From 31e1662a8feeae2b2872d2d4cefe4396467ce17c Mon Sep 17 00:00:00 2001 From: acse-ej321 <89605848+acse-ej321@users.noreply.github.com> Date: Wed, 14 May 2025 19:50:51 +0100 Subject: [PATCH 1/5] extend demo with gmsh python api examples --- demos/immersed_fem/immersed_fem.py.rst | 274 +++++++++++++++++++++++-- 1 file changed, 254 insertions(+), 20 deletions(-) diff --git a/demos/immersed_fem/immersed_fem.py.rst b/demos/immersed_fem/immersed_fem.py.rst index 42db8688d0..15d806da1a 100644 --- a/demos/immersed_fem/immersed_fem.py.rst +++ b/demos/immersed_fem/immersed_fem.py.rst @@ -1,41 +1,76 @@ Creating Firedrake-compatible meshes in Gmsh ============================================ -The purpose of this demo is to summarize the -key structure of a ``gmsh.geo`` file that creates a -Firedrake-compatible mesh. For more details about Gmsh, please +The purpose of this demo is to demonstrate methods available +through Gmsh to create meshes compatible with Firedrake. It overviews +the creation the same mesh, three different ways: + +* Constructing a GEO file +* Using the Gmsh API +* Using OpenCASCADE through Gmsh + +For more details about Gmsh, please refer to the `Gmsh documentation `_. The Gmsh syntax used in this document is for Gmsh version 4.4.1 . +.. code-block:: none + + import matplotlib.pyplot as plt + from firedrake import * + import gmsh + As example, we will construct and mesh the following geometry: a rectangle with a disc in the middle. In the picture, numbers in black refer to Gmsh point tags, whereas numbers in -read refer to Gmsh curve tags (see below). +red refer to Gmsh curve tags (see below). .. image:: immerseddomain.png :width: 400px :align: center -The first thing we define are four corners of a rectangle. -We specify the x,y, and z(=0) coordinates, as well as the target -element size at these corners (which we set to 0.5). +Relative to a central origin, the rectangle is parameterised by its length L, and width, W. +Likewise, the disc is parameterised its radius, R. The target element size is set to be +finer around the disc compared to the background rectangle. .. code-block:: none - Point(1) = {-6, 2, 0, 0.5}; - Point(2) = {-6, -2, 0, 0.5}; - Point(3) = { 6, -2, 0, 0.5}; - Point(4) = { 6, 2, 0, 0.5}; + x0, y0, z0 = 0., 0., 0. + L = 12. + W = 4. + R = 1 + dx_rec = 0.5 + dx_disc = 0.1 + +Constructing a GEO file +----------------------- +The first thing we need to do is to create a Gmsh ``gmsh.geo``, +which is the geometry recipe for Gmsh. + +We begin by defining the four corners of a bounding rectangle. We specify the x,y, +and z(=0) coordinates, as well as the target element size at these +corners (which we set to 0.5). + +.. code-block:: none + + Point(1) = {x0 - L/2, y0 + W/2, z0, dx_rec}; + Point(2) = {x0 - L/2, y0 - W/2, z0, dx_rec}; + Point(3) = {x0 + L/2, y0 - W/2, z0, dx_rec}; + Point(4) = {x0 + L/2, y0 + W/2, z0, dx_rec}; + +.. note:: + Gmsh tracks most objects through a combination of its dimension + and an integer tag which must be unique to the object. For example, + ``Point(1)`` has dimension 0 and a unique tag 1. Then, we define 5 points to describe a circle. .. code-block:: none - Point(5) = { 0, 0, 0, 0.1}; - Point(6) = { 1, 0, 0, 0.1}; - Point(7) = {-1, 0, 0, 0.1}; - Point(8) = { 0, 1, 0, 0.1}; - Point(9) = { 0, -1, 0, 0.1}; + Point(5) = {x0, y0, z0, dx_disc}; + Point(6) = {x0 + R, y0, z0, dx_disc}; + Point(7) = {x0 - R, y0, z0, dx_disc}; + Point(8) = {x0, y0 + R, z0, dx_disc}; + Point(9) = {x0, y0 - R, z0, dx_disc}; Then, we create 8 edges: 4 for the rectangle and 4 for the circle. Note that the Gmsh command ``Circle`` requires the arc to be @@ -90,8 +125,209 @@ you can type the following command in the terminal .. note:: - Depending on your version of gmsh and DMPlex, the - gmsh option ``-format msh2`` may be omitted. + The ``-2`` flag indicates whether the mesh will be 2 or 3 dimensions. Depending on your + version of Gmsh and DMPlex, the Gmsh option ``-format msh2`` may be omitted. + +Using the Gmsh API +------------------ +We can alternatively use python commands enabled through the Gmsh API to build, save, and +read the mesh into Firedrake from within a python script. This allows for parameter flexibility +and improved readibility of the mesh generation code. + +We first need to ``initialize`` the Gmsh API and create a new empty mesh model. + +.. code-block:: none + + gmsh.initialize() + model = gmsh.model + model.add("gmsh_api_demo") + +As before, we define the four rectangle corner points and target element size. + +.. code-block:: none + + rectangle_points = [ + model.geo.addPoint(x0 - L/2, y0 + W/2, z0, dx_rec, 1), # top left + model.geo.addPoint(x0 - L/2, y0 - W/2, z0, dx_rec, 2), # bottom left + model.geo.addPoint(x0 + L/2, y0 - W/2, z0, dx_rec, 3), # bottom right + model.geo.addPoint(x0 + L/2, y0 + W/2, z0, dx_rec, 4) # top right + ] + +Then, we define 5 points to describe a circle. + +.. code-block:: none + + center = model.geo.addPoint(x0, y0, z0, 5) + circle_points = [ + model.geo.addPoint(x0 - R, y0, z0, dx_disc, 6), + model.geo.addPoint(x0, y0 + R, z0, dx_disc, 7), + model.geo.addPoint(x0 + R, y0, z0, dx_disc, 8), + model.geo.addPoint(x0, y0 - R, z0, dx_disc, 9) + ] + +Then, we create 8 edges: 4 for the rectangle and 4 for the circle. + +.. code-block:: none + + rectangle_lines = [ + model.geo.addLine(rectangle_points[0], rectangle_points[1], 1), # left + model.geo.addLine(rectangle_points[1], rectangle_points[2], 2), # bottom + model.geo.addLine(rectangle_points[2], rectangle_points[3], 3), # right + model.geo.addLine(rectangle_points[3], rectangle_points[0], 4) # top + ] + + circle_arcs =[ + model.geo.addCircleArc(circle_points[0], center, circle_points[1], 5), + model.geo.addCircleArc(circle_points[1], center, circle_points[2], 6), + model.geo.addCircleArc(circle_points[2], center, circle_points[3], 7), + model.geo.addCircleArc(circle_points[3], center, circle_points[0], 8) + ] + +We then combine the edges into a closed loop for both the rectangle and +the circle used to define a surface for the area outside and inside the +inscribed circle, respectively. In the ``addPlaneSurface`` function by +convention, the first ``Curve Loop`` defines the outer boundary and +anything after in the list is treated as a hole in the domain. These need +to be registered to the model with ``syncronize`` before we can use them. + +.. code-block:: none + + rectangle_loop = model.geo.addCurveLoop(rectangle_lines, 9) + circle_loop = model.geo.addCurveLoop(circle_arcs, 10) + + punched_surface = model.geo.addPlaneSurface([rectangle_loop,circle_loop], 1) + circle_surface = model.geo.addPlaneSurface([circle_loop], 2) + model.geo.synchronize() + +Finally, we group together some edges and define ``Physical`` entities. + +.. code-block:: none + + model.addPhysicalGroup(1, [rectangle_lines[1], rectangle_lines[3]], 11, name = "HorEdges") + model.addPhysicalGroup(1, [rectangle_lines[0], rectangle_lines[2]], 12, name = "VerEdges") + model.addPhysicalGroup(1, circle_arcs, 13, name = "Circle") + model.addPhysicalGroup(2, [punched_surface], 3, name = "PunchedDom") + model.addPhysicalGroup(2, [circle_surface], 4, name = "Disc") + +A number of meshing options are available. In particular, the algorithm for mesh generation +and can be set globally or for individual surfaces. + +* 2D: 1: MeshAdapt, 2: Automatic, 3: Initial mesh only, 5: Delaunay, 6: Frontal-Delaunay (default),\ + 7: BAMG, 8: Frontal-Delaunay for Quads, 9: Packing of Parallelograms, 11: Quasi-structured Quad +* 3D: Delaunay (default) 3: Initial mesh only 4: Frontal 7: MMG3D 9: R-tree 10: HXT +For more information see the `Gmesh documentation on algorithms `_. + +When writing the mesh to file, the format is determined by the file extension. For example, +`.msh2` for Gmsh 2.x, `.msh` for GMSH 4.x. + +.. code-block:: none + + gmsh.option.setNumber("Mesh.Algorithm", 6) + gmsh.option.setNumber("Mesh.MshFileVersion", 4.1) + gmsh.model.mesh.generate(2) + gmsh.write('gmsh_api_demo.msh') + gmsh.finalize() + +.. note:: + + Best practice is to shut down the Gmsh API kernel after finalising the mesh. + +Using OpenCASCADE through Gmsh +------------------------------- +Using OpenCASCADE through Gmsh, we define higher level geometries such as rectangles +and discs directly. It also has addition 3D capability not illustrated here. + +As with the Gmsh API, we ``initialize`` and start constructing a new mesh model. + +.. code-block:: none + + gmsh.initialize() + gmsh.model.add("gmsh_occ_demo") + +We first use OpenCASCADE to create a rectangle and a cylinder object. This automates +the create of points, lines, and surfaces. Both objects need to be registered to the +model with ``syncronize`` before we can use them. + +.. code-block:: none + + rectangle_obj = gmsh.model.occ.addRectangle(x0 - L/2, y0 - W/2, z0, L, W, 1) + cylinder_obj = gmsh.model.occ.addCylinder(x0, y0, z0, 0, 0, 1, R, 2) + gmsh.model.occ.synchronize() + +As the default behavior of the ``cut`` function, utilized to create the hole, is to +delete the original objects, we set ``removeTool=False`` to retain the cylinder object. +We also save the tag of the combined object for later use and register the new object +to the model with ``syncronize``. + +.. code-block:: none + + punched_surface = gmsh.model.occ.cut([(2, rectangle_obj)], [(3, cylinder_obj)], removeTool = False) + punched_surface_tag = punched_surface[0][0][1] + gmsh.model.occ.synchronize() + +We then extact the boundary from the objects. The ``getBoundary`` function takes and +returns a list of tuples ``(dimension, tag)``. We extract the cylinder surface and points +along with the punched surface lines to define the ``Physical`` groups. + +.. code-block:: none + + circle_surface = gmsh.model.getBoundary([(3, cylinder_obj)], True, True, False) + punched_lines = gmsh.model.getBoundary([(2, punched_surface_tag)], True, True, False) + circle_points = gmsh.model.getBoundary([(3, cylinder_obj)], True, True, True) + +We set the mesh resolution using ``setSize``. The choice here is to first set all the +zero-dimensional points to the background size, and then override the mesh size for the +points on the circle boundary. Another strategy documented in the Gmsh manual is to +identify the desired points by a bounding box search. + +.. code-block:: none + + gmsh.model.mesh.setSize(gmsh.model.occ.getEntities(0), dx_rec) + gmsh.model.mesh.setSize(circle_points, dx_disc) + +We parse just the line tags to create a list of physical group tags. In this case the +assignment of the lines was done manually through trial and inspection. +TODO: add a function to automatically assign the lines to the correct physical group. + +.. code-block:: none + + circle_surface_tags = [abs(line) for dim,line in circle_surface] + punched_line_tags = [abs(line) for dim,line in punched_lines] + gmsh.model.addPhysicalGroup(1, [punched_line_tags[1], punched_line_tags[4]], 11, name = "HorEdges") + gmsh.model.addPhysicalGroup(1, [punched_line_tags[2], punched_line_tags[3]], 12, name = "VertEdges") + gmsh.model.addPhysicalGroup(1, [punched_line_tags[0]], 13, name = "CircleEdge") + gmsh.model.addPhysicalGroup(2, [punched_surface_tag], 3, name = "PunchedDom") + model.addPhysicalGroup(2, [circle_surface_tags[-1]], 4, name = "Disc") + +.. code-block:: none + + gmsh.option.setNumber("Mesh.Algorithm", 6) + gmsh.model.mesh.generate(2) + gmsh.write('gmsh_occ_demo.msh') + gmsh.finalize() + +Compare Meshes +----------- +We can load and check the generated meshes in Firedrake + +.. code-block:: none + + meshes = [Mesh('gmsh_occ_demo.msh', name = "Gmsh API"), + Mesh('gmsh_api_demo.msh', name = "Gmsh OpenCASCADE")] + fig, ax = plt.subplots(len(meshes), 1, figsize = (8, len(meshes)*3), tight_layout=True) + for m, ax in zip(meshes, ax): + triplot(m, axes=ax) + ax.set_title(f'Mesh via {m.name}, # cells: {m.num_cells()}') + ax.legend(loc='upper left') + + fig.savefig("gmsh_demo.png", dpi = 400) + +.. image:: gmsh_demo.png + :width: 400px + :align: center + +Illustrate Features +------------------- To illustrate how to access all these features within Firedrake, we consider the following interface problem. Denoting by @@ -125,8 +361,6 @@ The resulting weak formulation reads as follows: The following Firedrake code shows how to solve this variational problem using linear Lagrangian finite elements. :: - from firedrake import * - # load the mesh generated with Gmsh mesh = Mesh('immersed_domain.msh') From 4e59573a974720b9ae01abc151d4b9d4f822a17e Mon Sep 17 00:00:00 2001 From: acse-ej321 <89605848+acse-ej321@users.noreply.github.com> Date: Wed, 14 May 2025 19:51:21 +0100 Subject: [PATCH 2/5] add compare image of generated meshes --- demos/immersed_fem/gmsh_demo.png | Bin 0 -> 2719657 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 demos/immersed_fem/gmsh_demo.png diff --git a/demos/immersed_fem/gmsh_demo.png b/demos/immersed_fem/gmsh_demo.png new file mode 100644 index 0000000000000000000000000000000000000000..1533c0d9f83b7fd1f34f336013d0efbc2c47280f GIT binary patch literal 2719657 zcmeGEcTiQ?_5})~wrxb)R#cE+Mgc)2XIoT2lH?$v34-J(2ncAapn`&cfowo>l$=#0 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X?BSK6f3zyl`srxu?@Isq@E`vdvXR-! literal 0 HcmV?d00001 From d26b576e83ce215ddd8900080ed5e68a9eee5cc4 Mon Sep 17 00:00:00 2001 From: acse-ej321 <89605848+acse-ej321@users.noreply.github.com> Date: Thu, 15 May 2025 09:51:46 +0100 Subject: [PATCH 3/5] minor formating --- demos/immersed_fem/immersed_fem.py.rst | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) diff --git a/demos/immersed_fem/immersed_fem.py.rst b/demos/immersed_fem/immersed_fem.py.rst index 15d806da1a..fd2ac9220d 100644 --- a/demos/immersed_fem/immersed_fem.py.rst +++ b/demos/immersed_fem/immersed_fem.py.rst @@ -43,6 +43,7 @@ finer around the disc compared to the background rectangle. Constructing a GEO file ----------------------- + The first thing we need to do is to create a Gmsh ``gmsh.geo``, which is the geometry recipe for Gmsh. @@ -130,6 +131,7 @@ you can type the following command in the terminal Using the Gmsh API ------------------ + We can alternatively use python commands enabled through the Gmsh API to build, save, and read the mesh into Firedrake from within a python script. This allows for parameter flexibility and improved readibility of the mesh generation code. @@ -215,6 +217,7 @@ and can be set globally or for individual surfaces. * 2D: 1: MeshAdapt, 2: Automatic, 3: Initial mesh only, 5: Delaunay, 6: Frontal-Delaunay (default),\ 7: BAMG, 8: Frontal-Delaunay for Quads, 9: Packing of Parallelograms, 11: Quasi-structured Quad * 3D: Delaunay (default) 3: Initial mesh only 4: Frontal 7: MMG3D 9: R-tree 10: HXT + For more information see the `Gmesh documentation on algorithms `_. When writing the mesh to file, the format is determined by the file extension. For example, @@ -233,7 +236,8 @@ When writing the mesh to file, the format is determined by the file extension. F Best practice is to shut down the Gmsh API kernel after finalising the mesh. Using OpenCASCADE through Gmsh -------------------------------- +------------------------------ + Using OpenCASCADE through Gmsh, we define higher level geometries such as rectangles and discs directly. It also has addition 3D capability not illustrated here. @@ -307,13 +311,13 @@ TODO: add a function to automatically assign the lines to the correct physical g gmsh.finalize() Compare Meshes ------------ +-------------- We can load and check the generated meshes in Firedrake .. code-block:: none meshes = [Mesh('gmsh_occ_demo.msh', name = "Gmsh API"), - Mesh('gmsh_api_demo.msh', name = "Gmsh OpenCASCADE")] + Mesh('gmsh_api_demo.msh', name = "Gmsh OpenCASCADE")] fig, ax = plt.subplots(len(meshes), 1, figsize = (8, len(meshes)*3), tight_layout=True) for m, ax in zip(meshes, ax): triplot(m, axes=ax) From a0efb928c49edeac52a30e7c1a9516b012ac115a Mon Sep 17 00:00:00 2001 From: acse-ej321 <89605848+acse-ej321@users.noreply.github.com> Date: Thu, 15 May 2025 11:40:07 +0100 Subject: [PATCH 4/5] updated broken url link --- demos/immersed_fem/immersed_fem.py.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/demos/immersed_fem/immersed_fem.py.rst b/demos/immersed_fem/immersed_fem.py.rst index fd2ac9220d..7291957f3d 100644 --- a/demos/immersed_fem/immersed_fem.py.rst +++ b/demos/immersed_fem/immersed_fem.py.rst @@ -218,7 +218,7 @@ and can be set globally or for individual surfaces. 7: BAMG, 8: Frontal-Delaunay for Quads, 9: Packing of Parallelograms, 11: Quasi-structured Quad * 3D: Delaunay (default) 3: Initial mesh only 4: Frontal 7: MMG3D 9: R-tree 10: HXT -For more information see the `Gmesh documentation on algorithms `_. +For more information see the `Gmesh documentation on algorithms `_. When writing the mesh to file, the format is determined by the file extension. For example, `.msh2` for Gmsh 2.x, `.msh` for GMSH 4.x. From 61584e8f609af81c0185e3c4740ae2988f7f5422 Mon Sep 17 00:00:00 2001 From: acse-ej321 <89605848+acse-ej321@users.noreply.github.com> Date: Thu, 15 May 2025 16:16:30 +0100 Subject: [PATCH 5/5] swap 3D cylinder for 2D disc, and improve variable clarity --- demos/immersed_fem/immersed_fem.py.rst | 191 +++++++++++++------------ 1 file changed, 100 insertions(+), 91 deletions(-) diff --git a/demos/immersed_fem/immersed_fem.py.rst b/demos/immersed_fem/immersed_fem.py.rst index 7291957f3d..3385749d84 100644 --- a/demos/immersed_fem/immersed_fem.py.rst +++ b/demos/immersed_fem/immersed_fem.py.rst @@ -13,7 +13,7 @@ For more details about Gmsh, please refer to the `Gmsh documentation `_. The Gmsh syntax used in this document is for Gmsh version 4.4.1 . -.. code-block:: none +.. code-block:: python import matplotlib.pyplot as plt from firedrake import * @@ -28,11 +28,11 @@ red refer to Gmsh curve tags (see below). :width: 400px :align: center -Relative to a central origin, the rectangle is parameterised by its length L, and width, W. -Likewise, the disc is parameterised its radius, R. The target element size is set to be -finer around the disc compared to the background rectangle. +Relative to a central origin, ``(x0, y0, z0)``, the rectangle is parameterised by its length ``L``, +and width, ``W``. Likewise, the disc is parameterised its radius, ``R``. The target element size is +set to ``dx_rec=0.5`` and ``dx_disc=0.1`` to generate finer triangles around the disc. -.. code-block:: none +.. code-block:: python x0, y0, z0 = 0., 0., 0. L = 12. @@ -49,29 +49,30 @@ which is the geometry recipe for Gmsh. We begin by defining the four corners of a bounding rectangle. We specify the x,y, and z(=0) coordinates, as well as the target element size at these -corners (which we set to 0.5). +corners. .. code-block:: none - Point(1) = {x0 - L/2, y0 + W/2, z0, dx_rec}; - Point(2) = {x0 - L/2, y0 - W/2, z0, dx_rec}; - Point(3) = {x0 + L/2, y0 - W/2, z0, dx_rec}; - Point(4) = {x0 + L/2, y0 + W/2, z0, dx_rec}; + Point(1) = {-6, 2, 0, 0.5}; + Point(2) = {-6, -2, 0, 0.5}; + Point(3) = { 6, -2, 0, 0.5}; + Point(4) = { 6, 2, 0, 0.5}; .. note:: - Gmsh tracks most objects through a combination of its dimension - and an integer tag which must be unique to the object. For example, - ``Point(1)`` has dimension 0 and a unique tag 1. + Gmsh tracks most objects through a combination of its dimension, ``dim`` + and an integer tag, ``tag``, which must be unique to the object. For example, + ``Point(1)`` has dimension 0 and a unique tag 1, while ``Line(1)`` has + dimension 1 and a unique tag 1. Then, we define 5 points to describe a circle. .. code-block:: none - Point(5) = {x0, y0, z0, dx_disc}; - Point(6) = {x0 + R, y0, z0, dx_disc}; - Point(7) = {x0 - R, y0, z0, dx_disc}; - Point(8) = {x0, y0 + R, z0, dx_disc}; - Point(9) = {x0, y0 - R, z0, dx_disc}; + Point(5) = { 0, 0, 0, 0.1}; + Point(6) = { 1, 0, 0, 0.1}; + Point(7) = {-1, 0, 0, 0.1}; + Point(8) = { 0, 1, 0, 0.1}; + Point(9) = { 0, -1, 0, 0.1}; Then, we create 8 edges: 4 for the rectangle and 4 for the circle. Note that the Gmsh command ``Circle`` requires the arc to be @@ -105,7 +106,7 @@ Then, we define two plane surfaces: the rectangle without the disc first, and th Plane Surface(2) = {10}; Finally, we group together some edges and define ``Physical`` entities. -Firedrake uses the tags of these physical identities to distinguish +Firedrake uses the ``tag`` of each physical entity to distinguish between parts of the mesh (see the concrete example at the end of this page). .. code-block:: none @@ -138,7 +139,7 @@ and improved readibility of the mesh generation code. We first need to ``initialize`` the Gmsh API and create a new empty mesh model. -.. code-block:: none +.. code-block:: python gmsh.initialize() model = gmsh.model @@ -146,70 +147,71 @@ We first need to ``initialize`` the Gmsh API and create a new empty mesh model. As before, we define the four rectangle corner points and target element size. -.. code-block:: none +.. code-block:: python rectangle_points = [ - model.geo.addPoint(x0 - L/2, y0 + W/2, z0, dx_rec, 1), # top left - model.geo.addPoint(x0 - L/2, y0 - W/2, z0, dx_rec, 2), # bottom left - model.geo.addPoint(x0 + L/2, y0 - W/2, z0, dx_rec, 3), # bottom right - model.geo.addPoint(x0 + L/2, y0 + W/2, z0, dx_rec, 4) # top right + model.geo.addPoint(x0 - L/2, y0 + W/2, z0, dx_rec, tag = 1), # top left + model.geo.addPoint(x0 - L/2, y0 - W/2, z0, dx_rec, tag = 2), # bottom left + model.geo.addPoint(x0 + L/2, y0 - W/2, z0, dx_rec, tag = 3), # bottom right + model.geo.addPoint(x0 + L/2, y0 + W/2, z0, dx_rec, tag = 4) # top right ] Then, we define 5 points to describe a circle. -.. code-block:: none +.. code-block:: python - center = model.geo.addPoint(x0, y0, z0, 5) + center = model.geo.addPoint(x0, y0, z0, tag = 5) circle_points = [ - model.geo.addPoint(x0 - R, y0, z0, dx_disc, 6), - model.geo.addPoint(x0, y0 + R, z0, dx_disc, 7), - model.geo.addPoint(x0 + R, y0, z0, dx_disc, 8), - model.geo.addPoint(x0, y0 - R, z0, dx_disc, 9) + model.geo.addPoint(x0 - R, y0, z0, dx_disc, tag = 6), + model.geo.addPoint(x0, y0 + R, z0, dx_disc, tag = 7), + model.geo.addPoint(x0 + R, y0, z0, dx_disc, tag = 8), + model.geo.addPoint(x0, y0 - R, z0, dx_disc, tag = 9) ] Then, we create 8 edges: 4 for the rectangle and 4 for the circle. -.. code-block:: none +.. code-block:: python rectangle_lines = [ - model.geo.addLine(rectangle_points[0], rectangle_points[1], 1), # left - model.geo.addLine(rectangle_points[1], rectangle_points[2], 2), # bottom - model.geo.addLine(rectangle_points[2], rectangle_points[3], 3), # right - model.geo.addLine(rectangle_points[3], rectangle_points[0], 4) # top + model.geo.addLine(rectangle_points[0], rectangle_points[1], tag = 1), # left + model.geo.addLine(rectangle_points[1], rectangle_points[2], tag = 2), # bottom + model.geo.addLine(rectangle_points[2], rectangle_points[3], tag = 3), # right + model.geo.addLine(rectangle_points[3], rectangle_points[0], tag = 4) # top ] circle_arcs =[ - model.geo.addCircleArc(circle_points[0], center, circle_points[1], 5), - model.geo.addCircleArc(circle_points[1], center, circle_points[2], 6), - model.geo.addCircleArc(circle_points[2], center, circle_points[3], 7), - model.geo.addCircleArc(circle_points[3], center, circle_points[0], 8) + model.geo.addCircleArc(circle_points[0], center, circle_points[1], tag = 5), + model.geo.addCircleArc(circle_points[1], center, circle_points[2], tag = 6), + model.geo.addCircleArc(circle_points[2], center, circle_points[3], tag = 7), + model.geo.addCircleArc(circle_points[3], center, circle_points[0], tag = 8) ] We then combine the edges into a closed loop for both the rectangle and the circle used to define a surface for the area outside and inside the inscribed circle, respectively. In the ``addPlaneSurface`` function by convention, the first ``Curve Loop`` defines the outer boundary and -anything after in the list is treated as a hole in the domain. These need -to be registered to the model with ``syncronize`` before we can use them. +anything after in the list is treated as the boundary of a hole (or holes) +in the domain. The integerThese need to be registered to the model with ``syncronize`` +before we can use them. -.. code-block:: none +.. code-block:: python - rectangle_loop = model.geo.addCurveLoop(rectangle_lines, 9) - circle_loop = model.geo.addCurveLoop(circle_arcs, 10) + rectangle_loop = model.geo.addCurveLoop(rectangle_lines, tag = 9) + circle_loop = model.geo.addCurveLoop(circle_arcs, tag = 10) - punched_surface = model.geo.addPlaneSurface([rectangle_loop,circle_loop], 1) - circle_surface = model.geo.addPlaneSurface([circle_loop], 2) + punched_surface = model.geo.addPlaneSurface([rectangle_loop,circle_loop], tag = 1) + circle_surface = model.geo.addPlaneSurface([circle_loop], tag = 2) model.geo.synchronize() Finally, we group together some edges and define ``Physical`` entities. -.. code-block:: none +.. code-block:: python - model.addPhysicalGroup(1, [rectangle_lines[1], rectangle_lines[3]], 11, name = "HorEdges") - model.addPhysicalGroup(1, [rectangle_lines[0], rectangle_lines[2]], 12, name = "VerEdges") - model.addPhysicalGroup(1, circle_arcs, 13, name = "Circle") - model.addPhysicalGroup(2, [punched_surface], 3, name = "PunchedDom") - model.addPhysicalGroup(2, [circle_surface], 4, name = "Disc") + model.addPhysicalGroup(dim = 1, tags = [rectangle_lines[1], rectangle_lines[3]], tag = 11, name="HorEdges") + model.addPhysicalGroup(dim = 1, tags = [rectangle_lines[0], rectangle_lines[2]], tag = 12, name="VerEdges") + model.addPhysicalGroup(dim = 1, tags = circle_arcs, tag = 13, name="Circle") + model.addPhysicalGroup(dim = 2, tags = [punched_surface], tag = 3, name="PunchedDom") + model.addPhysicalGroup(dim = 2, tags = [circle_surface], tag = 4, name="Disc") A number of meshing options are available. In particular, the algorithm for mesh generation and can be set globally or for individual surfaces. @@ -218,92 +220,99 @@ and can be set globally or for individual surfaces. 7: BAMG, 8: Frontal-Delaunay for Quads, 9: Packing of Parallelograms, 11: Quasi-structured Quad * 3D: Delaunay (default) 3: Initial mesh only 4: Frontal 7: MMG3D 9: R-tree 10: HXT -For more information see the `Gmesh documentation on algorithms `_. +For more information see the `Gmesh documentation `_. When writing the mesh to file, the format is determined by the file extension. For example, `.msh2` for Gmsh 2.x, `.msh` for GMSH 4.x. -.. code-block:: none +.. code-block:: python gmsh.option.setNumber("Mesh.Algorithm", 6) gmsh.option.setNumber("Mesh.MshFileVersion", 4.1) gmsh.model.mesh.generate(2) gmsh.write('gmsh_api_demo.msh') - gmsh.finalize() - -.. note:: - Best practice is to shut down the Gmsh API kernel after finalising the mesh. + We close the Gmsh API kernel after finalising the mesh. + + .. code-block:: python + + gmsh.finalize() Using OpenCASCADE through Gmsh ------------------------------ Using OpenCASCADE through Gmsh, we define higher level geometries such as rectangles -and discs directly. It also has addition 3D capability not illustrated here. +and discs directly. It also has additional 3D capability, and integration not illustrated +here. Please see the `Gmsh documentation `_ +for more details. As with the Gmsh API, we ``initialize`` and start constructing a new mesh model. -.. code-block:: none +.. code-block:: python gmsh.initialize() + model = gmsh.model gmsh.model.add("gmsh_occ_demo") We first use OpenCASCADE to create a rectangle and a cylinder object. This automates the create of points, lines, and surfaces. Both objects need to be registered to the model with ``syncronize`` before we can use them. -.. code-block:: none +.. code-block:: python - rectangle_obj = gmsh.model.occ.addRectangle(x0 - L/2, y0 - W/2, z0, L, W, 1) - cylinder_obj = gmsh.model.occ.addCylinder(x0, y0, z0, 0, 0, 1, R, 2) - gmsh.model.occ.synchronize() + rectangle_obj_tag = model.occ.addRectangle(x0 - L/2, y0 - W/2, z0, L, W, tag = 1) + disc_obj_tag = model.occ.addDisk(x0, y0, z0, rx = R, ry = R, tag = 2) + model.occ.synchronize() -As the default behavior of the ``cut`` function, utilized to create the hole, is to -delete the original objects, we set ``removeTool=False`` to retain the cylinder object. -We also save the tag of the combined object for later use and register the new object -to the model with ``syncronize``. +To create the whole, we use the method ``occ.cut`` with the option ``removeTool=False`` to +retain the disc interior (which would be otherwise deleted by default). The ``occ.cut`` method +takes and returns a list of tuples ``(dimension, tag)`` as do other functions such as +``getBoundary`` used below. We save the tag of the combined object for later use +and register the new object to the model with ``syncronize``. -.. code-block:: none +.. code-block:: python - punched_surface = gmsh.model.occ.cut([(2, rectangle_obj)], [(3, cylinder_obj)], removeTool = False) + punched_surface = model.occ.cut([(2, rectangle_obj_tag)], [(2, disc_obj_tag)], removeTool=False) punched_surface_tag = punched_surface[0][0][1] - gmsh.model.occ.synchronize() + model.occ.synchronize() -We then extact the boundary from the objects. The ``getBoundary`` function takes and -returns a list of tuples ``(dimension, tag)``. We extract the cylinder surface and points -along with the punched surface lines to define the ``Physical`` groups. +We then extact the boundary from the objects. We extract the the punched surface +lines along with disc points to define the ``Physical`` groups. It returns boundaries +per entity (``combined = false``) or as a single shape (``combined = true``), and +adjust the signs to reflect orientation if ``oriented = true``. The boundary operator +is applied down to point-level, or dimension 0, when ``recursive = True``. -.. code-block:: none +.. code-block:: python - circle_surface = gmsh.model.getBoundary([(3, cylinder_obj)], True, True, False) - punched_lines = gmsh.model.getBoundary([(2, punched_surface_tag)], True, True, False) - circle_points = gmsh.model.getBoundary([(3, cylinder_obj)], True, True, True) + punched_lines = model.getBoundary([(2, punched_surface_tag)], + combined = True, oriented = True, recursive = False) + disc_points = model.getBoundary([(2, disc_obj_tag)], + combined = True, oriented = True, recursive = True) We set the mesh resolution using ``setSize``. The choice here is to first set all the zero-dimensional points to the background size, and then override the mesh size for the points on the circle boundary. Another strategy documented in the Gmsh manual is to identify the desired points by a bounding box search. -.. code-block:: none +.. code-block:: python - gmsh.model.mesh.setSize(gmsh.model.occ.getEntities(0), dx_rec) - gmsh.model.mesh.setSize(circle_points, dx_disc) + model.mesh.setSize(gmsh.model.occ.getEntities(0), dx_rec) + model.mesh.setSize(disc_points, dx_disc) We parse just the line tags to create a list of physical group tags. In this case the assignment of the lines was done manually through trial and inspection. TODO: add a function to automatically assign the lines to the correct physical group. -.. code-block:: none +.. code-block:: python - circle_surface_tags = [abs(line) for dim,line in circle_surface] punched_line_tags = [abs(line) for dim,line in punched_lines] - gmsh.model.addPhysicalGroup(1, [punched_line_tags[1], punched_line_tags[4]], 11, name = "HorEdges") - gmsh.model.addPhysicalGroup(1, [punched_line_tags[2], punched_line_tags[3]], 12, name = "VertEdges") - gmsh.model.addPhysicalGroup(1, [punched_line_tags[0]], 13, name = "CircleEdge") - gmsh.model.addPhysicalGroup(2, [punched_surface_tag], 3, name = "PunchedDom") - model.addPhysicalGroup(2, [circle_surface_tags[-1]], 4, name = "Disc") + model.addPhysicalGroup(dim = 1, tags = [punched_line_tags[1], punched_line_tags[4]], tag = 11, name="HorEdges") + model.addPhysicalGroup(dim = 1, tags = [punched_line_tags[2], punched_line_tags[3]], tag = 12, name="VertEdges") + model.addPhysicalGroup(dim = 1, tags = [punched_line_tags[0]], tag = 13, name="CircleEdge") + model.addPhysicalGroup(dim = 2, tags = [punched_surface_tag], tag = 3, name="PunchedDom") + model.addPhysicalGroup(dim = 2, tags = [disc_obj_tag], tag = 4, name="Disc") -.. code-block:: none +.. code-block:: python gmsh.option.setNumber("Mesh.Algorithm", 6) gmsh.model.mesh.generate(2) @@ -314,7 +323,7 @@ Compare Meshes -------------- We can load and check the generated meshes in Firedrake -.. code-block:: none +.. code-block:: python meshes = [Mesh('gmsh_occ_demo.msh', name = "Gmsh API"), Mesh('gmsh_api_demo.msh', name = "Gmsh OpenCASCADE")]