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adaptmesh

Create triangular meshes using adaptive finite elements.

PyPI PyPI - License ci DOI

The user feeds in a polygon and a low quality mesh is created. Then the low quality mesh gets improved by adaptive finite elements and mesh smoothing. The approach is detailed in the following paper:

@article{adaptmesh,
    title={A simple technique for unstructured mesh generation via adaptive finite elements},
    author={Gustafsson, Tom},
    volume={54},
    doi={10.23998/rm.99648},
    number={2},
    journal={Rakenteiden Mekaniikka},
    year={2021},
    pages={69--79}
}

Installation

pip install adaptmesh

Dependencies

  • numpy
  • scipy for sparse linear algebra
  • matplotlib for an efficient search of points inside a polygon
  • scikit-fem for adaptive finite elements

Examples

The mesh generator is called through the function adaptmesh.triangulate.

Square with default settings

from adaptmesh import triangulate

m = triangulate([(0., 0.),
                 (1., 0.),
                 (1., 1.),
                 (0., 1.),])
                 
# m.p are the points
# m.t are the elements

Example mesh 1

Non-convex shape

from adaptmesh import triangulate

m = triangulate([(0.0, 0.0),
                 (1.1, 0.0),
                 (1.2, 0.5),
                 (0.7, 0.6),
                 (2.0, 1.0),
                 (1.0, 2.0),
                 (0.5, 1.5),], quality=0.95)  # default: 0.9

Example mesh 2

Holes

m = triangulate([(0., 0.),
                 (1., 0.),
                 (1., 1.),
                 (0., 1.),],
                holes=[[(.25, .25),
                        (.75, .25),
                        (.75, .75),
                        (.25, .75)]])

Example mesh 3

Subdomains

m1 = triangulate([(0., 0.),
                  (1., 0.),
                  (.7, 1.),
                  (0., 1.),],
                 split=[(1, 8),
                        (2, 6)],
                 quality=0.91)

m2 = triangulate([(0., 2.),
                  (2., 2.),
                  (2., 0.),
                  (1., 0.),
                  (.7, 1.),
                  (0., 1.)],
                 split=[(3, 8),
                        (4, 6)],
                 quality=0.91)

m = m1 + m2

Multiple meshes can be joined to emulate subdomains. However, the nodes must match. Above, segments are splitted to facilitate the matching, e.g., [(1, 8), (2, 6)] means that the second and the third segments are split using eight and six equispaced extra nodes, respectively.

Example mesh 4

Licensing

The main source code of adaptmesh is distributed under the MIT License.

adaptmesh ships with customized versions of the following packages:

  • tri v0.3.1.dev0 (ported to Python 3; Copyright (c) 2015 Martijn Meijers; MIT; source)
  • optimesh v0.6.3 (trimmed down version with minor changes to the edge flipping; Copyright (c) 2018-2020 Nico Schlömer; the last version with MIT; source)
  • meshplex v0.12.3 (trimmed down version with minor changes, i.e. removal of unnecessary imports; Copyright (c) 2017-2020 Nico Schlömer; the last version with MIT; source)

The licenses of the included packages can be found also in LICENSE.md and the respective subdirectories, i.e. ./adaptmesh/*/LICENSE. See LICENSE.md for more information.

Changelog

Unreleased

[0.3.3] - 2022-02-04

  • Fixed: Properly respect segments in the initial triangulation.

[0.3.2] - 2021-09-28

  • Fixed: Rendering of README in pypi.

[0.3.1] - 2021-09-28

  • Fixed: Support for scikit-fem>=4.

[0.3.0] - 2021-06-22

  • Fixed: Support for scikit-fem>=3. Dependency update broke the mesh refinement.

[0.2.0] - 2021-01-20

  • Added: keyword argument split of triangulate allows further splitting the provided segments. This is useful because the segment endpoints are always preserved in the final mesh.
  • Added: keyword argument holes of triangulate allows specifying additional polygonal areas inside the domain that will be free of triangles in the final mesh.