PDE-Based Gradient Limiting for Mesh Size Functions

Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.377-388, September 19-22 2004

MESHING
RESEARCH
CORNER

13th International Meshing Roundtable
Willimasburg, Virginia, USA
September 19-22, 2004

Dept. of Mathematics, Massachusetts Institute of Technology,
persson@math.mit.edu

Abstract
We propose a new method for limiting the gradients in a mesh size function by solving a non-linear partial differential equation on the background mesh. Our gradient limiting Hamilton-Jacobi equation simplifies the generation of mesh size functions significantly, by decoupling size constraints at specic locations from the mesh grading requirements. We derive an analytical solution for convex domains which shows the results are optimal, and we describe how to implement ecient solvers on various types of meshes. We demonstrate our size functions with a proposed new mesh generation algorithm, using examples with curvature, feature size, and numerical adaptation.

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