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Add Padua points #15

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Add Padua points #15

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alexfikl
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@alexfikl alexfikl commented Oct 30, 2020

This mostly just adds the Padua nodes for arbitrary orders (see wiki). Padua nodes are meant to be a unisolvent set of nodes for PN on the square with optimal growth of the Lebesgue constant.

Some questions / remarks:

  • What would be some cool things to check?
  • These points are not very symmetric. In particular, they have different numbers of nodes on faces. Will the face mass matrices still work?
  • For the standard case, there's also an associated Chebychev-Gauss-type quadrature. Worth adding?
  • The order of the nodes is a bit haphazard at the moment. Would be useful to sort them in lexicographic order like the tensor product case.

@alexfikl alexfikl marked this pull request as draft October 30, 2020 03:41
@alexfikl alexfikl changed the title Add padua points and some helpers Add Padua points and some helpers Oct 30, 2020
@alexfikl alexfikl changed the title Add Padua points and some helpers Add Padua points Oct 30, 2020
@inducer
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inducer commented Oct 31, 2020

These points are not very symmetric. In particular, they have different numbers of nodes on faces. Will the face mass matrices still work?

Hmm. Probably. There's a face homogeneity assumption there currently which we would need to break. Fortunately, the data structures can take this. It's just the logic that needs some help.

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