Cell-wise volume integration

Hello Paraview Forum,
I’m looking for a possibility to perform cell-wise volume integration of Finite Element Method stress results. Consider, the 3D principal stress field is point-wise available for a given geometry. Now I want to calculate the volume integral cell-wise for example of the maximum principle stress S_Max: Integral(S_Max) over individual cell volume dV_Cell so in the end I have the volume integral for each cell of the given geometry.

Does anybody know how this can be accomplished in Paraview? I was not able to do it with “IntegrateVariable” filter. I have to say that I’m not a Paraview expert, so please apologize my limited ability in this context :slight_smile:

Many thanks!

Hi @ROC_Para,

Welcome to the ParaView discourse! Thanks for posting your problem.

Indeed, I couldn’t find one single filter that integrates the scalar field cell by cell and retains it as a cell field. However, if your field uses linear basis functions and your mesh is comprised of tetrahedra, then I believe that the integral per cell should be the average value of the nodes comprising the cell multiplied by the volume of the cell.

Using that formula, you can use the following workflow:

  • Use the “Point To Cell Data” filter to perform an average of your values cell-wise
  • Use the “Cell Size” filter to compute your cell volumes
  • Use a “Calculator” filter to multiply your averaged value cell field with your volume field

The resulting cell field should have the value of your scalar integrated in each cell provided my initial hypotheses were correct.

Hope that helps!



Thank you!

You can also use the “integrate variables” filter. This operates on cell data. So you will still need to use “Point To Cell Data”.