[firedrake] Question on mixed solves: RHS is not defined in product function space

[Eike Mueller]

Dear firedrakers,

assume I want to do the following solve of a mixed system:

V1 = FunctionSpace(mesh, 'RT', 1)
V2 = FunctionSpace(mesh, 'DG', 0)

W = V1 * V2
lmbda = 1
u, p = TrialFunctions(W)
v, q = TestFunctions(W)
f = Function(V1)
g = Function(V2)

a = (p*q - q*div(u) + lmbda*inner(v, u) + div(v)*p)*dx

L = (dot(u,f)+p*g)*dx

u = Function(W)
solve(a == L, u, solver_parameters=...)

But now I take out the line

L = (dot(u,f)+p*g)*dx

and assume that somewhere I calculate instead:

L1 = dot(TestFunction(V1),f)*dx
L2 = TestFunction(V2)*g*dx

L1 and L2 taken together contain the same information as L, but I can’t write L=L1+L2, because L1 and L2 were not defined using the mixed function spaces (assume that I calculated L1 and L2 somewhere else in the code, and I only use the mixed function spaces in this subroutine).
So given L1 and L2, how can I build L, which can be used in the solve? What I currently do is this:

m_u = dot(TestFunction(V1),TrialFunction(V1))*dx
m_p = TestFunction(V2)*TrialFunction(V2)*dx
f_u = Function(V1)
f_p = Function(V2)
solve(m_u=L1,f_u)
solve(m_p=L2,f_p)
L = (dot(u,f_u)+p*f_g)*dx

which I believe does the right thing, but it involves mass solves. Is there a better way? Can I copy the data over directly?

Thanks a lot,

Eike

--

Dr Eike Hermann Mueller
Research Associate (PostDoc)

Department of Mathematical Sciences
University of Bath
Bath BA2 7AY, United Kingdom

+44 1225 38 5803
e.mueller at bath.ac.uk
http://people.bath.ac.uk/em459/

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