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. Lawrence