how to calculate the total energy?

[Yiyang Zhang]

For example, consider the sine-Gordon equation, which is in Step-25. 

With the help of the DataPostprocessor class, we can output a plot for the energy density.

But then, how could we calculate the total energy?

The best scenario would be computing the energy density and total energy at the same time...

[Wolfgang Bangerth]

Yiyang -- it's not easily possible to do it both at the same time
(because DataPostprocessor only creates output, but not do any kind of
integration -- so you are missing some information). But it's easy to do
by hand. For example, for the Laplace equation, you would do something
like this (pseudo-code):

double compute_energy ()
{
FEValues fe_values (...);
std::vector<Tensor<1,dim> > solution_gradients (n_q_points);

double energy = 0;

for (cell=...)
{
fe_values.reinit(cell);
fe_values.get_function_gradients (solution,
solution_gradients);

for (q=0...n_q_points)
energy += solution_gradients[q] * solution_gradients[q] *
fe_values.JxW(q);
}

return energy;
}

Best
W.

[Yiyang Zhang]

Thank you so much, Prof. Bangerth. 

[llf m]

Dear Wolfgang,

how to do this in distributed parallel mode( to sum up the energy in all processors)?

as the vector and matrix has the "compress(...::add)" function,

what about a scalar?

在 2017年9月16日星期六 UTC+8上午12:19:01，Wolfgang Bangerth写道：

[llf m]

Sorry, I misused the Utilities::MPI::sum() function and thought it might not work right at first.

Now I use the Utilities::MPI::sum() function to sum up the energy in all processors, is that right? 

在 2019年6月4日星期二 UTC+8上午8:50:25，llf m写道：

[Wolfgang Bangerth]

On 6/3/19 7:52 PM, llf m wrote:
> Sorry, I misused the Utilities::MPI::sum() function and thought it might not
> work right at first.
> Now I use the Utilities::MPI::sum() function to sum up the energy in all
> processors, is that right?

Yes -- each processor loops over its locally owned cells, and then you use the
function above to sum up over all processors.

Best
W.

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