creating a 1D Primitive operator similar to Grad in ufl

Question

What does it take to create a Primitive ufl operator in 1d that returns the function

$$\int_0^x{u(t)dt}$$

that is similar to other ufl operator and can be used in forms?

I tried

class Primitive(ufl.Coefficient, dolfin.cpp.Expression):
    def __init__(self,f,mesh,element,constant= 0.0, **kwargs):
        dolfin.cpp.Expression.__init__(self)
        self._f = f
        self._mesh = mesh
        self._constant = constant
        subdomains = CellFunction('size_t',mesh)
        self._subdomains = subdomains
        dx = Measure('dx',domain=mesh)[subdomains]
        self._dx=dx
        self._F = Form(f*dx(1))

        ufl.Coefficient.__init__(self, element, count=self.id())

    def eval(self, values, x):

        inside_function = lambda y: y<=x[0]
        domain = AutoSubDomain(inside_function=inside_function)
        self._subdomains.set_all(0)
        domain.mark(self._subdomains,1)
        F = self._F
        values[0] = assemble(F) + self._constant

    def eval_cell(self, values, x, cell):
       self.eval(values,x)

    def ufl_evaluate(self,x, component, derivatives):
        values = np.zeros(1,dtype='d')
        self.eval(values,x)
        return values[0]

I can then do

mesh = UnitInterval(100)
V = FunctionSpace(mesh,'CG',1)
u = Expression("x[0]")
Pu = Primitive(u,mesh, V.ufl_element())
plot(Pu,mesh=mesh)

My question: is this enough to make Pu behave like other ufl operators [ exp(u), ln(u) ...] in forms?

creating a 1D Primitive operator similar to Grad in ufl

1 Answer