The seven-triangle longest-side partition of triangles and mesh quality improvement

  • Authors:

  • Alberto Márquez;Auxiliadora Moreno-González;Ángel Plaza;José P. Suárez

  • Affiliations:

  • Department of Applied Mathematics I, University of Seville, Spain;Department of Applied Mathematics I, University of Seville, Spain;Department of Mathematics, University of Las Palmas de Gran Canaria, Spain;Department of Cartography and Graphic Engineering, University of Las Palmas de Gran Canaria, Spain

  • Venue:
  • Finite Elements in Analysis and Design
  • Year:
  • 2008

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Abstract

A new triangle partition, the seven-triangle longest-edge partition, based on the trisection of the edges is presented and the associated mesh quality improvement property, discussed. The seven-triangle longest-edge (7T-LE) partition of a triangle t is obtained by putting two equally spaced points per edge. After cutting off three triangles at the corners, the remaining hexagon is subdivided further by joining each point of the longest-edge of t to the base points of the opposite sub-triangle. Finally, the interior quadrangle is subdivided into two sub-triangles by the shortest diagonal. The self-improvement property of the 7T-LE partition is discussed, delimited and compared to the parallel property of the four-triangle longest-edge (4T-LE) partition. Global refinement strategies, combining longest-edge with self-similar partitions, are proposed, based on the theoretical geometrical properties.