1.3. 3D Orthogonal Grid

This is very similar to the previous 2D Orthogonal Grid tutorial. We use the two partitioners again (KBA and Parmetis).

1.3.1. Mesh and KBA partition

A simple orthogonal 3D mesh with KBA partitioner. We will run with 8 processes, so we will partition the domain in 2x2x2 parts with cuts placed exactly at x=0, y=0, and z=0.

-- Setup the mesh
nodes = {}
n_cells = 10
length = 2.
xmin = -length / 2.
dx = length / n_cells
for i = 1, (n_cells + 1) do
  k = i - 1
  nodes[i] = xmin + k * dx
end
meshgen = mesh.OrthogonalMeshGenerator.Create({
  node_sets = { nodes, nodes, nodes },
  partitioner = mesh.KBAGraphPartitioner.Create({
    nx = 2,
    ny = 2,
    nz = 2,
    xcuts = { 0. },
    ycuts = { 0. },
    zcuts = { 0. },
  }),
})
mesh.MeshGenerator.Execute(meshgen)
-- Set Material IDs
mesh.SetUniformMaterialID(0)

1.3.2. Export the mesh

The resulting mesh partition is shown below

-- Exporting the mesh
mesh.ExportToPVTU("ortho_3D_KBA")

1.3.3. Mesh (again) and Parmetis partition

A simple orthogonal 3D mesh with Parmetis partitioner.

meshgen = mesh.OrthogonalMeshGenerator.Create({
  node_sets = { nodes, nodes, nodes },
  partitioner = mesh.PETScGraphPartitioner.Create({ type = "parmetis" }),
})
mesh.MeshGenerator.Execute(meshgen)
-- Set Material IDs
vol0 = logvol.RPPLogicalVolume.Create({ infx = true, infy = true, infz = true })
mesh.SetMaterialIDFromLogicalVolume(vol0, 0)

1.3.4. Export the mesh

Note that now, both partitioners are not giving the same result. The Parmetis partition is shown below

-- Exporting the mesh
mesh.ExportToPVTU("ortho_3D_Parmetis")

---

1.3.5. The complete input is below:

You can copy/paste the text below or look in the file named tutorials/meshing/ortho_3D.lua:

-- Setup the mesh
nodes = {}
n_cells = 10
length = 2.
xmin = -length / 2.
dx = length / n_cells
for i = 1, (n_cells + 1) do
  k = i - 1
  nodes[i] = xmin + k * dx
end

meshgen = mesh.OrthogonalMeshGenerator.Create({
  node_sets = { nodes, nodes, nodes },
  partitioner = mesh.KBAGraphPartitioner.Create({
    nx = 2,
    ny = 2,
    nz = 2,
    xcuts = { 0. },
    ycuts = { 0. },
    zcuts = { 0. },
  }),
})
mesh.MeshGenerator.Execute(meshgen)

-- Set Material IDs
mesh.SetUniformMaterialID(0)


-- Exporting the mesh
mesh.ExportToPVTU("ortho_3D_KBA")


meshgen = mesh.OrthogonalMeshGenerator.Create({
  node_sets = { nodes, nodes, nodes },
  partitioner = mesh.PETScGraphPartitioner.Create({ type = "parmetis" }),
})
mesh.MeshGenerator.Execute(meshgen)

-- Set Material IDs
vol0 = logvol.RPPLogicalVolume.Create({ infx = true, infy = true, infz = true })
mesh.SetMaterialIDFromLogicalVolume(vol0, 0)


-- Exporting the mesh
mesh.ExportToPVTU("ortho_3D_Parmetis")