Use element indices particle.ei in curvilinear search

[erikvansebille]

While the Morton encoding for the curvilinear search (#2175) is very fast, it turns out to be even faster to use the element indices (particle.ei) in the search.

Using the benchmark script in OceanParcels/parcels-benchmarks@9a39630 (#5), we get the following speed-up:

Running 4_999_696 particles with parcels v4
Execution time 1: 44 seconds
Execution time 2: 1 seconds

where execution 1 is with the Morton search (since particle.ei = None) and execution 2 is with the code in this PR to use the particle.ei.

Note that this is the most optimal case where particles don't move between searches, but that is actually very often the case because

1. A Kernel loop requires multiple Field interpolations at the same location
2. Most particles move less than one grid cell between Kernel loops

[erikvansebille]

@fluidnumerics-joe, there's a failing unit test in the uxgrid part:

FAILED tests/v4/test_particleset_execute.py::test_uxstommelgyre_pset_execute - KeyError: 'FACE'

with detailed error

parcels/particleset.py:543: in execute
    self._kernel.execute(self, endtime=next_time, dt=dt)
parcels/kernel.py:261: in execute
    f(pset[evaluate_particles], self._fieldset)
parcels/application_kernels/advection.py:103: in AdvectionEE
    (u1, v1) = fieldset.UV[particles]
               ^^^^^^^^^^^^^^^^^^^^^^
parcels/field.py:338: in __getitem__
    return self.eval(key.time, key.depth, key.lat, key.lon, key)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
parcels/field.py:305: in eval
    position = self.grid.search(z, y, x, ei=_ei)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
parcels/uxgrid.py:91: in search
    bcoords = try_face(fi)
              ^^^^^^^^^^^^
parcels/uxgrid.py:77: in try_face
    bcoords, err = self._get_barycentric_coordinates_latlon(y, x, fid)
                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
parcels/uxgrid.py:117: in _get_barycentric_coordinates_latlon
    n_nodes = self.uxgrid.n_nodes_per_face[fi].to_numpy()
              ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
../../miniconda3/envs/parcels/lib/python3.13/site-packages/xarray/core/dataarray.py:902: in __getitem__
    return self._getitem_coord(key)
           ^^^^^^^^^^^^^^^^^^^^^^^^
../../miniconda3/envs/parcels/lib/python3.13/site-packages/xarray/core/dataarray.py:896: in _getitem_coord
    _, key, var = _get_virtual_variable(self._coords, key, dim_sizes)
                  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Probably has to do with basegrid.ravel and .unravel now expecting an ndarray (since they are vectorized)

Can you see if you can fix this for uxgrid?

[fluidnumerics-joe]

Taking a look :)

[VeckoTheGecko]

Looks good! Some minor clarifications but otherwise LGTM

[VeckoTheGecko]

Happy to merge when you're ready @erikvansebille :)