Multi-block decomposition and meshing of 2D domain using Ginzburg-Landau PDE

Authors: Jovana Jezdimirović, Alexandre Chemin, Jean François Remacle

Abstract: An in-depth method to generate multi-block decomposition of the arbitrary 2D domain using 2D cross fields solution of Ginzburg-Landau partial differential equation (PDE) is presented. It is relied on parameterization of multi-block decomposition of the domain, obtained by using particular PDE for the purpose of generating direction fields, appropriate number and localization of singular points and their separatrices. We have proved that solutions of particular PDE imply locally integrable vector fields and have adequate distribution of singularities, advocating its usage. Multi-block graph was generated by the separatrices and extraordinary vertices of the domain (singularities, corners and separatrices intersections) and obtained blocks were parameterized/remeshed. As a result, a mechanism to obtain multi-block structured all-quad mesh in automatic manner is developed.

  • Paper (in proceedings of the 28th International Meshing Roundtable)
  • The code will soon be available in Gmsh

Paper: Computing cross fields, a PDE approach based on Ginzburg-Landau theory

We developed an innovative way to compute cross fields in order to spawn points which are consistent with a square grid. The mathematical background is built step by step to highlight the meaningful use of Ginzburg-Landau functional. An interesting result is obtained over the sphere: the anti-cube. The computation is extended to asterisk fields for equilateral triangular grid.

Beaufort, Pierre-Alexandre et al. « Computing cross fields A PDE approach based on the Ginzburg-Landau theory », Procedia Engineering, vol. 203, 2017, p. 219‑31. <>.