[deal.II] Mesh generation issue

[Peng Wei]

Hi all,

I was trying to adapt the mesh generation method introduced by Konstantin 
Ladutenko posted 
here: 
https://groups.google.com/forum/#!searchin/dealii/sphere$20mesh%7Csort:date/dealii/pvqNQUM3eyM/o0USYKbGBQAJ

But even though I ran exactly the same code, I got a messed-up mesh (see 
attached grid-0.eps). 

As far as my understanding (a beginner), the trouble-maker is the following 
piece of code:

// 
--
 
 // skip the first and last elements in radii vector as far as they are 
already used.

for (unsigned int i = 1; i < radii.size() - 1; ++i)

{

// Find tangental faces in cells and refine in tangental 
direction.

for (auto cell : triangulation.active_cell_iterators()) {

if (grid_center.distance (cell->center())  < radii[i-1]) 
continue;

for (unsigned int f=0; f < 
GeometryInfo::faces_per_cell;  ++f)

{

bool is_tangental = true;

const double dist = grid_center.distance 
(cell->face(f)->vertex(0));

for (unsigned int v=0; v < 
GeometryInfo::vertices_per_face;  ++v)

{

double dist2 = grid_center.distance 
(cell->face(f)->vertex(v));

if (std::abs( dist2 - dist) > min_width)

{

is_tangental = false;

break;

}

}

if (is_tangental)

{

// Number of faces is two time larger than 
number of axis.


cell->set_refine_flag(RefinementCase::cut_axis(f/2));

break;

}

}  // end of for all faces

}  // end of for all cells

triangulation.execute_coarsening_and_refinement ();

// Scale to current radius

for (auto cell : triangulation.active_cell_iterators())

{

for (unsigned int v=0; v < 
GeometryInfo::vertices_per_cell;   ++v)

{

const double dist = grid_center.distance 
(cell->vertex(v));

if (dist > radii[i-1]*1.0001 && dist < outer_radius 
* 0.)

for (int j = 0; j < dim; ++j)

cell->vertex(v)(j) *= radii[i]/dist;

}  // end of for all vertices

}  // end of for all cells

Triangulation   tmp;

GridGenerator::flatten_triangulation(triangulation,tmp);

triangulation.clear();

triangulation.copy_triangulation(tmp);
}  // end of all radii
// 
--
 

In particular, I tried with three layers (i.e., only three values in the 
input vector radii, std::vector radii = {0.1, 0.9, 1.0};)
It seems that the upper-left cell is cut incorrectly, see also the attached 
grid.eps. The cut_axis is done with the following code:


cell->set_refine_flag(RefinementCase::cut_axis(f/2));

For that particular cell, f = 0. Thus I expect anisotropic cutting along 
x-axis. But in fact it is cut isotropically. 

I am using dealii version 8.5.0.

Many thanks for any advice.

Best,
Peng

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grid-0.eps
Description: PostScript document


grid.eps
Description: PostScript document

Re: [deal.II] interpolating boundary values from a previously found FE solution

[Jaekwang Kim]

Dr. Bangerth

Is there any example tutorial related to the first approach? 


*"You can build a ConstraintMatrix object that sets boundary DoFs of V to 
the corresponding values of U. This should be easy to do." *

On Friday, March 30, 2018 at 8:15:23 AM UTC-5, Wolfgang Bangerth wrote:
>
> On 03/29/2018 11:18 PM, Mustafa Aggul wrote: 
> > 
> > suppose I assemble a system and solve it. Say my solution is U. In the 
> next 
> > step, I want to solve a different problem for V. My desire is to make V 
> > exactly same as U on the boundaries. 
> > 
>
> You can build a ConstraintMatrix object that sets boundary DoFs of V to 
> the 
> corresponding values of U. This should be easy to do. 
>
> Alternatively, you could solve for a function D so that V=U+D. D should 
> then 
> simply have zero boundary values. 
>
> Best 
>   W. 
>
> -- 
>  
> Wolfgang Bangerth  email: bang...@colostate.edu 
>  
> www: http://www.math.colostate.edu/~bangerth/ 
>
>

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[deal.II] Adding rows on system matrix connecting to dof

[Jaekwang Kim]

Hi, all 

I have a question on using deal.ii for solving unknown boundary condition 
problem. 
I have thought the most minimized related to my question. 

where I consider a navies slip boundary condition, and I have tried to 
solve this with finite difference.
For more demonstration please see following screenshot. 




Finite Difference Formulation might be...





where the last raw of matrix is added to show boundary condition at lower 
plate.

 

and I think problem is generally well posed so that I can solve this with 







Now, I am trying to solve same problem using finite element method...





The description of same boundary condition in weak form will look like 

 

 has on the boundary



for (unsigned int face=0; faceface(face)->boundary_id() == 2)

{  for (unsigned int q=0; q