On the Discrete Core of Quadrilateral Mesh Refinement

Matthias Müller-Hannemann and Karsten Weihe

International Journal For Numerical Methods in Engineering, vol 46, no. 4, pp. 593-622, 1999

not available

quadrilateral mesh refinement; discrete model; bidirected flows; quality control; meshing templates; branchings

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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