Poisson equation on L-shaped / spherical geometry

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This simple example shows the application of the Poisson equation on a L-shaped geometry, as an add-on for this example.

import felupe as fem
import numpy as np

lower = fem.Rectangle(a=(0, 0), b=(3, 1), n=(31, 11))
upper = fem.Rectangle(a=(2, 1), b=(3, 4), n=(11, 31))
mesh = fem.MeshContainer(meshes=[lower, upper], merge=True, decimals=6).stack()

region = fem.RegionQuad(mesh)
u = fem.Field(region, dim=1)
field = fem.FieldContainer([u])

region_edges = fem.RegionQuadBoundary(mesh, only_surface=True)
edges = np.unique(region_edges.mesh_faces().cells)

boundaries = fem.BoundaryDict(
    fixed=fem.Boundary(u, mask=np.isin(np.arange(mesh.npoints), edges)),
)
boundaries.plot(show_lines=False).show()

solid = fem.SolidBody(umat=fem.Laplace(), field=field)
load = fem.SolidBodyForce(field=field, values=1.0)

step = fem.Step([solid, load], boundaries=boundaries)
job = fem.Job([step]).evaluate()

view = mesh.view(point_data={"Field": u.values})
view.plot("Field").show()

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For spherical geometries:

import felupe as fem
import numpy as np

circle = fem.Circle(sections=[0, 90], n=7)
mesh = circle.revolve(axis=0, phi=360, n=37).sweep(decimals=4)

region = fem.RegionHexahedron(mesh)
u = fem.Field(region, dim=1)
field = fem.FieldContainer([u])

region_surface = fem.RegionHexahedronBoundary(mesh, only_surface=True)
surface = np.unique(region_surface.mesh_faces().cells)

boundaries = fem.BoundaryDict(
    fixed=fem.Boundary(u, mask=np.isin(np.arange(mesh.npoints), surface)),
)
boundaries.plot(show_lines=False).show()

solid = fem.SolidBody(umat=fem.Laplace(), field=field)
load = fem.SolidBodyForce(field=field, values=1.0)

step = fem.Step([solid, load], boundaries=boundaries)
job = fem.Job([step]).evaluate()

view = mesh.view(point_data={"Field": u.values})
plotter = view.plot("Field")
plotter.mesh.clip("z", invert=True, value=0.0, inplace=True)
plotter.show()