Re: [deal.II] Re: How to compute convergence rate of L2 norm of error without exact solution? And how to compute convergence rate of in different golobally refinement?

2019-03-19 Thread Wolfgang Bangerth 
On 2/27/19 2:40 AM, chucui1...@gmail.com wrote:
> 
> I have used SolutionTransfer as you say, but if I set a phi_0 fixed, then 
> project it into finite element space and get a vector phi_0_h, then I get 
> phi_0_h/2, phi_0_h/4, phi_0_h/8 by using SolutionTransfer, but the norm 
> of (phi_0_h- phi_0_h/2), (phi_0_h/2- phi_0_h/4), (phi_0_h/4- phi_0_h/8) are 
> so 
> big, and I cannot get exact value when I compute the convergence rate. So I 
> wander how to deal with it?
> 
> And the attached is the test code, and the results is:
> phi_0_norm_58:  0.335377  phi_0_norm_68:  0.317158  phi_0_norm_78:  0.277344

Chucui,
have you solved this problem since?

It's not quite clear to me what exactly you are doing here, i.e., which of the 
quantities you have above are *computed* on each mesh, and which ones are 
interpolated from the previous mesh.

Best
  W.


-- 

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

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[deal.II] Re: How to compute convergence rate of L2 norm of error without exact solution? And how to compute convergence rate of in different golobally refinement?

2019-02-27 Thread chucui1016 
Dear Prof. Arndt,

I have used SolutionTransfer as you say, but if I set a phi_0 fixed, then 
project it into finite element space and get a vector phi_0_h, then I get 
phi_0_h/2, phi_0_h/4, phi_0_h/8 by using SolutionTransfer, but the norm 
of (phi_0_h- phi_0_h/2), (phi_0_h/2- phi_0_h/4), (phi_0_h/4- phi_0_h/8) are 
so big, and I cannot get exact value when I compute the convergence rate. 
So I wander how to deal with it? 

And the attached is the test code, and the results is:
phi_0_norm_58:  0.335377  phi_0_norm_68:  0.317158  phi_0_norm_78:  0.277344

Thank you very much!

Best,
Chucui

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// Then we need to include the header file for the sparse direct solver
// UMFPACK:
#include 

// This includes the library for the incomplete LU factorization that will be
// used as a preconditioner in 3D:
#include 

// This is C++:
#include 
#include 
#include 
#include 
#include 
using namespace std;
// As in all programs, the namespace dealii is included:
namespace Step22
{
  using namespace dealii;


  template 
  class StokesProblem
  {
  public:
StokesProblem (const unsigned int phi_degree);
void run ();
  private:
void setup_dofs_pbc_rf (const int refine_number);
void phi_0_trans ();
 
double norm_compute_phi_0 (const Vector solu_1,
 const Vector solu_2); 
void create_mesh();
void refine_mesh ();

const unsigned int   degree;

Triangulation   triangulation_active;
Triangulation   triangulation;
FE_Qfe_phi;

DoFHandler  dof_handler_phi;
ConstraintMatrix constraints_phi;
Vector phi_0, phi_0_5, phi_0_6, phi_0_7, phi_0_8, tmp_phi_0_5, tmp_phi_0_6, tmp_phi_0_7, tmp_phi_0_8;
 
double time_step, time;
const double A, B, sita_0, eps, m, eps_4, tau, k_0, C_L, D_u, L_1, L_2, L_0, T_M, C_0, C_1, eps_F, e_L_T_M;//, s;
unsigned int timestep_number = 1;
  
  };

  
  template 
  StokesProblem::StokesProblem (const unsigned int phi_degree)
:
degree (phi_degree),
fe_phi (degree),
dof_handler_phi (triangulation),
time_step (1e-4),
timestep_number (1),
A (100.0), 
B (1.0), 
sita_0 (1*numbers::PI/4), 
eps (0.01), 
m (4.0), 
eps_4 (1./15.0), 
tau (3.0), 
k_0 (0.0), 
C_L (0.6), 
D_u (0.0001), 
L_1 (0.0), 
L_2 (0.0), 
L_0 (0.5), 
T_M (1.0), 
C_0 (1.0), 
C_1 (1.0),
eps_F (1.0),
e_L_T_M (0.0)
  {}  


  template 
  class InitialValues_phi : public Function
  {
  public:
InitialValues_phi () : Function() {}

virtual double value (const Point   ,
  const unsigned int  component = 0) const;

  };
  
  
  template 
  double InitialValues_phi::value (const Point   ,
   const unsigned int component) const
  {
  const double C_0 = 1.0,
   C_1 = 1.0,
   A = 100.0;
  const double delta = 0.1, r0 = std::sqrt(0.018);
  double phi_value = 0, e_value = 0, q_value = 0, s_value = 0, r = 0, T_value = 0;
   r = std::sqrt((p[0] - 0.28125) * (p[0] - 0.28125) + (p[1] - 0.28125) * (p[1] - 0.28125)) ;
 phi_value = -0.5 * std::tanh((r0-r)/delta) + 0.5;
 //phi_value = 0.5 * std::cos(p[0]) * std::cos(p[1]) +0.5;
 return phi_value;
  
  }  

  template 
  class InitialValuesConv : public Function
  {
  public:
InitialValuesConv () : Function() {}

virtual double value (const Point   ,
  const unsigned int  component = 0) const;

  };


  template 
  double
  InitialValuesConv::value (const Point  ,
 const unsigned int component) const
  {

[deal.II] Re: How to compute convergence rate of L2 norm of error without exact solution? And how to compute convergence rate of in different golobally refinement?

2019-02-27 Thread chucui1016 
Dear Prof. Arndt,

I have used SolutionTransfer as you say, but if I set a phi_0 fixed, then 
project it into finite element space and get a vector phi_0_h, then I get 
phi_0_h/2, phi_0_h/4, phi_0_h/8 by using SolutionTransfer, but the norm 
of (phi_0_h- phi_0_h/2), (phi_0_h/2- phi_0_h/4), (phi_0_h/4- phi_0_h/8) are 
so big, and I cannot get exact value when I compute the convergence rate. 
So I wander how to deal with it? 

And the attached is the test code, and the results is:
phi_0_norm_58:  0.335377  phi_0_norm_68:  0.317158  phi_0_norm_78:  0.277344

Thank you very much!

Best,
Chucui

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[deal.II] Re: How to compute convergence rate of L2 norm of error without exact solution? And how to compute convergence rate of in different golobally refinement?

2019-02-21 Thread chucui1016 
Dear Prof.Arndt,

Thank you very much! I understand what you say. It helps me a lot!

Best,
Chucui

在 2019年2月21日星期四 UTC+8下午7:31:20，Daniel Arndt写道：
>
> Chucui,
>
>
> For Question 1, I write a code to compute the L2 norm of (solution_1 - 
>> solution_2):
>> [...]
>>
>> Is that right?
>>
> You can just take the difference of the two variables and use 
> VectorTools::integrate_difference with a Functions::ZeroFunction as "exact 
> solution".
>  
>  
>
>>
>> For question 2, as the 2 solution vectors have different sizes, we don't 
>> have the same cells, so the cell loop cannot compute altogether:
>> typename DoFHandler::active_cell_iterator
>> cell_1 = dof_handler_1.begin_active(),
>> endc_1 = dof_handler_1.end(); 
>> typename DoFHandler::active_cell_iterator
>> cell_2 = dof_handler_2.begin_active();  
>> for (; cell_1!=endc_2; ++cell_1, ++cell_2)
>>   {}
>>
>> I wander how to solve this problem?
>>
> You need to interpolate the solution computed on the coarser mesh to the 
> finer mesh using SolutionTransfer(
> https://www.dealii.org/current/doxygen/deal.II/classSolutionTransfer.html, 
> explained e.g. in 
> https://www.dealii.org/current/doxygen/deal.II/step_26.html). Then, you 
> can take the difference just as in your first question.
>
> Best,
> Daniel
>

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[deal.II] Re: How to compute convergence rate of L2 norm of error without exact solution? And how to compute convergence rate of in different golobally refinement?

2019-02-21 Thread Daniel Arndt 
Chucui,


For Question 1, I write a code to compute the L2 norm of (solution_1 - 
> solution_2):
> [...]
>
> Is that right?
>
You can just take the difference of the two variables and use 
VectorTools::integrate_difference with a Functions::ZeroFunction as "exact 
solution".
 
 

>
> For question 2, as the 2 solution vectors have different sizes, we don't 
> have the same cells, so the cell loop cannot compute altogether:
> typename DoFHandler::active_cell_iterator
> cell_1 = dof_handler_1.begin_active(),
> endc_1 = dof_handler_1.end(); 
> typename DoFHandler::active_cell_iterator
> cell_2 = dof_handler_2.begin_active();  
> for (; cell_1!=endc_2; ++cell_1, ++cell_2)
>   {}
>
> I wander how to solve this problem?
>
You need to interpolate the solution computed on the coarser mesh to the 
finer mesh using 
SolutionTransfer(https://www.dealii.org/current/doxygen/deal.II/classSolutionTransfer.html,
 
explained e.g. in 
https://www.dealii.org/current/doxygen/deal.II/step_26.html). Then, you can 
take the difference just as in your first question.

Best,
Daniel

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[deal.II] Re: How to compute convergence rate of L2 norm of error without exact solution? And how to compute convergence rate of in different golobally refinement?

2019-02-21 Thread chucui1016 
Hi, all,

If there is no function to compute convergence above, I need to write the 
code by myself.

For Question 1, I write a code to compute the L2 norm of (solution_1 - 
solution_2):

template 
  double StokesProblem::norm_compute (const Vector solu_1,
  const Vector solu_2)
  {
QGauss   quadrature_formula(degree+2);

FEValues fe_values (fe, quadrature_formula,
 update_values|
 update_quadrature_points  |
 update_JxW_values |
 update_gradients);
  
const unsigned int   dofs_per_cell   = fe.dofs_per_cell;

const unsigned int   n_q_points  = quadrature_formula.size();
FullMatrix   local_con_rate_matrix (dofs_per_cell, 
dofs_per_cell);
std::vector local_dof_indices (dofs_per_cell); 

std::vector solu_1_values(n_q_points);
std::vector solu_2_values(n_q_points);

double norm_12 = 0, norm_24 = 1,norm_12_square = 0, norm_24_square = 1, 
rate_124 = 0, con_rate = 0; 
typename DoFHandler::active_cell_iterator
cell = dof_handler.begin_active(),
endc = dof_handler.end();   
for (; cell!=endc; ++cell)
  {
fe_values.reinit (celli);  
fe_values.get_function_values (solu_1, solu_1_values);
fe_values.get_function_values (solu_2, solu_2_values);
for (unsigned int q=0; q::active_cell_iterator
cell_1 = dof_handler_1.begin_active(),
endc_1 = dof_handler_1.end(); 
typename DoFHandler::active_cell_iterator
cell_2 = dof_handler_2.begin_active();  
for (; cell_1!=endc_2; ++cell_1, ++cell_2)
  {}

I wander how to solve this problem?

Thanks in advance!
Best,
Chucui

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