Coefficients

Coefficients represent fields defined on the mesh. These can be either scalar or vector-valued. They are used in various components of mufem, including reports, boundary conditions, and models.

Coefficients are registered to the Coefficient Manager either automatically by models or manually by users.

Coefficient Manager

The mufem.CoefficientFunctionManager manages all scalar and vector coefficient functions used in the simulation. Once registered, coefficients can be used in reports or exported using the Field Exporter.

coefficient_manager = sim.get_coefficient_manager()

Coefficients are registered in two main ways:

1. Via a model:

   Models automatically register coefficients when added to the simulation. As an example, the Refinement Model registers several coefficients

   model = mufem.RefinementModel()
   sim.get_model_manager().add_model(model)
   
   print(sim.get_coefficient_manager().list_functions())
   

   ['Cell Volume', 'Element Type', 'Refinement Level', 'Global Cell Index', 'Position']
   

2. Manually by user:

   Users can define and register their own coefficients, see User Coefficients, using:

   cff = mufem.CffConstantScalar(1.23)
   sim.get_coefficient_manager().register_user("MyScalar", cff)
   
   print(sim.get_coefficient_manager().list_functions())
   

   ['MyScalar', ...]
   

User Coefficients

Several types of coefficients are available in mufem.

Constant Scalar Coefficient

mufem.CffConstantScalar defines a scalar field with a constant value.

cff_constant_scalar = mufem.CffConstantScalar(value=1.23)

Sinusoidal Coefficient

mufem.CffSinusoidal defines a time-varying sinusoidal scalar field.

cff_sin = mufem.CffSinusoidal(amplitude=2.0, frequency=50.0, phase=30.0)

Time Table Coefficient

mufem.CffTimeTable defines a piecewise scalar function over time.

cff_time_table = mufem.CffTimeTable(time=[0.1, 0.2, 0.3], value=[1.0, 2.0, 3.0])

Expression-Based Coefficient

mufem.CffExpressionScalar defines a scalar field via a mathematical expression.

cff_expression = mufem.CffExpressionScalar("sqrt(x()^2 + y()^2)")

Expressions support standard functions and mesh coordinates.

Constant Vector Coefficient

mufem.CffConstantVector defines a constant 3D vector field.

cff_vector = mufem.CffConstantVector(1.0, 2.0, 3.0)

Composite Vector Coefficient

mufem.CffVectorComponent builds a vector field from three scalar coefficients.

x = mufem.CffConstantScalar(1.0)
y = mufem.CffConstantScalar(2.0)
z = mufem.CffConstantScalar(3.0)

cff_composite = mufem.CffVectorComponent(cff_x=x, cff_y=y, cff_z=z)

Example

import mufem

sim = mufem.Simulation.New("My Case", f"data/geometry.mesh", print_only_warnings=True)
cff_manager = sim.get_coefficient_manager()

# Scalar coefficients
cff_manager.register_user("MyCffConstantScalar", mufem.CffConstantScalar(1.23))
cff_manager.register_user("MyCffSinusoidal", mufem.CffSinusoidal(amplitude=2., frequency=50., phase=30.))
cff_manager.register_user("MyCffTimeTable", mufem.CffTimeTable(time=[0.1, 0.2, 0.3], value=[1.0, 2.0, 3.0]))
cff_manager.register_user("MyCffExpression", mufem.CffExpressionScalar("sqrt(x()^2 + y()^2)"))

# Vector coefficients
cff_vector = mufem.CffConstantVector(x=1.0, y=2.0, z=3.0)
cff_manager.register_user("MyCffConstantVector", cff_vector)

x = mufem.CffConstantScalar(1.0)
y = mufem.CffConstantScalar(2.0)
z = mufem.CffConstantScalar(3.0)
composite = mufem.CffVectorComponent(cff_x=x, cff_y=y, cff_z=z)
cff_manager.register_user("MyCffCompositeVector", composite)

# List all available coefficient names
print(cff_manager.list_functions())

['MyCffExpression', 'MyCffTimeTable', 'MyCffSinusoidal', 'MyCffConstantScalar', 'MyCffCompositeVector', 'MyCffConstantVector']