def test_union(show=False):
geo = dmsh.Union(
[dmsh.Circle([-0.5, 0.0], 1.0),
dmsh.Circle([+0.5, 0.0], 1.0)])
X, cells = dmsh.generate(geo, 0.15, show=show, tol=1.0e-10)
ref_norms = [3.0088043884612756e+02, 1.5785099320497183e+01, 1.5]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-12)
return X, cells
def test_union(show=False):
geo = dmsh.Union([
dmsh.Rectangle(-1.0, +0.5, -1.0, +0.5),
dmsh.Rectangle(-0.5, +1.0, -0.5, +1.0)
])
X, cells = dmsh.generate(geo, 0.15, show=show, tol=1.0e-10)
ref_norms = [1.7868961429998612e+02, 1.1117047580567053e+01, 1.0]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-12)
return X, cells
def sartenTriangulation(size, edge_size):
"""
Triangulación de silueta de una sartén de cocina
"""
c = dmsh.Circle([0, 0], size)
r = dmsh.Rectangle(-2.5*size, -size*0.9, -size/8, size/8)
geo = dmsh.Union([c, r])
points, cells = dmsh.generate(geo, edge_size)
return Triangulation(points, cells)
def test_boundary_step():
geo = dmsh.Union([dmsh.Circle([-0.5, 0.0], 1.0), dmsh.Circle([+0.5, 0.0], 1.0)])
geo.show()
a = geo.boundary_step([-0.5, 0.9])
assert numpy.array_equal(a, [-0.5, 1.0])
a = geo.boundary_step([-0.5, 0.6])
assert numpy.array_equal(a, [-0.5, 1.0])
a = geo.boundary_step([0.05, 0.05])
assert_equality(a, [-4.4469961425821203e-01, 9.9846976285554556e-01], 1.0e-10)
def test_union(show=False):
geo = dmsh.Union([
dmsh.Rectangle(-1.0, +0.5, -1.0, +0.5),
dmsh.Rectangle(-0.5, +1.0, -0.5, +1.0)
])
X, cells = dmsh.generate(geo, 0.15, show=show, tol=1.0e-5)
ref_norms = [
1.8432376349018622e02, 1.1278734993846784e01, 1.0000000000000000e00
]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-10)
return X, cells
def test_boundary_step2():
geo = dmsh.Union(
[dmsh.Circle([-0.5, 0.0], 1.0),
dmsh.Circle([+0.5, 0.0], 1.0)])
np.random.seed(0)
pts = np.random.uniform(-2.0, 2.0, (2, 100))
pts = geo.boundary_step(pts)
# geo.plot()
# import matplotlib.pyplot as plt
# plt.plot(pts[0], pts[1], "xk")
# plt.show()
assert np.all(np.abs(geo.dist(pts)) < 1.0e-12)
def test_union_rectangles(show=False):
geo = dmsh.Union([
dmsh.Rectangle(-1.0, +0.5, -1.0, +0.5),
dmsh.Rectangle(-0.5, +1.0, -0.5, +1.0)
])
X, cells = dmsh.generate(geo, 0.15, show=show, tol=1.0e-5, max_steps=100)
ref_norms = [
1.8417796811774514e02, 1.1277323166424049e01, 1.0000000000000000e00
]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-10)
return X, cells
def test_union_circles(show=False):
geo = dmsh.Union(
[dmsh.Circle([-0.5, 0.0], 1.0),
dmsh.Circle([+0.5, 0.0], 1.0)])
X, cells = dmsh.generate(geo, 0.15, show=show, tol=1.0e-5, max_steps=100)
geo.plot()
ref_norms = [
3.0080546580519666e02, 1.5775854476745508e01, 1.5000000000000000e00
]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-10)
return X, cells
def test_union(show=False):
angles = numpy.pi * numpy.array([3.0 / 6.0, 7.0 / 6.0, 11.0 / 6.0])
geo = dmsh.Union(
[
dmsh.Circle([numpy.cos(angles[0]), numpy.sin(angles[0])], 1.0),
dmsh.Circle([numpy.cos(angles[1]), numpy.sin(angles[1])], 1.0),
dmsh.Circle([numpy.cos(angles[2]), numpy.sin(angles[2])], 1.0),
]
)
X, cells = dmsh.generate(geo, 0.2, show=show, tol=1.0e-10)
ref_norms = [4.0372522103229670e02, 2.1155465970807523e01, 1.9999337650692937e00]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-10)
return X, cells
def main():
fig = plt.figure()
position = 231
geo = dmsh.Union(
[dmsh.Rectangle(-1.0, +0.5, -1.0, +0.5), dmsh.Rectangle(-0.5, +1.0, -0.5, +1.0)]
)
for it in [1, 3, 5, 10, 30, 50]:
ax = fig.add_subplot(position)
drawPlot(it, ax, geo)
position += 1
plt.show()
def test_union_three_circles(show=False):
angles = np.pi * np.array([3.0 / 6.0, 7.0 / 6.0, 11.0 / 6.0])
geo = dmsh.Union([
dmsh.Circle([np.cos(angles[0]), np.sin(angles[0])], 1.0),
dmsh.Circle([np.cos(angles[1]), np.sin(angles[1])], 1.0),
dmsh.Circle([np.cos(angles[2]), np.sin(angles[2])], 1.0),
])
X, cells = dmsh.generate(geo, 0.2, show=show, tol=1.0e-5, max_steps=100)
ref_norms = [
4.0359760255235619e02, 2.1162741423521961e01, 2.0000000000000000e00
]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-10)
return X, cells
def test_union(show=False):
angles = numpy.pi * numpy.array([3.0 / 6.0, 7.0 / 6.0, 11.0 / 6.0])
geo = dmsh.Union([
dmsh.Circle(
[numpy.cos(angles[0]), numpy.sin(angles[0])], 1.0),
dmsh.Circle(
[numpy.cos(angles[1]), numpy.sin(angles[1])], 1.0),
dmsh.Circle(
[numpy.cos(angles[2]), numpy.sin(angles[2])], 1.0),
])
X, cells = dmsh.generate(geo, 0.2, show=show, tol=1.0e-10)
ref_norms = [
4.1390554922002769e+02, 2.1440246410944471e+01, 1.9947113226010518e+00
]
assert_norm_equality(X.flatten(), ref_norms, 1.0e-12)
return X, cells
def _create_mesh(filename):
poly = dmsh.Polygon(
[
[-295.0, 0.0],
[-160.0, 0.0],
[-50.0, 110.0],
[-50.0, 190.0],
[+50.0, 190.0],
[+50.0, 110.0],
[+160.0, 0.0],
[+295.0, 0.0],
[+405.0, 110.0],
[+405.0, 235.0],
[+200.0, 430.0],
[+170.0, 400.0],
[+355.0, 235.0],
[-355.0, 235.0],
[-170.0, 400.0],
[-200.0, 430.0],
[-405.0, 235.0],
[-405.0, 110.0],
]
)
geo = dmsh.Union(
[
poly,
dmsh.Circle([-295.0, 110.0], 110.0),
dmsh.Circle([+295.0, 110.0], 110.0),
dmsh.Circle([-160.0, 110.0], 110.0),
dmsh.Circle([+160.0, 110.0], 110.0),
]
)
X, cells = dmsh.generate(
geo,
35.0,
# show=True
)
X, cells = optimesh.lloyd(X, cells, 1.0e-3, 100)
X = numpy.column_stack([X[:, 0], X[:, 1], numpy.zeros(X.shape[0])])
meshio.write_points_cells(filename, X, {"triangle": cells})
return
def polygon2geo(polygon):
# exterior boundary (dmsh does not include the last point twice to close the polygon such as shapely)
e = list(polygon.exterior.coords.xy)
boundary_e = [[e[0][i], e[1][i]] for i in range(len(e[0]) - 1)]
outer = dmsh.Polygon(boundary_e)
print(boundary_e)
# interior boundary
inner = []
for int in polygon.interiors:
h = list(int.coords.xy)
boundary_h = [[h[0][i], h[1][i]] for i in range(len(h[0]) - 1)]
hole = dmsh.Polygon(boundary_h)
inner.append(hole)
if len(inner) > 1:
inner = dmsh.Union(inner)
geo = dmsh.Difference(outer, inner)
elif len(inner) == 1:
inner = inner[0]
geo = dmsh.Difference(outer, inner)
else:
geo = outer
return geo
def test_boundary_step():
geo = dmsh.Union(
[dmsh.Circle([-0.5, 0.0], 1.0),
dmsh.Circle([+0.5, 0.0], 1.0)])
a = geo.boundary_step([-0.5, 0.9])
assert np.array_equal(a, [-0.5, 1.0])
a = geo.boundary_step([-0.5, 0.6])
assert np.array_equal(a, [-0.5, 1.0])
a = geo.boundary_step([0.05, 0.05])
assert_equality(a, [-4.4469961425821203e-01, 9.9846976285554556e-01],
1.0e-10)
pts = np.array([[-5.0, 0.0], [4.1, 0.0]])
pts = geo.boundary_step(pts.T).T
ref = np.array([[-1.5, 0.0], [1.5, 0.0]])
assert np.all(np.abs(pts - ref) < 1.0e-10)
pts = np.array([[-0.9, 0.0], [1.1, 0.0]])
pts = geo.boundary_step(pts.T).T
ref = np.array([[-1.5, 0.0], [1.5, 0.0]])
assert np.all(np.abs(pts - ref) < 1.0e-10)
geo = dmsh.Difference(
dmsh.Circle([0.0, 0.0], 1.0),
dmsh.Polygon([[0.0, 0.0], [1.5, 0.4], [1.5, -0.4]]),
)
X, cells = dmsh.generate(geo, 0.1, tol=1.0e-10)
save(X, cells, "pacman.svg")
r = dmsh.Rectangle(-1.0, +1.0, -1.0, +1.0)
c = dmsh.Circle([0.0, 0.0], 0.3)
geo = dmsh.Difference(r, c)
X, cells = dmsh.generate(geo, lambda pts: np.abs(c.dist(pts)) / 5 + 0.05, tol=1.0e-10)
save(X, cells, "rectangle-hole-refinement.svg")
geo = dmsh.Union([dmsh.Circle([-0.5, 0.0], 1.0), dmsh.Circle([+0.5, 0.0], 1.0)])
X, cells = dmsh.generate(geo, 0.15)
save(X, cells, "union-circles.svg")
geo = dmsh.Union(
[dmsh.Rectangle(-1.0, +0.5, -1.0, +0.5), dmsh.Rectangle(-0.5, +1.0, -0.5, +1.0)]
)
X, cells = dmsh.generate(geo, 0.15)
save(X, cells, "union-rectangles.svg")
angles = np.pi * np.array([3.0 / 6.0, 7.0 / 6.0, 11.0 / 6.0])
geo = dmsh.Union(
[
dmsh.Circle([np.cos(angles[0]), np.sin(angles[0])], 1.0),
else:
raise ValueError("Quadrature precision too high on triangle")
assert abs(np.sum(qwgts) -
1) < 1e-12 #Ensures that the weights do indeed sum to 1.
return rspts, qwgts
def Isopmap(x, y, r, s, shapefcn):
S, dSdr, dSds = shapefcn(r, s)
j11, j12 = dSdr[:, 0].dot(x), dSdr[:, 0].dot(y)
j21, j22 = dSds[:, 0].dot(x), dSds[:, 0].dot(y)
detJ = j11 * j22 - j12 * j21
dSdx = (j22 * dSdr - j12 * dSds) / detJ
dSdy = (-j21 * dSdr + j11 * dSds) / detJ
return S, dSdx, dSdy, detJ
if __name__ == '__main__':
import dmsh
geo1 = dmsh.Circle((0, 0), 1)
geo2 = dmsh.Rectangle(0.5, 1.5, 0, 1)
geo = dmsh.Union((geo1, geo2))
P, T, E, B = dmsh.generate(geo, .5)
fem = FEM_P2CG(P, T, E, B)
fem.show_mesh2D()
A = fem.IsoStiffnessAssembler(lambda x, y: 1)
