Mesh size functions for implicit geometries and PDE-based gradient limiting

Authors:
Per-Olof Persson
Affiliations:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
Venue:
Engineering with Computers
Year:
2006

Citing 0
Cited 7

Topology, Accuracy, and Quality of Isosurface Meshes Using Dynamic Particles

IEEE Transactions on Visualization and Computer Graphics
An anisotropic scale-invariant unstructured mesh generator suitable for volumetric imaging data

Journal of Computational Physics
A hybrid variational front tracking-level set mesh generator for problems exhibiting large deformations and topological changes

Journal of Computational Physics
PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab

Structural and Multidisciplinary Optimization
Adaptive tetrahedral remeshing for modified solid models

Graphical Models
Automatic boundary evolution tracking via a combined level set method and mesh warping technique: application to hydrocephalus

MeshMed'12 Proceedings of the 2012 international conference on Mesh Processing in Medical Image Analysis
Preserving isotropic element size functions in adaptivity, quadrilateral and hexahedral mesh generation

Advances in Engineering Software

Quantified Score

Hi-index	0.01

Visualization

Abstract

Mesh generation and mesh enhancement algorithms often require a mesh size function to specify the desired size of the elements. We present algorithms for automatic generation of a size function, discretized on a background grid, by using distance functions and numerical PDE solvers. The size function is adapted to the geometry, taking into account the local feature size and the boundary curvature. It also obeys a grading constraint that limits the size ratio of neighboring elements. We formulate the feature size in terms of the medial axis transform, and show how to compute it accurately from a distance function. We propose a new Gradient Limiting Equation for the mesh grading requirement, and we show how to solve it numerically with Hamilton–Jacobi solvers. We show examples of the techniques using Cartesian and unstructured background grids in 2D and 3D, and applications with numerical adaptation and mesh generation for images.