points.

• merged (list) – List of function values at each point (None if outside mesh).

flatiron_tk.functions.utils.compute_flowrate(flow_physics, id, previous=False)

Computes the flow rate across a specified boundary in the Navier-Stokes simulation.

Parameters:

• flow_physics (TransientNavierStokes, SteadyNavierStokes, or SteadyStokes) – The flow physics object containing the solution and mesh information.

• id (int) – The boundary ID across which to compute the flow rate.

• previous (bool, optional) – If True, use the previous time step’s solution for transient simulations. Default is False.

Returns:

flowrate – A function representing the flow rate across the specified boundary.

Return type:

dolfinx.fem.Function

flatiron_tk.functions.utils.constant(mesh: Mesh, value: float | tuple) → dolfinx.fem.Constant

Create a dolfinx.fem.Constant with a specified value on a given mesh.

Parameters:

• mesh (flatiron_tk.Mesh) – The mesh to associate the constant with.

• value (float or tuple) – The value to assign to the constant. Can be a single float or a tuple of floats.

Returns:

The constant object defined on the mesh with the specified value.

Return type:

dolfinx.fem.Constant