Mesh Hierarchy support when working with Netgen mesh

Signed-off-by: Umberto Zerbinati <[email protected]>

firedrake/mg/mesh.py

@@ -9,6 +9,11 @@
 from firedrake.cython import mgimpl as impl
 from .utils import set_level
 
+try:
+    import netgen
+except ImportError:
+    netgen = None
+    ngsPETSc = None
 
 __all__ = ("HierarchyBase", "MeshHierarchy", "ExtrudedMeshHierarchy", "NonNestedHierarchy",
            "SemiCoarsenedExtrudedHierarchy")
@@ -80,6 +85,7 @@ def __getitem__(self, idx):
 
 def MeshHierarchy(mesh, refinement_levels,
                   refinements_per_level=1,
+                  order=1,
                   reorder=None,
                   distribution_parameters=None, callbacks=None,
                   mesh_builder=firedrake.Mesh):
@@ -102,6 +108,13 @@ def MeshHierarchy(mesh, refinement_levels,
         callback receives the refined DM (and the current level).
     :arg mesh_builder: Function to turn a DM into a ``Mesh``. Used by pyadjoint.
     """
+    if netgen and isinstance(mesh, netgen.libngpy._meshing.Mesh):
+        try:
+            from ngsPETSc import NetgenHierarchy
+        except ImportError:
+            raise ImportError("Unable to import ngsPETSc. Please ensure that ngsolve is installed and available to Firedrake.")
+        return NetgenHierarchy(mesh, refinement_levels, order=order, digits=8, adaptive=False)
+
     cdm = mesh.topology_dm
     cdm.setRefinementUniform(True)
     dms = []

tests/multigrid/test_netgen.py

@@ -0,0 +1,38 @@
+from firedrake import *
+import pytest
+
+
+def test_netgen_mg_circle():
+    try:
+        from netgen.geom2d import Circle, CSG2d
+    except ImportError:
+        pytest.skip(reason="Netgen unavailable, skipping Netgen test.")
+    geo = CSG2d()
+
+    circle = Circle(center=(0, 0), radius=1.0, mat="mat1", bc="circle")
+    geo.Add(circle)
+
+    ngmesh = geo.GenerateMesh(maxh=0.75)
+
+    nh = MeshHierarchy(ngmesh, 2, order=3)
+    mesh = nh[-1]
+
+    V = FunctionSpace(mesh, "CG", 3)
+
+    u = TrialFunction(V)
+    v = TestFunction(V)
+
+    a = dot(grad(u), grad(v))*dx
+    labels = [i+1 for i, name in enumerate(ngmesh.GetRegionNames(codim=1)) if name in ["circle"]]
+    bcs = DirichletBC(V, zero(), labels)
+    x, y = SpatialCoordinate(mesh)
+
+    f = 4+0*x
+    L = f*v*dx
+    exact = (1-x**2-y**2)
+
+    u = Function(V)
+    solve(a == L, u, bcs=bcs, solver_parameters={"ksp_type": "cg",
+                                                 "pc_type": "mg"})
+    expect = Function(V).interpolate(exact)
+    assert (norm(assemble(u - expect)) <= 1e-6)