On The Discrete Core of Quadrilateral Mesh Refinement
Hannemann, Matthias Muller and Karsten Weihe
International Journal for Numerical Engineering, John Wiley & Sons, Num 46, pp.593-622, 1999
Fachbereich Mathematik, Technische Universitat Berlin, Germany
Email:karsten.weihe@uni-konstanz.de
Abstract
We present a new approach to quadrilateral mesh refinement, which reduces the
problem to its structural core. The resulting problem formulation belongs to a
class of discrete problems, network-flow problems, which has been thoroughly
investigated and is well understood. The network-flow model is flexible enough
to allow the simultaneous incorporation of various aspects such as the control
of angles and aspect ratios, local density control, and templates (meshing
primitives) for the internal refinement of mesh elements. We show that many
different variants of the general quadrilateral mesh-refinement problem are
covered. In particular, we present a novel strategy, which provably finds a
conformal refinement unless there is none.
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