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
13th International Meshing Roundtable
Willimasburg, Virginia, USA
September 19-22, 2004
Dept. of Mathematics, Massachusetts Institute of Technology,
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 specic 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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