diff --git a/meshmode/mesh/processing.py b/meshmode/mesh/processing.py
index 2b9895775b059ef0b389421465c9cb79fcd12eec..32016cd63afc3e2fd7379c3b3ba5b5f46ed05548 100644
--- a/meshmode/mesh/processing.py
+++ b/meshmode/mesh/processing.py
@@ -35,6 +35,7 @@ __doc__ = """
 .. autofunction:: perform_flips
 .. autofunction:: find_bounding_box
 .. autofunction:: merge_disjoint_meshes
+.. autofunction:: map_mesh
 .. autofunction:: affine_map
 """
 
@@ -271,34 +272,46 @@ def merge_disjoint_meshes(meshes, skip_tests=False):
 # }}}
 
 
-# {{{ affine map
+# {{{ map
 
-def affine_map(mesh, A=None, b=None):  # noqa
-    """Apply the affine map *f(x)=Ax+b* to the geometry of *mesh*."""
+def map_mesh(mesh, f):  # noqa
+    """Apply the map *f* to the mesh. *f* needs to accept and return arrays of
+    shape ``(ambient_dim, npoints)``."""
 
-    if A is None:
-        A = np.eye(mesh.ambient_dim)  # noqa
-
-    if b is None:
-        b = np.zeros(A.shape[0])
-
-    vertices = np.einsum("ij,jv->iv", A, mesh.vertices) + b[:, np.newaxis]
+    vertices = f(mesh.vertices)
 
     # {{{ assemble new groups list
 
     new_groups = []
 
     for group in mesh.groups:
-        nodes = (
-                np.einsum("ij,jen->ien", A, group.nodes)
-                + b[:, np.newaxis, np.newaxis])
-        new_groups.append(group.copy(nodes=nodes))
+        new_groups.append(group.copy(nodes=f(group.nodes)))
 
     # }}}
 
     from meshmode.mesh import Mesh
     return Mesh(vertices, new_groups, skip_tests=True,
-            nodal_adjacency=mesh.nodal_adjacency_init_arg())
+            nodal_adjacency=mesh.nodal_adjacency_init_arg(),
+            facial_adjacency_groups=mesh._facial_adjacency_groups)
+
+# }}}
+
+
+# {{{ affine map
+
+def affine_map(mesh, A=None, b=None):  # noqa
+    """Apply the affine map *f(x)=Ax+b* to the geometry of *mesh*."""
+
+    if A is None:
+        A = np.eye(mesh.ambient_dim)  # noqa
+
+    if b is None:
+        b = np.zeros(A.shape[0])
+
+    def f(x):
+        return np.einsum("ij,jv->iv", A, x) + b[:, np.newaxis]
+
+    return map_mesh(mesh, f)
 
 # }}}