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import time
import matplotlib.pyplot as plt
import meshplex
import numpy as np
import pygmsh
import dmsh
def _compute_num_boundary_points(total_num_points):
# The number of boundary points, the total number of points, and the number of cells
# are connected by two equations (the second of which is approximate).
#
# Euler:
# 2 * num_points - num_boundary_edges - 2 = num_cells
#
# edge_length = 2 * np.pi / num_boundary_points
# tri_area = np.sqrt(3) / 4 * edge_length ** 2
# num_cells = int(np.pi / tri_area)
#
# num_boundary_points = num_boundary_edges
#
# Hence:
# 2 * num_points =
# num_boundary_points + 2 + np.pi / (np.sqrt(3) / 4 * (2 * np.pi / num_boundary_points) ** 2)
#
# We need to solve
#
# + num_boundary_points ** 2
# + (sqrt(3) * pi) * num_boundary_points
# + (2 - 2 * num_points) * (sqrt(3) * pi)
# = 0
#
# for the number of boundary points.
sqrt3_pi = np.sqrt(3) * np.pi
num_boundary_points = -sqrt3_pi / 2 + np.sqrt(
3 / 4 * np.pi**2 - (2 - 2 * total_num_points) * sqrt3_pi
)
return num_boundary_points
def dmsh_circle(num_points):
target_edge_length = 2 * np.pi / _compute_num_boundary_points(num_points)
geo = dmsh.Circle([0.0, 0.0], 1.0)
X, cells = dmsh.generate(geo, target_edge_length)
return X, cells
def gmsh_circle(num_points):
geom = pygmsh.built_in.Geometry()
target_edge_length = 2 * np.pi / _compute_num_boundary_points(num_points)
geom.add_circle(
[0.0, 0.0, 0.0], 1.0, lcar=target_edge_length, num_sections=4, compound=True
)
mesh = pygmsh.generate_mesh(geom, remove_lower_dim_cells=True, verbose=False)
return mesh.points[:, :2], mesh.cells[0].data
data = {
"dmsh": {"n": [], "time": [], "q": [], "version": dmsh.__version__},
"gmsh": {"n": [], "time": [], "q": [], "version": pygmsh.get_gmsh_version()},
}
for num_points in range(1000, 10000, 1000):
print(num_points)
# dmsh
t = time.time()
pts, cells = dmsh_circle(num_points)
t = time.time() - t
mesh = meshplex.MeshTri(pts, cells)
avg_q = np.sum(mesh.cell_quality) / len(mesh.cell_quality)
data["dmsh"]["n"].append(len(pts))
data["dmsh"]["time"].append(t)
data["dmsh"]["q"].append(avg_q)
# gmsh
t = time.time()
pts, cells = gmsh_circle(num_points)
t = time.time() - t
mesh = meshplex.MeshTri(pts, cells)
avg_q = np.sum(mesh.cell_quality) / len(mesh.cell_quality)
data["gmsh"]["n"].append(len(pts))
data["gmsh"]["time"].append(t)
data["gmsh"]["q"].append(avg_q)
# plot condition number
for key, value in data.items():
plt.plot(value["n"], value["time"], "-x", label=key + " " + value["version"])
plt.xlabel("num points")
plt.title("generation time [s]")
plt.grid()
plt.legend()
plt.show()
# plt.savefig("time.svg", transparent=True, bbox_inches="tight")
plt.close()
# plot CG iterations number
for key, value in data.items():
plt.plot(value["n"], value["q"], "-x", label=key + " " + value["version"])
plt.xlabel("num points")
plt.title("average cell quality")
plt.grid()
plt.legend()
plt.show()
# plt.savefig("average-cell-quality.svg", transparent=True, bbox_inches="tight")
plt.close()
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