Hi,
For various projects I have noticed that collapsing a mixed function space that includes a vector component takes unreasonably long (it is by orders of magnitude the longest executing line in the entire code). For simple 3D geometry with higher-order spaces, the execution-time becomes intractable.
Here a MWE illustrating the issue:
from dolfinx import mesh, fem
from basix.ufl import element, mixed_element
from mpi4py import MPI
import time
nx:int = 5 # Number of elements in x
ny:int = 5 # Number of elements in y
nz:int = 5 # Number of elements in z
Pu:int = 4 # Polynomial order velocity
Pp:int = 4 # Polynomial order pressure
# Create square quad mesh
start = time.time()
domain = mesh.create_unit_cube(MPI.COMM_WORLD, nx,ny,nz, mesh.CellType.hexahedron)
Ve = element("Lagrange", domain.basix_cell(), Pu, shape=(domain.geometry.dim,))
Qe = element("Lagrange", domain.basix_cell(), Pp)
W_el = mixed_element([Ve, Qe])
W = fem.functionspace(domain, W_el)
print(f"Meshing and creating mixed space: {time.time()-start}"); start = time.time()
V, WV_map = W.sub(0).collapse()
print(f"Collapsing V: {time.time()-start}"); start = time.time()
Q, WQ_map = W.sub(1).collapse()
print(f"Collapsing Q: {time.time()-start}")
with output:
- Meshing and creating mixed space: 0.05801892280578613
- Collapsing V: 4.216069936752319
- Collapsing Q: 0.002038717269897461
It is striking that collapsing Q is 2000 times quicker than collapsing V.
It also scales strangely; for nx=ny=nz=10 (double the elements in all directions, a factor 8 in DOFs) I get:
- Meshing and creating mixed space: 0.06880497932434082
- Collapsing V: 161.0486958026886
- Collapsing Q: 0.0062062740325927734
(Factor 3 for Q, but factor 40! for V. Now they differ by a factor 25000)
Any thoughts? I hope I am making a novice mistake…
Best,
Stein