From b64ed40fe5b8b8de90a1144e6caf455f8aa7f0d9 Mon Sep 17 00:00:00 2001 From: "David A. Ham" Date: Wed, 19 Feb 2025 17:08:41 +0000 Subject: [PATCH] immersed mesh documentation (#4052) * immersed mesh documentation --- docs/source/images/sin_mesh.png | Bin 0 -> 88663 bytes docs/source/mesh-coordinates.rst | 24 ++++++++++++++++++ .../regression/test_mesh_generation.py | 15 +++++++++++ 3 files changed, 39 insertions(+) create mode 100644 docs/source/images/sin_mesh.png diff --git a/docs/source/images/sin_mesh.png b/docs/source/images/sin_mesh.png new file mode 100644 index 0000000000000000000000000000000000000000..e491cec89efe8dc53ab0db0919cc583e94f48993 GIT binary patch literal 88663 zcmeEuWl&sQv@Fg50S0#u8a%i=1a}B-!QI{62_z7l!6CRqa3{D!a6)i*e~0hBdjH@5 zTQ$^7O-=3EvUaat-RlsgtSF6&Oo$8x1%>)aMnV+|3MLQ=3VH*C0DQwawelBu<8zhN zc2#pQcl9uK{sN_7?CNOi;A(4SLhk;>*~QAi{v$IRD>Ex2xuvVCqYEDki{1bG1+#;* z1xt#vwlgpalB3LL7bqxn915YV=OATt10lnxXO))qUu>%)N)d(N!QXB+}cro#((JmhXp*)z%M=TCGZ-PZcJG=Pw=@Xi0i9IYOI=Y?fq#1h+ zUFcn}I9wh%DA?m|u9F8M1)?jWXPZG+4sLFoc8k?Pl$4Z~S9?=vDhoBH(l0t{YP}}l 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space +-------------------------------------------- + +A useful special case of creating a mesh on modified coordinates is to immerse +a lower dimensional mesh in a higher dimension, for example to create a mesh of +a two-dimensional manifold immersed in 3D. + +This is accomplished by setting the value dimension of the new +:py:func:`~.VectorFunctionSpace` to that of the space in which it should be +immersed. For example, a mesh of square bent into a sine wave using +linear (flat) elements can be created with: + +.. literalinclude:: ../../tests/firedrake/regression/test_mesh_generation.py + :language: python3 + :dedent: + :start-after: start_immerse + :end-before: end_immerse + + +.. figure:: images/sin_mesh.png + :align: center + + A sine-wave shaped triangle mesh immersed in three-dimensional space. + Replacing the mesh geometry of an existing function --------------------------------------------------- diff --git a/tests/firedrake/regression/test_mesh_generation.py b/tests/firedrake/regression/test_mesh_generation.py index d2efe2a8b4..b7cffa6777 100644 --- a/tests/firedrake/regression/test_mesh_generation.py +++ b/tests/firedrake/regression/test_mesh_generation.py @@ -520,3 +520,18 @@ def test_split_comm_dm_mesh(): bad_comm = COMM_WORLD.Split(color=(rank % nspace), key=rank) with pytest.raises(ValueError): mesh2 = Mesh(dm, comm=bad_comm) # noqa: F841 + + +def test_immerse_mesh(): + """This test exists to ensure that the code used in the manual runs + correctly.""" + + # start_immerse + mesh = UnitSquareMesh(10, 10) + x, y = SpatialCoordinate(mesh) + coord_fs = VectorFunctionSpace(mesh, "CG", 1, dim=3) + new_coord = assemble(interpolate(as_vector([x, y, sin(2*pi*x)]), coord_fs)) + new_mesh = Mesh(new_coord) + # end_immerse + + new_mesh # Variable reference to silence linter.