> On 25 Jun 2019, at 11:49, Matthew Knepley <knepley@gmail.com> wrote:
>
> On Tue, Jun 25, 2019 at 6:44 AM Ham, David A <david.ham@imperial.ac.uk> wrote:
> I *think* that the concept is that the physical cell is mapped to the reference cell, so you are pulling back reference values through that mapping to get physical values.
>
>
> Ah. I named them the opposite way :) This is a good window into how my mind works. I thought
> since the Jacobian maps reference to real (and phi for that matter) that the default direction of any
> mapping should be ref-to-real. It seems like this is the overwhelming convention in large deformations.
If you have a mapping
\phi : \hat{K} \to K
Then
\phi^* : Alt^k(K) \to Alt^k(\hat{K})
is the pullback defined by
\phi^* w(v_1, ..., v_k) = w(\phi v_1, ... \phi v_k), v_i \in \hat{K}, w \in Alt^k(K)
So at least differential geometry says the pullback goes in the opposite direction to the mapping.
Yes, exactly. So if the mapping is ref-to-real, then then pulllback should be real-to-ref, which is what I needed for
dual basis application. I needed ref-to-real for cell integration (since tabulations are in ref), which I called pushforward.
Thanks,
Matt
Lawrence