Function

class dolfin.functions.function.Function(*args, **kwargs)

Bases: ufl.coefficient.Coefficient, dolfin.cpp.function.Function

This class represents a function \(u_h\) in a finite element function space \(V_h\), given by

\[u_h = \sum_{i=1}^n U_i \phi_i,\]

where \(\{\phi_i\}_{i=1}^n\) is a basis for \(V_h\), and \(U\) is a vector of expansion coefficients for \(u_h\).

Arguments

There is a maximum of three arguments. The first argument must be a Function or a FunctionSpace.

If instantiated from another Function, the (optional) second argument must be an integer denoting the number of sub functions to extract.

In addition can a name argument be passed overruling the default name

Examples

Create a Function:

• from a FunctionSpace V

  f = Function(V)
  

• from another Function f

  g = Function(f)
  

• from a FunctionSpace V and a GenericVector v

  Warning: this constructor is intended for internal libray use only

  g = Function(V, v)
  

• from a FunctionSpace and a filename containg a GenericVector

  g = Function(V, 'MyVectorValues.xml')
  

Initialize Function.

assign(rhs)

Assign either a Function or linear combination of Functions.

Arguments

rhs (_Function_)

A Function or a linear combination of Functions. If a linear combination is passed all Functions need to be in the same FunctionSpaces.

split(deepcopy=False)

Extract any sub functions.

A sub function can be extracted from a discrete function that is in a MixedFunctionSpace or in a VectorFunctionSpace. The sub function resides in the subspace of the mixed space.

Arguments

deepcopy

Copy sub function vector instead of sharing

str(verbose=False)

Return an informative str representation of itself

sub(i, deepcopy=False)

Return a sub function.

The sub functions are numbered from i = 0..N-1, where N is the total number of sub spaces.

Arguments

i : int

The number of the sub function

ufl_element()

Return ufl element

ufl_evaluate(x, component, derivatives)

Function used by ufl to evaluate the Function