Whitney 1-form and 2-form Questions

General
1

Hey I’m new here and I have some general dumb questions hopefully someone could answer.

  1. Are Whitney 1-forms the same as lowest order Nedelec elements?
  2. Are Whitney 2-forms the same as lowest order Raviart-Thomas elements?
  3. Is it possible to create a second order Whitney 2-form element?
  4. Why are Whitney p-forms not used in NGSolve?
  5. Would you recommend using something other than Whitney p-forms when solving the full Maxwell’s equations?
  6. Can I use NGSolve to create the Hodge Star matrices for edge and face elements and use those in my own particle in cell code?
2
  1. I think so
  2. I think so
  3. I don’t know second order Whitney 2-form elements, but we use second (and higher) order Raviart-Thomas elements
  4. We have them, however we call them by their ‘proxy’
  5. We recommend higher order Nedelec elements
  6. sure, you have to know what your matrix shall represent. I don’t know if you can use it in your code

Joachim

3

Thank you for getting back to me! :smile:
Can you recommend a “Nedelec for dummies” document? I have tried to study NGSolve’s codebase to understand but it’s difficult to get a super clear idea of how higher order Nedelec elements are implemented. For example, what do the basis functions look like, and how are the degrees of freedom calculated?

When using higher order Nedelec elements for Maxwell’s equations, do you define the electric field on edges with Nedelec 1st kind elements, and magnetic field on edges and faces with Nedelec 2nd kind elements? How would you know which elements to use and how to the define the fields with the correct degrees of freedom?

4

I would not call it ‘Nedelec for dummies’, but Sabine Zaglmayr’s thesis is an excellent reference for high order H(curl) elements, available from here:

if you have little time, have a look here:

Joachim