Q-Morph: An indirect approach to advancing front quad meshing. $Q$-Morph is a new algorithm for generating all-quadrilateral meshes on bounded three-dimensional surfaces. After first triangulating the surface, the triangles are systematically transformed to create an all-quadrilateral mesh. An advancing front algorithm determines the sequence of triangle transformations. Quadrilaterals are formed by using existing edges in the triangulation, by inserting additional nodes, or by performing local transformations to the triangles. A method, typically used for recovering the boundary of a Delaunay mesh, is used on interior triangles to recover quadrilateral edges. Any number of triangles may be merged to form a single quadrilateral. Topological clean-up and smoothing are used to improve final element quality. $Q$-Morph generates well-aligned rows of quadrilaterals parallel to the boundary of the domain while maintaining a limited number of irregular internal nodes. The proposed method also offers the advantage of avoiding expensive intersection calculations commonly associated with advancing front procedures. A series of examples of $Q$-Morph meshes are also presented to demonstrate the versatility of the proposed method.

References in zbMATH (referenced in 21 articles )

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  1. Oñate, Eugenio: Structural analysis with the finite element method. Linear statics. Volume 2: Beams, plates and shells (2013)
  2. Remacle, J.-F.; Lambrechts, J.; Seny, B.; Marchandise, E.; Johnen, A.; Geuzainet, C.: Blossom-Quad: a non-uniform quadrilateral mesh generator using a minimum-cost perfect-matching algorithm (2012)
  3. Schiffer, T.; Aurenhammer, F.; Demuth, M.: Computing convex quadrangulations (2012)
  4. Lu, Linfa; Qian, Xiaoyuan; Shi, Xiquan; Liu, Fengshan: Quading triangular meshes with certain topological constraints (2011)
  5. Burgos, Manuel A.; Chia, Juan M.; Corral, Roque; López, Carlos: Rapid meshing of turbomachinery rows using semi-unstructured multi-block conformal grids (2010)
  6. Ghadimi, Parviz; Faizi Chekab, Mohammad A.; Maleki, Farzam Safarzadeh: A novel approach to node distribution for 2D mesh generation and its application in marine and ocean engineering (2010)
  7. Randrianarivony, Maharavo; Brunnett, Guido: Preparation of CAD and molecular surfaces for meshfree solvers (2008)
  8. Hartley, P.; Pillinger, I.: Numerical simulation of the forging process (2006)
  9. Kolk, Karsten; Kuhn, Günther: The advanced simulation of fatigue crack growth in complex 3D structures (2006)
  10. Lee, C.K.; Xu, Q.X.: A new automatic adaptive 3D solid mesh generation scheme for thin-walled structures (2005)
  11. Lo, S.H.; Wang, W.X.: Generation of tetrahedral mesh of variable element size by sphere packing over an unbounded 3D domain (2005)
  12. Lo, S.H.; Wang, W.X.: Generation of finite element mesh with variable size over an unbounded 2D domain (2005)
  13. Ramaswami, Suneeta; Siqueira, Marcelo; Sundaram, Tessa; Gallier, Jean; Gee, James: Constrained quadrilateral meshes of bounded size (2005)
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  15. Wang, Charlie C.L.; Tang, Kai: Non-self-overlapping structured grid generation on an $n$-sided surface (2004)
  16. White, David R.; Saigal, Sunil; Owen, Steven J.: CCSweep: automatic decomposition of multi-sweep volumes (2004)
  17. Lee, Y.K.; Lee, C.K.: A new indirect anisotropic quadrilateral mesh generation scheme with enhanced local mesh smoothing procedures (2003)
  18. Kovač, N.; Gotovac, S.; Poljak, D.: A new front updating solution applied to some engineering problems (2002)
  19. Tautges, Timothy J.: The generation of hexahedral meshes for assembly geometry: survey and progress (2001)
  20. Owen, Steven J.; Saigal, Sunil: H-Morph: An indirect approach to advancing front hex meshing (2000)

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