Mesh Generation and Computational Geometry Techniques

Mesh generation lies at the heart of numerical simulation, transforming continuous geometric domains into discrete elements suitable for computational analysis. Central to this process are strategies for partitioning space into tetrahedra, hexahedra, prisms or hybrid mixes, guided by geometric refinement criteria and quality metrics such as element shape regularity and size gradation. Techniques range from Delaunay triangulation and advancing-front methods to centroidal Voronoi tessellation and octree-based subdivision, often combined with local remeshing to adapt to evolving boundaries. Computational geometry underpins these algorithms, providing robust predicates for intersection tests, nearest-neighbour searches and topological manipulations. Recent advances emphasise adaptive and anisotropic meshing—aligning element orientation with solution features—and scalable parallel implementations that exploit distributed memory and multi-core architectures. Applications span fluid dynamics, climate modelling, structural mechanics and biomedical simulations, where mesh quality directly influences accuracy and convergence. The interplay of discretisation theory, geometric optimisation and high-performance computing has driven the field towards automated, high-fidelity mesh pipelines capable of handling complex geometries and multi-scale resolution requirements.

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Mesh Generation and Computational Geometry Techniques publication trend

The graph below shows the total number of articles in mesh generation and computational geometry techniques across all publications each year (not limited to Nature Index journals).

Technical terms

Delaunay triangulation: A triangulation in which no vertex lies inside the circum-circle of any triangle, maximising minimum angles and facilitating quality element generation.

Voronoi diagram: A partition of space into regions around input sites, dual to Delaunay triangulation and used in centroidal tessellation for isotropic meshing.

Centroidal Voronoi tessellation: A Voronoi diagram whose generating points coincide with the centroids of their cells, yielding optimised, uniform point distributions.

Hybrid mesh: A mesh combining different element types (e.g. prisms near boundaries and tetrahedra in the interior) to capture boundary layers and complex flow features.

References

1. A novel approach for large-scale hybrid mesh generation on distributed systems. Engineering Applications of Computational Fluid Mechanics (2024).
2. JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere. Geoscientific Model Development (2017).
3. Hybrid meshing using constrained Delaunay triangulation for viscous flow simulations. International Journal for Numerical Methods in Engineering (2016).
4. An improved local remeshing algorithm for moving boundary problems. Engineering Applications of Computational Fluid Mechanics (2016).