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Universal Meshes for Domains with Piecewise C2-regular Boundaries

Kim, Kyuwon, Adrian Lew

Research Notes, 26th International Meshing Roundtable, Sandia National Laboratories, September 18-21 2017

INTERNATIONAL
MESHING
ROUNTABLE

26th International Meshing Roundtable
Barcelona, Spain
September 18-21, 2017

Kyuwon Kim, Stanford University, US, q1kim@stanford.edu
Adrian Lew, Stanford University, US, lewa@stanford.edu

Research Note Abstract
The idea behind a universal mesh is that a background mesh can be deformed to obtain conforming meshes for a family of domains. Algorithms for universal meshes have so far been limited to geometries with C2-regular curves. We introduce an algorithm to generate conforming meshes for domains with C2-regular boundaries. The central idea of the algorithm divides the boundary into a finite number of C2-continuous curves, and edges of the background mesh are selected for each one of them so that the closest point projection of this set of edges onto the curve is a homeomorphism. We suggest conditions on the background mesh needed to guarantee that the algorithm selects a set of edges that is in fact homeomorphic to the boundary, the proof of which is still in progress.

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