[jlee-kitware]

Fields given their gradient; world derivatives from the field's view

Problem
A solver often knows its gradients better than the basis does: a lattice Boltzmann solver's central differences, a finite-volume reconstruction. world_gradient, world_jet and gradients could only differentiate the field's basis.

Approach

• Field(space, values, unit, gradient=g): g is a field on the same topology, with 3 values per entry for a scalar, and 3k row by row for a vector of k.
• world_gradient and world_jet ask the field's view. By default they differentiate the basis as before, from a mixin on every field view whose basis gives derivatives (_derivative_mixins in _space_parts). A view that already defines world_gradient keeps its own, so a space that computes its values can supply its derivatives.
• A field given its gradient reads g. Its world_jet pairs it with a NaN Hessian, which a gradient does not determine.
• gradients reads a given gradient, row by row for a vector, so flow_quantities and every kernel built on these use the solver's derivatives.
• A given gradient on polyhedral meshes is refused for now.

Verified
tack-vis on CPU and CUDA, including tests for world_gradient, world_jet, gradients and flow_quantities reading a given gradient, for the validation of g, and for point data keeping its gradient.