DoFs and solution points

Hi, I am curious about the concept of solution point.

What is difference between # of DoFs and # of solution points?

When i checked DoFs using h5ls, DoF value is 83,185,500.
However, i got 16,637,100 # of points in paraview information tab. This value is double the DoFs. I think “# of points” means # solution points. Is that right?

Many papers related to PyFr seem to use solution points. What is difference between DoFs and # of solution points?



The number of degrees of freedom of a run refers to the total number of variables of a solution. In the flux reconstruction scheme, the variables that defines the solution are the conserved variable at the solution points. At the solution points you have a number of variables depending on the system being solved. Eg for 3D compressible Navier–Stokes there are 5 variables.

Paraview is showing you the number of grid points in the vtu file, which for compressible Navier–Stokes will be a factor of 5 less than the number of variables in the vtu file. The number of grid points in the vtu file will depend on the options you used when exporting the pyfrs file. For example, if you used the -d 10 option when you exported the file, the number of points will be significantly different from your DoF number.

What you can see from the pyfrs file is that there are a number of datasets with the names soln_{ename}_p{n}. If you sum the size of all these datasets that will give you the DoFs. Eg. the hex partition on part 0 has 125*5*32064=20,040,000DoFs.