Extracting a component of FESystem for use elsewhere

[Corbin Foucart]

Hi everyone,

This might be a simple question, but I haven't found a straightforward answer in the "handling vector-valued problems" documentation.

If I have a Vector<double> which stores the solution to an FESystem, say 3 FE_DGQ fields for u, v, p, and I want to extract a new Vector<double> which corresponds to only the pressure, what's the best way to do this?

I'm not looking to write the data out for visualization, how to use the DataComponentInterpretation classes is clear to me. What I want to do is extract a separate Vector<double> which I can then add to another DG scalar field of the same type as p in the (u,v,p) system.

I don't need p at the quadrature points, only the nodal values to add to another nodal field.

Any advice would be appreciated!

Corbin

[Corbin Foucart]

I've found one way to do this, but I imagine it's not optimal:

• call DoFRenumbering::component_wise(fesys_dofh)
• Do the finite element solve
• then copy from one vector to another using the number of dofs in that component and an offset
• This isn't great, however, because I'd rather store the fesys dofh cell-by-cell for memory-friendliness, as almost all other operations are elemental

If there's a better way, I'd be glad to know :)

Best,

Corbin 

[Paras Kumar]

Hi Corbin,

The cell-wise solution corresponding to the p field could be determined as follows:

```

dealii::FEValuesExtractorScalar pressureExtractor(2); //assuming you have three scalar fields and pressure is the last one

dealii::Vector<double> solVecPerCell(nDOFsPerCell);

feValues[pressureExtractor].get_function_values(totalSolution, solVecPerCell); // here only the values corresponding to pressure are filled.

```

You could then use this cell-wise values of the p-field in whatever manner you wish.

Another alternative approach, which I employ, is to use BlockVector object, wherein one can easily get the total solution vector corresponding to any of the fields.

Best regards,

Paras

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[Corbin Foucart]

Hi Paras,

Thanks for the reply!

```

dealii::FEValuesExtractorScalar pressureExtractor(2); //assuming you have three scalar fields and pressure is the last one

dealii::Vector<double> solVecPerCell(nDOFsPerCell);

feValues[pressureExtractor].get_function_values(totalSolution, solVecPerCell); // here only the values corresponding to pressure are filled.

```

 

Suppose I have 2 DG elements of order 3, i.e., 16 DoFs per element. U, v, p -> 2*(16)*3 = 96 DoF in totalSolution.

It's my understanding that this will extract the pressure values from totalSolution into the *cell-local* Vector<double> solVecPerCell of length 16 (assuming FEValues was instantiated with a quadrature rule that contained the nodal locations, rather than the usual quadrature points). However, this isn't what I want to do. I want to take all 32 of the p nodal values and add them to another field with a DoFHandler instantiated using a single FE_DGQ element, rather than a system--therefore with a solution Vector<double> containing 32 DoF.

Maybe the way to go is a BlockVector object as you alternatively suggest, but my problem doesn't inherently have blocks. I'm simply looking to add, for example, the pressure field to another scalar DG field unrelated to the system; I'd rather keep the FESystem organized by (u,v,p) on each cell.

Best,

Corbin  

[Wolfgang Bangerth]

On 6/17/21 1:13 AM, Corbin Foucart wrote:
>
> Maybe the way to go is a BlockVector object as you alternatively suggest, but
> my problem doesn't inherently have blocks. I'm simply looking to add, for
> example, the pressure field to another scalar DG field unrelated to the
> system; I'd rather keep the FESystem organized by (u,v,p) on each cell.

Corbin,
if you don't want to go the route of block vectors, take a look at
DoFTools::extract_dofs(), which provides you with an index set of all of the
DoFs that correspond to specific vector components.

Best
W.

--
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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/