Ginzburg-Landau – Hextreme https://www.hextreme.eu Hexahedral Mesh Generation in Real Time Mon, 04 Nov 2019 18:46:21 +0000 en-US hourly 1 https://www.hextreme.eu/wp-content/uploads/2018/11/cropped-erc-1-32x32.jpg Ginzburg-Landau – Hextreme https://www.hextreme.eu 32 32 Multi-block decomposition and meshing of 2D domain using Ginzburg-Landau PDE https://www.hextreme.eu/multi-block-decomposition-and-meshing-of-2d-domain-using-ginzburg-landau-pde/ https://www.hextreme.eu/multi-block-decomposition-and-meshing-of-2d-domain-using-ginzburg-landau-pde/#comments Mon, 04 Nov 2019 18:43:00 +0000 http://www.hextreme.eu/?p=4603 Continue reading 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
]]> https://www.hextreme.eu/multi-block-decomposition-and-meshing-of-2d-domain-using-ginzburg-landau-pde/feed/ 1 Paper: Computing cross fields, a PDE approach based on Ginzburg-Landau theory https://www.hextreme.eu/paper-computing-cross-fields-a-pde-approach-based-on-ginzburg-landau-theory/ https://www.hextreme.eu/paper-computing-cross-fields-a-pde-approach-based-on-ginzburg-landau-theory/#respond Tue, 24 Oct 2017 09:07:01 +0000 http://www.hextreme.eu/?p=2443 Continue reading 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.

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