On 6/22/23 04:06, 'Jost Arndt' via deal.II User Group wrote:
N_{i,j} F, with N_{i,j,k} = (\phi_i \phi_k, \phi_j)
?
This would be a third order tensor. It would be sparse, because only those
entries ijk are nonzero where phi_i, phi_j, and phi_k overlap. But that would
still be quite a lot of entries. A back of the envelope calculation would be
that it's 10-100 times more memory than the mass matrix, depending on the
space dimension and the polynomial degree you use. That's not likely going to
fit into your computer's memory for all but the smallest problems :-)
Or do I simply have to use a Newton solver for (f g, \phi) for f and g?
It does not actually change anything. The N tensor above is just a convenient
way to write (f g, phi), but the problem is still nonlinear. If you need to
solve for both f and g, you're stuck with a nonlinear problem for which
Newton's method is one way to do it.
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
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