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Fix Netgen permutation #5034

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pbrubeck merged 7 commits into from
Jul 28, 2026
Merged

Fix Netgen permutation #5034

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9b1829d
Fix Netgen permutation
pbrubeck Apr 16, 2026
79f23e0
Deprecate permutation_tol, add test
pbrubeck Jul 28, 2026
44e9db0
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pbrubeck Jul 28, 2026
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pbrubeck Jul 28, 2026
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26 changes: 17 additions & 9 deletions firedrake/mesh.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2979,14 +2979,14 @@ def refine_marked_elements(self, mark, netgen_flags=None):
netgen_flags=netgen_flags)

@PETSc.Log.EventDecorator()
def curve_field(self, order, permutation_tol=1e-8, cg_field=None):
def curve_field(self, order, permutation_tol=None, cg_field=None):
'''Return a function containing the curved coordinates of the mesh.

This method requires that the mesh has been constructed from a
netgen mesh.

:arg order: the order of the curved mesh.
:arg permutation_tol: tolerance used to construct the permutation of the reference element.
:arg permutation_tol: ignored.
:arg cg_field: return a CG function field representing the mesh, as opposed to a DG field.
Defaults to the continuity of the coordinates of the original mesh.

Expand All @@ -2998,6 +2998,12 @@ def curve_field(self, order, permutation_tol=1e-8, cg_field=None):

if not hasattr(self, "netgen_mesh"):
raise ValueError("Cannot curve a mesh that has not been generated by netgen.")
if permutation_tol is not None:
warnings.warn(
"permutation_tol is no longer required to obtain the curved coordinates. "
"This kwarg will be removed in a future release.",
FutureWarning,
)

if cg_field is None:
cg_field = not self.coordinates.function_space().finat_element.is_dg()
Expand All @@ -3020,10 +3026,13 @@ def curve_field(self, order, permutation_tol=1e-8, cg_field=None):
fiat_element = new_coordinates.function_space().finat_element.fiat_equivalent
nodes = fiat_element.dual_basis()
ref_pts = []
for node in nodes:
# Assert singleton point for each node.
pt, = node.get_point_dict().keys()
ref_pts.append(pt)
entity_ids = fiat_element.entity_dofs()
for dim in sorted(entity_ids):
for entity in sorted(entity_ids[dim]):
for i in entity_ids[dim][entity]:
# Assert singleton point for each node.
pt, = nodes[i].get_point_dict().keys()
ref_pts.append(pt)
reference_points = np.array(ref_pts)

# Construct numpy arrays for physical domain data
Expand All @@ -3033,8 +3042,8 @@ def curve_field(self, order, permutation_tol=1e-8, cg_field=None):
curved_points = np.zeros(
(ng_dimension, reference_points.shape[0], self.geometric_dimension)
)
self.netgen_mesh.Curve(1)
self.netgen_mesh.CalcElementMapping(reference_points, physical_points)
# NOTE: This will segfault for MeshHierarchy on a netgen CSG geometry
self.netgen_mesh.Curve(order)
self.netgen_mesh.CalcElementMapping(reference_points, curved_points)
curved = ng_element.NumPy()["curved"]
Expand All @@ -3059,7 +3068,6 @@ def curve_field(self, order, permutation_tol=1e-8, cg_field=None):
permutation = find_permutation(
own_physical_points,
new_coordinates.dat.data_ro_with_halos[broken_indices].real,
tol=permutation_tol,
)
self.comm.Barrier()
# Apply the permutation to each cell in turn
Expand Down Expand Up @@ -3425,7 +3433,7 @@ def Mesh(meshfile, **kwargs):
# Curve the mesh, if requested
degree = netgen_flags.get("degree", 1)
if degree != 1:
permutation_tol = netgen_flags.get("permutation_tol", 1e-8)
permutation_tol = netgen_flags.get("permutation_tol", None)
cg = netgen_flags.get("cg", None)
coordinates = mesh.curve_field(
order=degree,
Expand Down
2 changes: 1 addition & 1 deletion firedrake/mg/netgen.py
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Original file line number Diff line number Diff line change
Expand Up @@ -242,7 +242,7 @@ def NetgenHierarchy(mesh, levs, flags, distribution_parameters=None):
order = flags.get("degree", 1)
if isinstance(order, int):
order = [order]*(levs+1)
permutation_tol = flags.get("permutation_tol", 1e-8)
permutation_tol = flags.get("permutation_tol", None)
refType = flags.get("refinement_type", "uniform")
optMoves = flags.get("optimisation_moves", False)
snap = flags.get("snap_to", "geometry")
Expand Down
18 changes: 15 additions & 3 deletions firedrake/netgen.py
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Expand Up @@ -80,8 +80,7 @@ def netgen_distribute(V: firedrake.functionspaceimpl.WithGeometryBase,


@PETSc.Log.EventDecorator()
def find_permutation(points_a: np.ndarray, points_b: np.ndarray,
tol: float = 1e-5):
def find_permutation(points_a: np.ndarray, points_b: np.ndarray):
""" Find all permutations between a list of two sets of points.

Given two numpy arrays of shape (ncells, npoints, dim) containing
Expand All @@ -95,7 +94,20 @@ def find_permutation(points_a: np.ndarray, points_b: np.ndarray,
if points_a.shape != points_b.shape:
raise ValueError("`points_a` and `points_b` must have the same shape.")

p = [np.where(cdist(a, b).T < tol)[1] for a, b in zip(points_a, points_b)]
# Match reference points instead of physical points to ensure scale invariance
dim = points_a.shape[-1]
vids = list(range(dim+1))
# Infer the affine mapping (A, b) from the image of the vertices (first dim+1 dofs)
bs = points_a[:, vids[:1], :]
As = points_a[:, vids[1:], :]
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As -= bs
Ainvs = np.linalg.inv(As)
# x_phys = A * x_ref + b <==> x_ref = inv(A) * (x_phys - b)
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# Multiply inv(A) from the right, since the data is row-major
ref_points_a = np.matmul(points_a - bs, Ainvs)
ref_points_b = np.matmul(points_b - bs, Ainvs)

p = [np.argmin(cdist(a, b), axis=0) for a, b in zip(ref_points_a, ref_points_b)]

if len(p) == 0:
return p
Expand Down
24 changes: 22 additions & 2 deletions tests/firedrake/regression/test_netgen.py
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Expand Up @@ -34,14 +34,34 @@ def test_netgen_csg_mesh_high_order():
assert mesh3.coordinates.function_space().ufl_element().degree() == order


def square_geometry(h):
def square_geometry(h, L=np.pi):
from netgen.geom2d import SplineGeometry
geo = SplineGeometry()
geo.AddRectangle((0, 0), (np.pi, np.pi), bc="rect")
geo.AddRectangle((0, 0), (L, L), bc="rect")
ngmesh = geo.GenerateMesh(maxh=h)
return ngmesh


def circle_geometry(h, R=1.0):
from netgen.geom2d import SplineGeometry
geo = SplineGeometry()
geo.AddCircle((0, 0), R, bc="circ")
ngmesh = geo.GenerateMesh(maxh=h)
return ngmesh


@pytest.mark.parametrize("scale", (1E-5, 1E5))
def test_high_order(scale):
# Test scale independence of high-order geometry
expected = np.pi * scale * scale
ngmesh = circle_geometry(h=scale/4, R=scale)

degree = 3
msh = Mesh(ngmesh, netgen_flags={"degree": degree})
assert msh.coordinates.function_space().ufl_element().degree() == degree
assert np.isclose(assemble(1*dx(domain=msh)), expected)


def poisson(h, degree=2):
import netgen
comm = COMM_WORLD
Expand Down
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