I am experiencing slow inter-mesh interpolation. Here is a MWE with the profiling library line-profiler :
from dolfinx import io, fem, mesh, cpp, geometry
import ufl
from mpi4py import MPI
import dolfinx.fem.petsc
import basix.ufl
from line_profiler import LineProfiler
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
def exact_sol(x):
return 2 -(x[0]**2 + x[1]**2)
def rhs():
return 4
def interpolate(sending_func,
receiving_func,):
'''
Interpolate sending_func to receiving_func,
each comming from separate meshes
'''
targetSpace = receiving_func.function_space
nmmid = dolfinx.fem.create_nonmatching_meshes_interpolation_data(
targetSpace.mesh,
targetSpace.element,
sending_func.ufl_function_space().mesh,
padding=1e-6,)
receiving_func.interpolate(sending_func, nmm_interpolation_data=nmmid)
return receiving_func
def solve(domain,u):
'''
Solve Poisson problem
'''
V = u.function_space
# Dirichlet BC
cdim = domain.topology.dim
fdim = cdim-1
domain.topology.create_connectivity(fdim,cdim)
bfacets = mesh.exterior_facet_indices(domain.topology)
u_bc = fem.Function(V)
u_bc.interpolate(exact_sol)
dirichlet_bcs = [fem.dirichletbc(u_bc, fem.locate_dofs_topological(V, fdim, bfacets))]
# Forms
u, v = ufl.TrialFunction(V), ufl.TestFunction(V)
a = ufl.inner(ufl.grad(u),ufl.grad(v))*ufl.dx
l = rhs()*v*ufl.dx
problem = dolfinx.fem.petsc.LinearProblem(a,l,
bcs=dirichlet_bcs,)
return problem.solve()
def write_post(mesh1,mesh2,u1,u2):
writer1, writer2 = io.VTKFile(mesh1.comm, f"out/result1.vtk",'w'),io.VTKFile(mesh2.comm, f"out/result2.vtk",'w')
writer1.write_function(u1)
writer2.write_function(u2)
writer1.close()
writer2.close()
def main():
# Mesh and problems
points_side = 128
mesh1 = mesh.create_unit_square(MPI.COMM_WORLD, points_side, points_side, mesh.CellType.triangle)
mesh2 = mesh.create_unit_square(MPI.COMM_WORLD, points_side, points_side, mesh.CellType.quadrilateral)
(V1, V2) = (fem.functionspace(mesh1, ("Lagrange", 1)),fem.functionspace(mesh2, ("Lagrange", 1)))
(u1, u2) = (fem.Function(V1),fem.Function(V2))
# Solve Poisson problem on mesh1
u1 = solve(mesh1,u1)
# Interpolate from mesh1 to mesh2
interpolate(u1,u2)
# Write post
#write_post(mesh1,mesh2,u1,u2)
if __name__=="__main__":
profiling = True
if profiling:
lp = LineProfiler()
lp.add_function(interpolate)
lp.add_function(solve)
lp.add_function(main)
lp.add_function(write_post)
lp.add_function(fem.Function.interpolate)
lp_wrapper = lp(main)
lp_wrapper()
lp.print_stats()
I solve a Poisson problem on a mesh that has 32K elements and interpolate the solution to a mesh that has 16K elements.
I run this with the latest development version of the software (dolfinx from March 26th). The profiling library outputs:
Total time: 4.25439 s
File: /root/shared/cases/test_profiling/main.py
Function: main at line 59
Line # Hits Time Per Hit % Time Line Contents
==============================================================
59 def main():
60 # Mesh and problems
61 1 863.0 863.0 0.0 points_side = 128
62 1 677506314.0 7e+08 15.9 mesh1 = mesh.create_unit_square(MPI.COMM_WORLD, points_side, points_side, mesh.CellType.triangle)
63 1 448408917.0 4e+08 10.5 mesh2 = mesh.create_unit_square(MPI.COMM_WORLD, points_side, points_side, mesh.CellType.quadrilateral)
64
65 1 84272193.0 8e+07 2.0 (V1, V2) = (fem.functionspace(mesh1, ("Lagrange", 1)),fem.functionspace(mesh2, ("Lagrange", 1)))
66 1 329775.0 329775.0 0.0 (u1, u2) = (fem.Function(V1),fem.Function(V2))
67 # Solve Poisson problem on mesh1
68 1 526576436.0 5e+08 12.4 u1 = solve(mesh1,u1)
69 # Interpolate from mesh1 to mesh2
70 1 2517292189.0 3e+09 59.2 interpolate(u1,u2)
71 # Write post
72 #write_post(mesh1,mesh2,u1,u2)
As you can see, the interpolation takes around 5 times more time. The padding used
for create_nonmatching_meshes_interpolation_data is rather small (1e-6), and null padding does not change these times.
Any help would be appreciated.