quadrature_map

class QuadratureMap(mesh, deg, material, cells=None)

Bases: object

Abstract data structure to handle a user-defined material in a form.

gradients

dictionary of gradients represented by Quadrature functions

Type:

dict

fluxes

dictionary of fluxes represented by Quadrature functions

Type:

dict

internal_state_variables

dictionary of internal state variables represented by Quadrature functions

Type:

dict

external_state_variables

dictionary of internal state variables represented by Quadrature functions

Type:

dict

dx

ufl.Measure defined with consistent quadrature degree

Type:

ufl.Measure

Parameters:

• mesh (dolfinx.mesh) – The underlying Mesh object

• deg (int) – Degree of quadrature space

• material (dolfinx_materials.Material) – A user-defined material object

• cells (list, np.ndarray) – List of cells affected by the material. If None (default), acts on all cells of the domain.

advance()

Advance in time by copying current state dictionary in old state. Must be used only after having converged globally.

derivative(F, u, du)

Computes derivative of non-linear form F

eval_quadrature(ufl_expr, fem_func)

Evaluates an expression at quadrature points and updates the corresponding function.

project_on(name, interp)

Computes a projection onto standard FE space.

Parameters:

• name (str) – Name of the field to project

• interp (tuple) – Tuple of interpolation space info to project on, e.g. (“DG”, 0). Shape is automatically deduced.

register_external_state_variable(name, ext_state_var)

Registers a UFL expression as an external state variable.

Parameters:

• name (str) – Name of the external state variable field

• ext_state_var (float, np.ndarray, UFL expression) – Constant or UFL expression to register, e.g. fem.Function(V, name=”Temperature”)

register_gradient(name, gradient)

Registers a UFL expression as a gradient.

Parameters:

• name (str) – Name of the gradient field

• gradient (UFL expression) – UFL expression to register, e.g. ufl.grad(u)

update()

Perform constitutive update call.

update_external_state_variables()

Update material external state variables with dolfinx values.

update_initial_state(field_name, value=None)

Update a material field with corresponding dolfinx object.

update_material_properties()

Update material properties from provided values.

update_material_rotation_matrix()

Update material rotation matrix with dolfinx values.