pymesh2d 0.1.8.dev0

pymesh2D: Delaunay-based mesh generation in Python

pymesh2D is a Python-based unstructured mesh-generator for two-dimensional polygonal geometries, providing a range of relatively simple, yet effective two-dimensional meshing algorithms. pymesh2D includes variations on the "classical" Delaunay refinement technique, a new "Frontal"-Delaunay refinement scheme, a non-linear mesh optimisation method, and auxiliary mesh and geometry pre- and post-processing facilities.

This code is a translation of MESH2D, a MATLAB / OCTAVE-based tool developed by Darren Engwirda.

Algorithms implemented in pymesh2D are "probably-good" - ensuring convergence, geometrical and topological correctness, and providing guarantees on algorithm termination and worst-case element quality bounds. Support for user-defined "mesh-spacing" functions and "multi-part" geometry definitions is also provided, allowing pymesh2D to handle a wide range of complex domain types and user-defined constraints. pymesh2D typically generates very high-quality output, appropriate for a variety of finite-volume/element type applications.

pymesh2D is a simplified version of my JIGSAW mesh-generation algorithm (a C++ code). pymesh2D aims to provide a straightforward Python implementation of these Delaunay-based triangulation and mesh optimisation techniques.

Code Structure

pymesh2D is a pure Python package, consisting of a core library + associated utilities:

pymesh2D::
├── pymesh2d              -- core pymesh2D library functions. See refine, smooth, tridemo etc.
├── pymesh2d/aabb_tree    -- support for fast spatial indexing, via tree-based data-structures.
├── pymesh2d/geom_util    -- geometry processing, repair, etc.
├── pymesh2d/geomesh_util -- mesh gestion, export interpolation, etc.
├── pymesh2d/hfun_util    -- mesh-spacing definitions, limiters, etc.
├── pymesh2d/hjac_util    -- solver for Hamilton-Jacobi eqn's.
├── pymesh2d/mesh_ball    -- circumscribing balls, orthogonal balls etc.
├── pymesh2d/mesh_cost    -- mesh cost/quality functions, etc.
├── pymesh2d/mesh_file    -- mesh i/o via ASCII serialisation.
├── pymesh2d/mesh_util    -- meshing/triangulation utility functions.
├── pymesh2d/poly_data    -- polygon definitions for demo problems, etc.
└── pymesh2d/poly_test    -- fast inclusion test for polygons.

Quickstart

Installation

You can install pymesh2d directly from PyPI:

pip install pymesh2d

If you want to install it in developer mode (for local development and contribution):

pip install -e .

Examples

python -m pymesh2d.tridemo  0; % a very simple example to get everything started.
python -m pymesh2d.tridemo  1; % investigate the impact of the "radius-edge" threshold.
python -m pymesh2d.tridemo  2; % Frontal-Delaunay vs. Delaunay-refinement refinement.
python -m pymesh2d.tridemo  3; % explore impact of user-defined mesh-size constraints.
python -m pymesh2d.tridemo  4; % explore impact of "hill-climbing" mesh optimisations.
python -m pymesh2d.tridemo  5; % assemble triangulations for "multi-part" geometries.
python -m pymesh2d.tridemo  6; % assemble triangulations with "internal" constraints.
python -m pymesh2d.tridemo  7; % investigate the use of "quadtree"-type refinement.
python -m pymesh2d.tridemo  8; % explore use of custom, user-defined mesh-size functions.
python -m pymesh2d.tridemo  9; % larger-scale problem, mesh refinement + optimisation. 
python -m pymesh2d.tridemo 10; % medium-scale problem, mesh refinement + optimisation. 

More examples available in BlueMath.

References

If you make use of pymesh2D please include a reference to the following! pymesh2D is a translation of MESH2D, designed to provide a simple and easy-to-understand implementation of Delaunay-based mesh-generation techniques. For a much more advanced and fully three-dimensional mesh-generation library, see the JIGSAW package. MESH2D makes use of the AABBTREE and FINDTRIA packages to compute efficient spatial queries and intersection tests.

[1] - Darren Engwirda, Locally-optimal Delaunay-refinement and optimisation-based mesh generation, Ph.D. Thesis, School of Mathematics and Statistics, The University of Sydney, September 2014.

[2] - Darren Engwirda, Unstructured mesh methods for the Navier-Stokes equations, Honours Thesis, School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, November 2005.