triellipt — Examples: Pulsating mesh

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Pulsating mesh

This example demonstrates the use of refinement and coarsening procedures in triellipt.

In what follows, we assume the following import is used:

Pythonimport triellipt as tri

Creating a mesh

The background mesh is created using Gmsh with the following .geo file:

R_0 = 1.00;  // Radius
S_0 = 0.02;  // Mesh size

Point(0) = {0, 0, 0};

Point(1) = {+ R_0, + 0.0, 0, S_0};
Point(2) = {+ 0.0, + R_0, 0, S_0};
Point(3) = {- R_0, + 0.0, 0, S_0};
Point(4) = {- 0.0, - R_0, 0, S_0};

Circle(1) = {1, 0, 2};
Circle(2) = {2, 0, 3};
Circle(3) = {3, 0, 4};
Circle(4) = {4, 0, 1};

Line Loop(1) = {1, 2, 3, 4};

Plane Surface(1) = {1};

Mesh.Algorithm = 6;

The mesh is saved as circ-gmsh.msh in the mesh subfolder. The mesh is then read as follows:

Pythonmesh = tri.mshread.getreader('mesh').read_mesh('circ-gmsh.msh')

The mesh is coarsened in the central region as follows:

Pythonmesh = mesh.reduced(shrink=2, detach=True)
mesh = mesh.reduced(shrink=3)
mesh = mesh.delmouths()

Creating an AMR unit

The next step is to create an AMR unit:

Pythonunit = tri.amr.getunit(mesh)

The unit can be provided with a data field.

For this we first create the node-based data as follows:

Pythondata = unit.from_func(func)

where func is a callable that defines the data field.

The data field can be constrained on hanging nodes:

Pythondata = unit.constrain(data)

Finally, we assign the data field to the unit:

Pythonunit.data[0] = data

Refinement step

The unit can be refined in a frontal manner:

Pythonfor _ in range(COUNT):
    unit = unit.refine(
       unit.front_coarse().trinums
    )

where COUNT is the number of refinement steps.

Here unit.front_coarse() returns a TriFront object that contains the numbers of triangles to refine.

The data field assigned to the unit is refined automatically during refinement.

Coarsening step

Coarsening can be performed after refinement as follows:

Pythonfor _ in range(COUNT):
    unit = unit.coarsen(
        unit.front_fine().trinums
    )

Here unit.front_fine() returns a TriFront object that contains the coarsening front. In this case, .trinums provide central triangles of super-triangles to coarsen.

The data field assigned to the unit is automatically interpolated during coarsening.

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