integration over domain for computed solutions

Question

Hi all,
I run poisson problem with different boundary conditions so I got different solutions at the end let's say 2 different solutions u1 and u2. Now, the problem is to compute this:
Integral / domain ( u1 * u2 ) dOmega.

Anyone know how to do this, please ?
Thanks in advance

Answer 1

Hi, you need

integral = assemble(u1*u2*dx)

Comments

thanks for the answer,
but could you tell me how to do it with C++ and what to put inside the UFL file ?

Thanks in advance

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Hi, in Cpp you can have a form file like this

# cg.ufl                                                                         
element = FiniteElement("CG", triangle, 1)                                       

u1 = Coefficient(element)                                                        
u2 = Coefficient(element)                                                        

form1 = u1*u2*dx                                                                 
forms = [form1]  

and then the cpp code is

#include <dolfin.h>                                                              
#include "cg.h"                                                                  

using namespace dolfin;                                                          

int main()                                                                       
{                                                                                
  UnitSquareMesh mesh(2, 2);                                                     

  Constant u1(10);                                                               
  Constant u2(10);                                                               

  cg::Form_form1 form1(mesh, u1, u2);                                            

  std::cout << assemble(form1) << std::endl;                                     

  return 0;                                                                      
}    

You might also want to take a look at this demo.

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thanks man,
your idea works great, it's a bit difficult to use FEniCS with C++ with so little documentation about the library and especially for beginners like me.
thank you again