[firedrake] difference between matrix-action and form-action

[Lawrence Mitchell]

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On 27/04/15 12:04, Eike Mueller wrote:
> Dear firedrakers,
> 
> Assume I have assembled a UFL form in the HDiv space:
> 
> form_uu = [a UFL form] mat_uu = assemble(form_uu,bcs=bcs)

This assembles an operator with bcs applied, useable in a linear
solver.  The rows /and/ columns corresponding to the BC nodes are the
identity.

> then shouldn’t the following two experssions fo exactly the same
> thing?
> 
> version A: with v.dat.vec as y: with u.dat.vec_ro as x: 
> mat_uu.M.handle.mult(x,y)

So this computes I_{Gamma} + A_{Omega \ Gamma}, i.e. on the boundary
nodes y is x elsewhere it's Ax.

> version B: v = self._mutilde._form_action(u)

This computes the action of A on u /without/ boundary conditions.
What are you expecting to see?, Ax on the non-boundary condition
nodes, bc-value on the boundary values?

> as fas as I can tell, only version B gives the correct result in my
> case.

Lawrence
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