[firedrake] square root of matrix

[Colin Cotter]

Hi Francis,
 Actually taking the sqrt of the Laplacian matrix doesn't give you the
right thing for SQG, because the mass matrix is involved. If you want to do
SQG with finite elements you really have to mesh the 3D domain and solve
the 3D Poisson equation on that, and extract the surface values.

all the best
--cjc

On 14 February 2017 at 15:47, Francis Poulin <fpoulin at uwaterloo.ca> wrote:

> Hello Colin,
>
> I don't have an answer to your question but I am very curious to know if
> someone else.
>
> In the Surface QG model, to determine the streamfunction from the buoyancy
> you need to solve an equation that looks like
>
> b = - (Laplacian)^1/2 \psi
>
> What people typically do is to transform everything into spectral space
> where it then becomes
>
> \hat b = - K \hat \psi
>
> It requires using FFT's, which are easily accessible, but I'm not sure if
> this is relevant to the problem you want to solve.
>
> If someone figures out how to do this in Firedrake I would be happy to add
> another SQG demo, since it would only require a minor change from the
> existing QG code.
>
> Cheers, Francis
>
> ------------------
> Francis Poulin
> Associate Professor
> Department of Applied Mathematics
> University of Waterloo
>
> email:           fpoulin at uwaterloo.ca
> Web:            https://uwaterloo.ca/poulin-research-group/
> Telephone:  +1 519 888 4567 x32637 <(519)%20888-4567>
>
> ------------------------------
> *From:* firedrake-bounces at imperial.ac.uk [firedrake-bounces at imperial.ac.uk]
> on behalf of Colin Cotter [colin.cotter at imperial.ac.uk]
> *Sent:* Tuesday, February 14, 2017 3:21 AM
> *To:* firedrake
> *Subject:* [firedrake] square root of matrix
>
> Dear all,
>   For weird reasons I'd like to solve Ux = y where U is the Cholesky
> square root of a given symmetric positive definite matrix A. Is there a way
> to abuse the PETSc solver interface into doing this?
>
> all the best
> --cjc
>
> --
> http://www.imperial.ac.uk/people/colin.cotter
>
> www.cambridge.org/9781107663916
>
>
>


-- 
http://www.imperial.ac.uk/people/colin.cotter

www.cambridge.org/9781107663916
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