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

[Eike Mueller]

Hi,

I think I just saw a rounding error, and the results are the same. I hadn’t realised that the numbers I compare are very large, so that an absolute difference of 1.E-5 is rounding error. I will simply normalise the numbers by the maximum before doing the comparison.

Thanks,

Eike

> On 27 Apr 2015, at 12:26, Eike Mueller <E.Mueller at bath.ac.uk> wrote:
> 
> Hi Lawrence,
> 
> ok, so if I apply the BCs to u before the multiplication and to v after the multiplication I would expect the result to be the same in both versions, but it doesn’t look like it.
> 
> Thanks,
> 
> Eike
> 
>> On 27 Apr 2015, at 12:19, Lawrence Mitchell <lawrence.mitchell at imperial.ac.uk> wrote:
>> 
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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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