Backward step#

The backward step is a mesh (or domain) in ${\mathbb{R}}^n$, $n\in \{2,3\}$. The domain is illustrated in the following figure.

When $n=3$, The domain is extended to the thrid axis, $z$-axis, perpendicular to the plane. The parameters are

backward_step(x1=1, x2=1, y1=0.25, y2=0.25, z=None, periodic=False)[source]#

Parameters:

x1float, default=1

See the illustration.

x2float, default=1

See the illustration.

y1float, default=0.25

See the illustration.

y2float, default=0.25

See the illustration.

zfloat, None, default=None

When it is None, it gives a two-dimensional domain. Otherwise, $(z>0)$, it gives a three-dimensional one.

periodicbool, default=False

When the domain is 3d, whether it is periodic along the z-axis?

>>> boundary_units_set = {
...     0: [1, 1, 1, 0],
...     1: [0, 1, 0, 1],
...     2: [1, 0, 1, 1],
... }

>>> boundary_units_set = {
...     0: [1, 1, 1, 0, 1, 1],
...     1: [0, 1, 0, 1, 1, 1],
...     2: [1, 0, 1, 1, 1, 1],
... }

Examples#

3d#

Below codes will lead to a three-dimensional backward step mesh of $3\ast 5\ast 5\ast 5$ elements (because the domain is splited into 3 regions).

>>> ph.config.set_embedding_space_dim(3)
>>> manifold = ph.manifold(3)
>>> mesh = ph.mesh(manifold)
>>> msepy, obj = ph.fem.apply('msepy', locals())
>>> manifold = obj['manifold']
>>> mesh = obj['mesh']
>>> msepy.config(manifold)('backward_step')
>>> msepy.config(mesh)([5, 5, 5])
>>> mesh.visualize(saveto=None_or_custom_path_3)  
<Figure size ...

2d#

To make a two-dimensional backward step mesh of $3\ast 24\ast 6$ elements, just do

>>> ph.config.set_embedding_space_dim(2)
>>> manifold = ph.manifold(2)
>>> mesh = ph.mesh(manifold)
>>> msepy, obj = ph.fem.apply('msepy', locals())
>>> manifold = obj['manifold']
>>> mesh = obj['mesh']
>>> msepy.config(manifold)('backward_step')
>>> msepy.config(mesh)([24, 6])
>>> mesh.visualize(saveto=None_or_custom_path_2)  
<Figure size ...

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