pygmsh结合了Gmsh的强大功能和Python的通用性。它从Gmsh自己的Python接口提供了有用的抽象，因此您可以更容易地创建复杂的几何图形。

要使用Pygmsh，请从pypi安装Gmsh和pygmsh:

[sudo] apt install python3-gmsh
pip install pygmsh

本文档包含许多小示例。

平面形状

代码:

import pygmsh

with pygmsh.geo.Geometry() as geom:
    geom.add_polygon(
        [
            [0.0, 0.0],
            [1.0, -0.2],
            [1.1, 1.2],
            [0.1, 0.7],
        ],
        mesh_size=0.1,
    )
    mesh = geom.generate_mesh()

# mesh.points, mesh.cells, ...
# mesh.write("out.vtk")

import pygmsh

with pygmsh.geo.Geometry() as geom:
    geom.add_circle([0.0, 0.0], 1.0, mesh_size=0.2)
    mesh = geom.generate_mesh()

import pygmsh

with pygmsh.geo.Geometry() as geom:
    lcar = 0.1
    p1 = geom.add_point([0.0, 0.0], lcar)
    p2 = geom.add_point([1.0, 0.0], lcar)
    p3 = geom.add_point([1.0, 0.5], lcar)
    p4 = geom.add_point([1.0, 1.0], lcar)
    s1 = geom.add_bspline([p1, p2, p3, p4])

    p2 = geom.add_point([0.0, 1.0], lcar)
    p3 = geom.add_point([0.5, 1.0], lcar)
    s2 = geom.add_spline([p4, p3, p2, p1])

    ll = geom.add_curve_loop([s1, s2])
    pl = geom.add_plane_surface(ll)

    mesh = geom.generate_mesh()

返回值也是meshio网格，因此可以将其存储到文件中。

mesh.write("test.vtk")

输出文件可以用各种工具进行可视化，例如ParaView。

拉伸

import pygmsh

with pygmsh.geo.Geometry() as geom:
    poly = geom.add_polygon(
        [
            [0.0, 0.0],
            [1.0, -0.2],
            [1.1, 1.2],
            [0.1, 0.7],
        ],
        mesh_size=0.1,
    )
    geom.extrude(poly, [0.0, 0.3, 1.0], num_layers=5)
    mesh = geom.generate_mesh()

from math import pi
import pygmsh

with pygmsh.geo.Geometry() as geom:
    poly = geom.add_polygon(
        [
            [0.0, 0.2, 0.0],
            [0.0, 1.2, 0.0],
            [0.0, 1.2, 1.0],
        ],
        mesh_size=0.1,
    )
    geom.revolve(poly, [0.0, 0.0, 1.0], [0.0, 0.0, 0.0], 0.8 * pi)
    mesh = geom.generate_mesh()

from math import pi
import pygmsh

with pygmsh.geo.Geometry() as geom:
    poly = geom.add_polygon(
        [
            [+0.0, +0.5],
            [-0.1, +0.1],
            [-0.5, +0.0],
            [-0.1, -0.1],
            [+0.0, -0.5],
            [+0.1, -0.1],
            [+0.5, +0.0],
            [+0.1, +0.1],
        ],
        mesh_size=0.05,
    )

    geom.twist(
        poly,
        translation_axis=[0, 0, 1],
        rotation_axis=[0, 0, 1],
        point_on_axis=[0, 0, 0],
        angle=pi / 3,
    )

    mesh = geom.generate_mesh()

OpenCASCADE

从3.0版开始，Gmsh支持OpenCASCADE (occ)，允许cad风格的几何规范。

from math import pi, cos
import pygmsh

with pygmsh.occ.Geometry() as geom:
    geom.characteristic_length_max = 0.1
    r = 0.5
    disks = [
        geom.add_disk([-0.5 * cos(7 / 6 * pi), -0.25], 1.0),
        geom.add_disk([+0.5 * cos(7 / 6 * pi), -0.25], 1.0),
        geom.add_disk([0.0, 0.5], 1.0),
    ]
    geom.boolean_intersection(disks)

    mesh = geom.generate_mesh()

# ellpsoid with holes
import pygmsh

with pygmsh.occ.Geometry() as geom:
    geom.characteristic_length_max = 0.1
    ellipsoid = geom.add_ellipsoid([0.0, 0.0, 0.0], [1.0, 0.7, 0.5])

    cylinders = [
        geom.add_cylinder([-1.0, 0.0, 0.0], [2.0, 0.0, 0.0], 0.3),
        geom.add_cylinder([0.0, -1.0, 0.0], [0.0, 2.0, 0.0], 0.3),
        geom.add_cylinder([0.0, 0.0, -1.0], [0.0, 0.0, 2.0], 0.3),
    ]
    geom.boolean_difference(ellipsoid, geom.boolean_union(cylinders))

    mesh = geom.generate_mesh()

# puzzle piece
import pygmsh

with pygmsh.occ.Geometry() as geom:
    geom.characteristic_length_min = 0.1
    geom.characteristic_length_max = 0.1

    rectangle = geom.add_rectangle([-1.0, -1.0, 0.0], 2.0, 2.0)
    disk1 = geom.add_disk([-1.2, 0.0, 0.0], 0.5)
    disk2 = geom.add_disk([+1.2, 0.0, 0.0], 0.5)

    disk3 = geom.add_disk([0.0, -0.9, 0.0], 0.5)
    disk4 = geom.add_disk([0.0, +0.9, 0.0], 0.5)
    flat = geom.boolean_difference(
        geom.boolean_union([rectangle, disk1, disk2]),
        geom.boolean_union([disk3, disk4]),
    )

    geom.extrude(flat, [0, 0, 0.3])

    mesh = geom.generate_mesh()

网格细化/边界层

# boundary refinement
import pygmsh

with pygmsh.geo.Geometry() as geom:
    poly = geom.add_polygon(
        [
            [0.0, 0.0],
            [2.0, 0.0],
            [3.0, 1.0],
            [1.0, 2.0],
            [0.0, 1.0],
        ],
        mesh_size=0.3,
    )

    field0 = geom.add_boundary_layer(
        edges_list=[poly.curves[0]],
        lcmin=0.05,
        lcmax=0.2,
        distmin=0.0,
        distmax=0.2,
    )
    field1 = geom.add_boundary_layer(
        nodes_list=[poly.points[2]],
        lcmin=0.05,
        lcmax=0.2,
        distmin=0.1,
        distmax=0.4,
    )
    geom.set_background_mesh([field0, field1], operator="Min")

    mesh = geom.generate_mesh()

# mesh refinement with callback
import pygmsh

with pygmsh.geo.Geometry() as geom:
    geom.add_polygon(
        [
            [-1.0, -1.0],
            [+1.0, -1.0],
            [+1.0, +1.0],
            [-1.0, +1.0],
        ]
    )
    geom.set_mesh_size_callback(
        lambda dim, tag, x, y, z: 6.0e-2 + 2.0e-1 * (x ** 2 + y ** 2)
    )

    mesh = geom.generate_mesh()

# ball with mesh refinement
from math import sqrt
import pygmsh


with pygmsh.occ.Geometry() as geom:
    geom.add_ball([0.0, 0.0, 0.0], 1.0)

    geom.set_mesh_size_callback(
        lambda dim, tag, x, y, z: abs(sqrt(x ** 2 + y ** 2 + z ** 2) - 0.5) + 0.1
    )
    mesh = geom.generate_mesh()

优化

pygmsh也可以优化现有的网格。

import meshio

mesh = meshio.read("mymesh.vtk")
optimized_mesh = pygmsh.optimize(mesh, method="")

您还可以使用命令行实用程序

pygmsh-optimize input.vtk output.xdmf

输入和输出可以是meshio支持的任何格式。

测试

要运行pygmsh单元测试，请签出此存储库并输入

pytest

建立文档

使用Sphinx构建文档。

建立文档，运行

sphinx-build -b html doc doc/_build

许可证

这个软件是在GPLv3许可证下发布的。