Re: [deal.II] Re: Mean Value Constraints

[Daniel Arndt]

Corbin,

- Using ARPACK might indeed be an option. Do you really need to know the
whole spectrum, though?
- Yes, you would just call AffineConstraints::add_line() to add constrain a
given DoF to zero. Note that it's a no-op if the DoF is already
constrained. This doesn't change the size of the linear system.
- You will need to include deal.II/lac/affine_constraints.templates.h,
deal.II/lac/affine_constraints.h only contains the declarations but not the
definitions.

Best,
Daniel

On Fri, May 19, 2023 at 12:04 PM Corbin Foucart 
wrote:

> I'm working on a similar pure Neumann problem with a rank-1 deficiency
> (pressure known only up to a constant). I've implemented the subspace
> projection method Konrad mentioned, with good results. However, I'm
> interested in comparing it to the single DoF constraint method, as well as
> an alternative penalization method alluded to in the paper by Bochev. I had
> a few questions:
>
>1. For a Sparse or ChunkSparse matrix object, is there a simple way of
>obtaining the eigenvalues? I know I can rebuild deal.ii with ARPACK, but
>this seems like overkill
>2. Exactly how would I use an AffineConstraints object to "pin" the
>degree of freedom? Is it a matter of a single call to
>AffineConstraints::add_line()? It's unclear to me from the documentation
>whether this would add an additional "row" to the linear system, or replace
>an existing one (I'd be looking to do the second)
>3. I've implemented the subspace projection by wrapping the
>ChunkSparse matrix class  and overriding the vmult() function; however, at
>the moment, I'm forced to copy an original ChunkSparse matrix object into
>the wrapped object because the
>AffineConstraints::distribute_local_to_global() function doesn't recognize
>the wrapped matrix --I receive a linker error
>
> libHDG_experimental.so: error: undefined reference to 'void
> dealii::AffineConstraints::distribute_local_to_global dealii::Vector >(dealii::FullMatrix const&, dealii::Vector const&,
> std::vector const&,
> HDG::LinearSystem::ChunkSparseWrapper&, dealii::Vector&, bool,
> std::integral_constant) const'
>
> I find that surprising, given that my wrapper class inherits publicly from
> ChunkSparseMatrix.
>
> Any guidance would be appreciated!
> Corbin
>
> On Monday, December 28, 2020 at 1:23:19 PM UTC-5 Wolfgang Bangerth wrote:
>
>> On 12/26/20 3:06 AM, Konrad Simon wrote:
>> > What one can also do is just constrain one DoF to a specific value
>> (this would
>> > also remove rigid motion in elasticity). But think about your solution
>> > variable: If it is in the Sobolev space H^1 then point evaluations may
>> not be
>> > defined for dimension larger than 2. Similarly if, for example, the
>> pressure
>> > in a mechanical or fluid problem is often just in L^2. Point
>> evaluations do
>> > not make sense there at all.
>>
>> Right, this is the correct approach: Constrain a single degree of freedom
>> to
>> zero (or any other value you choose) and solve the problem. Then you can
>> subtract the mean value of the solution *after* solving the linear
>> system.
>> (See VectorTools::subtract_mean_value and
>> VectorTools::compute_mean_value.)
>>
>> If you're uncomfortable with the ill-posedness of taking a point value,
>> you
>> can also take the mean value along a small segment of the boundary
>> (step-1) or
>> a small part of the domain. But in practice, this is not necessary and
>> Konrad's solution is what everyone seems to be doing.
>>
>> Best
>> W.
>>
>> --
>> 
>> Wolfgang Bangerth email: bang...@colostate.edu
>> www: http://www.math.colostate.edu/~bangerth/
>>
>> --
> The deal.II project is located at http://www.dealii.org/
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> .
>

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Re: [deal.II] Re: Mean Value Constraints

[Corbin Foucart]

I'm working on a similar pure Neumann problem with a rank-1 deficiency 
(pressure known only up to a constant). I've implemented the subspace 
projection method Konrad mentioned, with good results. However, I'm 
interested in comparing it to the single DoF constraint method, as well as 
an alternative penalization method alluded to in the paper by Bochev. I had 
a few questions:

   1. For a Sparse or ChunkSparse matrix object, is there a simple way of 
   obtaining the eigenvalues? I know I can rebuild deal.ii with ARPACK, but 
   this seems like overkill 
   2. Exactly how would I use an AffineConstraints object to "pin" the 
   degree of freedom? Is it a matter of a single call to 
   AffineConstraints::add_line()? It's unclear to me from the documentation 
   whether this would add an additional "row" to the linear system, or replace 
   an existing one (I'd be looking to do the second)
   3. I've implemented the subspace projection by wrapping the ChunkSparse 
   matrix class  and overriding the vmult() function; however, at the moment, 
   I'm forced to copy an original ChunkSparse matrix object into the wrapped 
   object because the AffineConstraints::distribute_local_to_global() function 
   doesn't recognize the wrapped matrix --I receive a linker error

libHDG_experimental.so: error: undefined reference to 'void 
dealii::AffineConstraints::distribute_local_to_global(dealii::FullMatrix const&, dealii::Vector const&, 
std::vector const&, 
HDG::LinearSystem::ChunkSparseWrapper&, dealii::Vector&, bool, 
std::integral_constant) const'

I find that surprising, given that my wrapper class inherits publicly from 
ChunkSparseMatrix.

Any guidance would be appreciated!
Corbin

On Monday, December 28, 2020 at 1:23:19 PM UTC-5 Wolfgang Bangerth wrote:

> On 12/26/20 3:06 AM, Konrad Simon wrote:
> > What one can also do is just constrain one DoF to a specific value (this 
> would 
> > also remove rigid motion in elasticity). But think about your solution 
> > variable: If it is in the Sobolev space H^1 then point evaluations may 
> not be 
> > defined for dimension larger than 2. Similarly if, for example, the 
> pressure 
> > in a mechanical or fluid problem is often just in L^2. Point evaluations 
> do 
> > not make sense there at all.
>
> Right, this is the correct approach: Constrain a single degree of freedom 
> to 
> zero (or any other value you choose) and solve the problem. Then you can 
> subtract the mean value of the solution *after* solving the linear system. 
> (See VectorTools::subtract_mean_value and VectorTools::compute_mean_value.)
>
> If you're uncomfortable with the ill-posedness of taking a point value, 
> you 
> can also take the mean value along a small segment of the boundary 
> (step-1) or 
> a small part of the domain. But in practice, this is not necessary and 
> Konrad's solution is what everyone seems to be doing.
>
> Best
> W.
>
> -- 
> 
> Wolfgang Bangerth email: bang...@colostate.edu
> www: http://www.math.colostate.edu/~bangerth/
>
>

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