[deal.II] Re: Discrete Galekin with periodic boundary condition

[Daniel Arndt]

Jaekwang,

It seems that I don't need to add_periodicity to the triangulation unless 
> it is parallel distributed triangulation? 
>
I would be heavily surprised if you get correct results without calling 
Triangulation::add_periodicity() if you are using discontinuous elements 
and a serial Triangulation.
Otherwise, you are not providing any kind of information to these objects 
that you want to treat specific boundaries as periodic ones. 
 

> By the way, when I 'add_periodicity', I have compiler error on the red 
>> line of the code. 
>>
>> Can you give me a clue to resolve this error? 
>>
>>   //original argument
>>
>> std::vector>
>> PeriodicFacePair::cell_iterator>> pairs;
>>
>> 
>>
>> GridTools::collect_periodic_faces(dof_handler,
>>
>>   /*b_id1*/ 6,
>>
>>   /*b_id2*/ 5,
>>
>>   /*direction*/ 0,
>>
>>   pairs);
>>
>> 
>>
>> triangulation.add_periodicity(pairs);
>>
> You need to call GridTools::collect_periodic_faces with a parameter of 
type 

std::vector::cell_iterator>> pairs;

if you want to use the resulting object for 
Triangulation::add_periodicity().
 
Best,
Daniel

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Re: [deal.II] Petrov-Galerkin stabilization approach to solve Navier-Stoke equations

[Sebastian Glane]

Hi Jie,

thanks a lot. The link to your repository was very helpful. I could 
significantly reduce the number of iterations using your implementation 
of computing the pressure laplacian through:


K_p = B diag(velocity_mass_matrix)^-1 B^T.

I have tested the dependence of the preconditioner on the time step and 
the mesh size and observed that it is likely to be mesh independent, 
i.e. if the mesh is refined the number of outer (GMRES) iterations does 
not change, which is great.


However there is a dependence on the size of the time step. Both 
variants with assembly and your implementation show an increase in the 
number of iterations.


time step
iterations with B B^T
iterations with assembly
1e-5
6 to 7
6 or 16 ringing
1e-4
8 to 9
18 to 19
1e-3
10 to 11
21 to 22
1e-2
12 to 14
24 to 27
1e-1
23 to 24
51 to 54


Did you make the same or similar observations? I have read some of the 
literature and as far as I understand it the preconditioner should be 
independent of the step size and viscosity.


Another point I would like to raise is related to  mesh independence, 
which is not quite true. In every step the solution of the pressure 
laplace matrix (K_p) requires by far the largest number of iterations. I 
am monitoring the iterations of all subsolvers:


 7 GMRES iterations for stokes system,  (A: 8, Kp: 682, Mp: 60)

For A (velocity block) one cycle of TrilinosWrappers::PreconditionAMG is 
used. Mp is preconditioned using PreconditionSSOR and for Kp I am using 
SparseILU. For the example quoted the pressure space has 4800 dofs. I am 
wondering why the SparseILU with roughly 100 iterations per precondition 
step does such a bad job in this case.


Of course, I don't expect you to answer all of this but it would great 
if you make some comments about your experience with this 
preconditioner. By the way I am also using an IMEX scheme in my solver, 
see https://github.com/sebglane/BoussinesqFluidSolver/tree/modular_version .


Best wishes,

Sebastian

On 01.11.18 17:30, Jie Cheng wrote:

Hi Sebastian,

I think what you described is correct. I could not see why it did not 
work out. But I recommend reading Timo's dissertation. Also, for the 
implementation, you can check out my code for the implicit scheme 
 
and explicit-implicit scheme 
.


Best,
Jie

On Thu, Nov 1, 2018 at 5:58 PM SebG > wrote:


Dear Jie, dear deai.ii user,

I am working on the Cahouet-Chabbard preconditioner in context
buoyancy-driven flow problems. Somehow my preconditioner does not
work quite well. The number of iterations depends on the time
step, which should not be the case. With more than 50 iterations
it is also quite large. I would like to ask if you or someone else
could provide some details of your implementation or give tips.

The velocity block of the system matrix is given by:
alpha / timestep * M + gamma * c * K .
M, K are the velocity mass and stiffness matrix. The scalars alpha
and gamma are related to the time discretization and c is a
dimensionless parameter. If I am not wrong, the Cahouet-Chabbard
Schur complement approximation is given by
S^-1 = alpha / timestep * K_p^-1 + gamma * c * M_p^-1 .

I am assembling the pressure stiffness and pressure mass matrix
explicitly. However my problem is a pure Dirichlet problem w.r.t.
the velocity, which in contrast mean that preconditioner is using
Neumann BCs. Therefore, I am constraining one pressure dof, which
regularizes the pressure laplace matrix. This approach is
discussed in another thread
.
For this reason I have two ConstraintMatrix object one for the
system matrix and one for the preconditioner.

I also attached my code which is based step-32 but in serial.

Best wishes,
Sebastian

Am Freitag, 20. Oktober 2017 09:36:07 UTC-7 schrieb Jie Cheng:

Hi Martin and Wolfgang

  Thank you very much for the helpful comments and references.
I'll start to read the works you mentioned.

Jie -- I think this would be a very interesting program
for others as well.
Would you be interested in contributing it to the code
gallery?


  I'd love to contribute after I work it out!

Jie

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[deal.II] Re: Discrete Galekin with periodic boundary condition

[Jaekwang Kim]

It seems that I don't need to add_periodicity to the triangulation unless 
it is parallel distributed triangulation? 


On Friday, November 9, 2018 at 9:45:53 AM UTC-6, Jaekwang Kim wrote:
>
> Thanks! Now it becomes clear to me. 
>
> By the way, when I 'add_periodicity', I have compiler error on the red 
> line of the code. 
>
> Can you give me a clue to resolve this error? 
>
>   //original argument
>
> std::vector
> PeriodicFacePair::cell_iterator>> pairs;
>
> 
>
> GridTools::collect_periodic_faces(dof_handler,
>
>   /*b_id1*/ 6,
>
>   /*b_id2*/ 5,
>
>   /*direction*/ 0,
>
>   pairs);
>
> 
>
> triangulation.add_periodicity(pairs);
>
> Error messages says that 
>
>
> *no viable conversion from*
>
> *  'vector *dealii::internal::DoFHandler::Iterators
> *  2>, false>::CellAccessor**>>>' to '**const*
>
>   *vector**>>>'*
>
> triangulation.add_periodicity(pairs);
>
> *  ^*
>
>
> also says that 
>
>
>   candidate constructor not viable: no known conversion from
>
>   'std::vector DoFHandler<2>::cell_iterator>
>
>   >' (aka 
> 'vector, 
> false> >
>
>   > >') to 'const
>
>   
> std::__1::vector
>   2> > >,
>
>   
> std::__1::allocator
>   2> > > > > &' for 1st argument
>
> vector(const vector& __x);
>
> *^*
>
>
>
>

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Re: [deal.II] Modelling Anistropic materials for electrostatic simulations

[phillip mobley]

Great,

Thank you Dr. Bangerth, I will start to look from some of the book. Thank
you for all of your help.

On Fri, Nov 9, 2018 at 1:29 PM Wolfgang Bangerth 
wrote:

>
> > Yes, it is true that there are many lackings in the theory of finite
> > element. For the most part, I am self taught and doing my best to learn
> > the material at hand. With that, I do have a final question, would you
> > be able to recommend some books or authors that I can start looking into
> > and reading?
>
> I learned finite elements from a more formal, mathematical perspective
> and so that's the kinds of books that I usually look things up in. The
> ones on my shelf are Brenner & Scott, and Braess. Braess is often a bit
> more intuitive, but it's still a math book at the end of the day. I also
> have a German one by Grossmann & Roos that I like because it is more
> written with applications in mind. This may not be useful to you because
> of the language, of course.
>
> There are many finite element books written from the engineering
> perspective. I don't know them well. You may want to go to the library
> and see whether they have anything by Zienkiewicz, Hughes, Oden,
> Wriggers, or others.
>
> Best
>   W.
>
> --
> 
> Wolfgang Bangerth  email: bange...@colostate.edu
> www: http://www.math.colostate.edu/~bangerth/
>
> --
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Re: [deal.II] Modelling Anistropic materials for electrostatic simulations

[Wolfgang Bangerth]

> Yes, it is true that there are many lackings in the theory of finite 
> element. For the most part, I am self taught and doing my best to learn 
> the material at hand. With that, I do have a final question, would you 
> be able to recommend some books or authors that I can start looking into 
> and reading?

I learned finite elements from a more formal, mathematical perspective 
and so that's the kinds of books that I usually look things up in. The 
ones on my shelf are Brenner & Scott, and Braess. Braess is often a bit 
more intuitive, but it's still a math book at the end of the day. I also 
have a German one by Grossmann & Roos that I like because it is more 
written with applications in mind. This may not be useful to you because 
of the language, of course.

There are many finite element books written from the engineering 
perspective. I don't know them well. You may want to go to the library 
and see whether they have anything by Zienkiewicz, Hughes, Oden, 
Wriggers, or others.

Best
  W.

-- 

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

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[deal.II] Re: Discrete Galekin with periodic boundary condition

[Jaekwang Kim]

Thanks! Now it becomes clear to me. 

By the way, when I 'add_periodicity', I have compiler error on the red line 
of the code. 

Can you give me a clue to resolve this error? 

  //original argument

std::vector::cell_iterator>> pairs;



GridTools::collect_periodic_faces(dof_handler,

  /*b_id1*/ 6,

  /*b_id2*/ 5,

  /*direction*/ 0,

  pairs);



triangulation.add_periodicity(pairs);

Error messages says that 


*no viable conversion from*

*  'vector, false>::CellAccessor**>>>' to '**const*

  *vector**>>>'*

triangulation.add_periodicity(pairs);

*  ^*


also says that 


  candidate constructor not viable: no known conversion from

  'std::vector::cell_iterator>

  >' (aka 
'vector, 
false> >

  > >') to 'const

  
std::__1::vector > >,

  
std::__1::allocator > > > > &' for 1st argument

vector(const vector& __x);

*^*



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