MESH2D is a MATLAB / OCTAVE-based unstructured mesh-generator for two-dimensional polygonal geometries, providing a range of relatively simple, yet effective two-dimensional meshing algorithms. MESH2D 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.
Algorithms implemented in MESH2D are "provably-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 MESH2D to handle a wide range of complex domain types and user-defined constraints. MESH2D typically generates very high-quality output, appropriate for a variety of finite-volume/element type applications.
MESH2D is a simplified version of my JIGSAW mesh-generation algorithm (a C++ code). MESH2D aims to provide a straightforward MATLAB / OCTAVE implementation of these Delaunay-based triangulation and mesh optimisation techniques.
MESH2D is a pure MATLAB / OCATVE package, consisting of a core library + associated utilities:
MESH2D::
├── MAIN-DIR. -- core MESH2D library functions. See REFINE2, SMOOTH2 and TRIDEMO, etc.
├── aabb-tree -- support for fast spatial indexing, via tree-based data-structures.
├── mesh-file -- support for mesh file text serialisation.
└── poly-data -- geometry data for example problems, image cache, etc.
After downloading and unzipping the current repository, navigate to the installation directory within MATLAB / OCTAVE and run the set of examples contained in tridemo.m:
tridemo( 0); % a very simple example to get everything started.
tridemo( 1); % investigate the impact of the "radius-edge" threshold.
tridemo( 2); % Frontal-Delaunay vs. Delaunay-refinement refinement.
tridemo( 3); % explore impact of user-defined mesh-size constraints.
tridemo( 4); % explore impact of "hill-climbing" mesh optimisations.
tridemo( 5); % assemble triangulations for "multi-part" geometries.
tridemo( 6); % assemble triangulations with "internal" constraints.
tridemo( 7); % investigate the use of "quadtree"-type refinement.
tridemo( 8); % explore use of custom, user-defined mesh-size functions.
tridemo( 9); % larger-scale problem, mesh refinement + optimisation.
tridemo(10); % medium-scale problem, mesh refinement + optimisation.
For OCTAVE users, performance can be improved by compiling elements of the MESH2D library. Running compile.m within the MESH2D installation directory will complete the build process (note: requires a -dev installation of OCTAVE).
If you make use of MESH2D please include a reference to the following! MESH2D is 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.