[deal.II] Re: Relation between Solution Error Behavior and Polynomial Approximation Degree

2017-11-28 Thread seven 
I see. 

Thanks,
Jiaqi

在 2017年11月27日星期一 UTC-5下午6:31:54，Jaekwang Kim写道：
>
> No, I typically, calculate values itself and use MATLAB to draw plots. 
>
> Thanks,
>
> Jaekwang 
>
> On Monday, November 27, 2017 at 3:24:46 PM UTC-6, seven wrote:
>>
>> Hello Jaekwang,
>>
>> I am trying to generate some log-log plots, and wondering if you used the 
>> functions in deal.ii to generate the figure. If not, what did you use?
>>
>> Thanks,
>> Jiaqi
>>
>> 在 2016年9月29日星期四 UTC-4上午11:41:48，Jaekwang Kim写道：
>>>
>>>
>>> <https://lh3.googleusercontent.com/-dkfwJvgPEmc/V-00Y-c4tzI/A5s/pb0Z-IBRe-An_S39dSDzxWg1k5GJlEbKQCLcB/s1600/step7plotting.jpg>
>>>
>>> Hi all, I have question on error behavior of FEM. 
>>>
>>> I thought that the order of error is O(h^p) where h is a mesh-size and p 
>>> is polynomial degree we use in approximation. 
>>>
>>> So, I thought that if I plot an error with number of mesh in log-log 
>>> scale, than the graph will show -p slope. 
>>> However, I the error behaves little bit different from my expectation.
>>>
>>> For example, I use a step7 tutorial program (which solves Helmholtz 
>>> decomposition and compares the FEM solution with exact solution.) 
>>>
>>> The error curve showed more steep slope whenever I increase polynomial 
>>> degree approximation however, the slope is not (-p). 
>>> I reached slope (-3) when I used fifth-degree polynomial 
>>> approximation...   
>>> You can check this behavior in attached picture. 
>>>
>>> Until now, I have considered, 
>>>
>>> 1. Mapping(From reference cell to real cell) degree (which is originally 
>>> set to 1 but I used higher mapping) 
>>> 2. Instead of Qgauss quadrature, I am using QgaussLobatto Quadrature for 
>>> any integration over cells. 
>>> 3. Shape function , again I tried to use QgaussLobatto node point for 
>>> this) 
>>>
>>> is there any suggestion that I need to fix more? 
>>> or my first prediction that the slope will show '-p' or error will just 
>>> behave O(h^p) was wrong?
>>>
>>> I am always thank you for all guys!
>>>
>>> Jaekwang Kim  
>>>
>>

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[deal.II] Re: Relation between Solution Error Behavior and Polynomial Approximation Degree

2017-11-27 Thread seven 
Hello Jaekwang,

I am trying to generate some log-log plots, and wondering if you used the 
functions in deal.ii to generate the figure. If not, what did you use?

Thanks,
Jiaqi

在 2016年9月29日星期四 UTC-4上午11:41:48，Jaekwang Kim写道：
>
>
> 
>
> Hi all, I have question on error behavior of FEM. 
>
> I thought that the order of error is O(h^p) where h is a mesh-size and p 
> is polynomial degree we use in approximation. 
>
> So, I thought that if I plot an error with number of mesh in log-log 
> scale, than the graph will show -p slope. 
> However, I the error behaves little bit different from my expectation.
>
> For example, I use a step7 tutorial program (which solves Helmholtz 
> decomposition and compares the FEM solution with exact solution.) 
>
> The error curve showed more steep slope whenever I increase polynomial 
> degree approximation however, the slope is not (-p). 
> I reached slope (-3) when I used fifth-degree polynomial approximation... 
>   
> You can check this behavior in attached picture. 
>
> Until now, I have considered, 
>
> 1. Mapping(From reference cell to real cell) degree (which is originally 
> set to 1 but I used higher mapping) 
> 2. Instead of Qgauss quadrature, I am using QgaussLobatto Quadrature for 
> any integration over cells. 
> 3. Shape function , again I tried to use QgaussLobatto node point for 
> this) 
>
> is there any suggestion that I need to fix more? 
> or my first prediction that the slope will show '-p' or error will just 
> behave O(h^p) was wrong?
>
> I am always thank you for all guys!
>
> Jaekwang Kim  
>

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[deal.II] Re: Vertices constraints inside the domain

2017-03-23 Thread seven 
Guess I figured it out. I didn't do 
constraints.distribute();


在 2017年3月23日星期四 UTC-4上午1:38:32，seven写道：
>
>
> Hello all,
>
> I am trying to project a solution in FE_DGP(sol_dg) to FE_Q (sol_cg), but 
> I only know the gradients of sol_dg and its values at some vertices, so I 
> want to fix values of sol_cg at the same vertices after the projection.
>
> The first method I tried is quite straightforward, but the resulting 
> global matirx is very ill-conditioned. I set the corresponding row to zero 
> except the diagonal entry, and then change the right hand size.
>
> for( ; cell_c!= endc;++cell_dg, ++cell_c ){
> const unit active_index = cell_dg->active_cell_index();
> if(interface_flag[active_index] == 1){
> fe_values_continuous.reinit(cell_c);
> fe_values_v_dg.reinit(cell_dg);
> fe_values_v_dg.get_function_values(solution, solu_dg);
> cell_c->get_dof_indices(local_dof_indices_c);
> for(unit vert=0; vert<4; ++vert){
> // local_dof_indices_c[vert] global index
> const unit index_i = local_dof_indices_c[vert];
> ls_rhs_continuous(index_i) = solu_dg[vert]* aver_diag;
> for(unit i=0; i<size_m; ++i)
> ls_matrix_continuous.set(local_dof_indices_c[vert], i, 0.);
> ls_matrix_continuous.set(index_i, index_i, aver_diag);
> }
> }
>
> } 
> so I want to use constraint matrix to do the same thing, but cannot get 
> the right answer. 
>
> for( ; cell_c!= endc;++cell_dg, ++cell_c ){
> const unit active_index = cell_dg->active_cell_index();
> if(interface_flag[active_index] == 1){
> fe_values_continuous.reinit(cell_c);
> fe_values_v_dg.reinit(cell_dg);
> fe_values_v_dg.get_function_values(solution, solu_dg);
> cell_c->get_dof_indices(local_dof_indices_c);
> for(unit vert=0; vert<4; ++vert){
> // local_dof_indices_c[vert] global index
> const unit index_i = local_dof_indices_c[vert];
> constraints.add_line(index_i);
> constraints.set_inhomogeneity(index_i, solu_dg[vert]);
> }
> }
> }
> constraints.close();
>
> cell_c = dof_handler_continuous.begin_active();
> cell_dg = dof_handler.begin_active();
> for( ; cell_c!=endc; ++cell_c, ++cell_dg){
> fe_values_dg.reinit(cell_dg);
> fe_values_dg.get_function_gradients(solution, grad_dg);
>
> ls_matrix = 0;
> ls_rhs = 0;
> fe_values_continuous.reinit(cell_c);
>
> for(unit q=0; q<n_q_points; ++q){
> for(unit i=0; i<dofs_per_cell_continuous; ++i){
> ls_rhs(i) += fe_values_continuous.shape_grad(i,q)
>   * fe_values_continuous.JxW(q)
>   * grad_dg[q];
> for(unit j=0; j<dofs_per_cell_continuous; ++j)
> ls_matrix(i,j) += fe_values_continuous.shape_grad(i,q)
>* fe_values_continuous.shape_grad(j,q)
>* fe_values_continuous.JxW(q);
> }
> }
> cell_c->get_dof_indices(local_dof_indices_c);
> constraints.distribute_local_to_global (ls_matrix, ls_rhs,
> local_dof_indices_c,
> ls_matrix_continuous, 
> ls_rhs_continuous);
>
> Any help would be appreciated
>
> Thanks,
> Jiaqi 
>

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[deal.II] Vertices constraints inside the domain

2017-03-22 Thread seven 

Hello all,

I am trying to project a solution in FE_DGP(sol_dg) to FE_Q (sol_cg), but I 
only know the gradients of sol_dg and its values at some vertices, so I 
want to fix values of sol_cg at the same vertices after the projection.

The first method I tried is quite straightforward, but the resulting global 
matirx is very ill-conditioned. I set the corresponding row to zero except 
the diagonal entry, and then change the right hand size.

for( ; cell_c!= endc;++cell_dg, ++cell_c ){
const unit active_index = cell_dg->active_cell_index();
if(interface_flag[active_index] == 1){
fe_values_continuous.reinit(cell_c);
fe_values_v_dg.reinit(cell_dg);
fe_values_v_dg.get_function_values(solution, solu_dg);
cell_c->get_dof_indices(local_dof_indices_c);
for(unit vert=0; vert<4; ++vert){
// local_dof_indices_c[vert] global index
const unit index_i = local_dof_indices_c[vert];
ls_rhs_continuous(index_i) = solu_dg[vert]* aver_diag;
for(unit i=0; iactive_cell_index();
if(interface_flag[active_index] == 1){
fe_values_continuous.reinit(cell_c);
fe_values_v_dg.reinit(cell_dg);
fe_values_v_dg.get_function_values(solution, solu_dg);
cell_c->get_dof_indices(local_dof_indices_c);
for(unit vert=0; vert<4; ++vert){
// local_dof_indices_c[vert] global index
const unit index_i = local_dof_indices_c[vert];
constraints.add_line(index_i);
constraints.set_inhomogeneity(index_i, solu_dg[vert]);
}
}
}
constraints.close();

cell_c = dof_handler_continuous.begin_active();
cell_dg = dof_handler.begin_active();
for( ; cell_c!=endc; ++cell_c, ++cell_dg){
fe_values_dg.reinit(cell_dg);
fe_values_dg.get_function_gradients(solution, grad_dg);

ls_matrix = 0;
ls_rhs = 0;
fe_values_continuous.reinit(cell_c);

for(unit q=0; qget_dof_indices(local_dof_indices_c);
constraints.distribute_local_to_global (ls_matrix, ls_rhs,
local_dof_indices_c,
ls_matrix_continuous, 
ls_rhs_continuous);

Any help would be appreciated

Thanks,
Jiaqi 

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