POST REFINEMENT ELEMENT SHAPE IMPROVEMENT FOR QUADRILATERAL MESHES
Matthew L. Staten, Scott A. Canann · 2007
Schneiders and Debye (1995) present two algorithms for quadrilateral mesh refinement. These algorithms refine quadrilateral meshes while maintaining mesh conformity. The first algorithm maintains conformity by introducing triangles. The second algorithm maintains conformity without triangles, but requires a larger degree of refinement. Both algorithms introduce nodes with non-optimal valences. Non-optimal valences create acute and obtuse angles, decreasing element quality. This paper presents techniques for improving the quality of quadrilateral meshes after Schneiders' refinement. Improvement techniques use topology and node valence optimization rather than shape metrics; hence, improvement is computationally inexpensive. Meshes refined and subsequently topologically improved contain no triangles, even though triangles are initially introduced by Schneiders' refinement. Triangle elimination is especially important for linear elements since linear triangles perform poorly. In addition...