2020/10/30 by Alexis Macq, Macq, Alexis, Maxence Reberol +11
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2010.16381
openalex publication_date 2020/10/30 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Cross field generation is often used as the basis for the construction of\nblock-structured quadrangular meshes, and the field singularities have a key\nimpact on the structure of the resulting meshes. In this paper, we extend\nGinzburg-Landau cross field generation methods with a new formulation that\nallows a user to impose inner singularities. The cross field is computed via\nthe optimization of a linear objective function with localized quadratic\nconstraints. This method consists in fixing singularities in small holes\ndrilled in the computational domain with specific degree conditions on their\nboundaries, which leads to non-singular cross fields on the drilled domain. We\nalso propose a way to calculate the Ginzburg-Landau energy of these cross\nfields on the perforated domain by solving a Neumann linear problem. This\nenergy converges to the energy of the Ginzburg-Landau functional as epsilon and\nthe radius of the holes tend to zero. To obtain insights concerning the sum of\nthe inner singularity degrees, we give: (i) an extension of the Ginzburg-Landau\nenergy to the piecewise smooth domain allowing to identify the positions and\ndegrees of the boundary singularities, and (ii) an interpretation of the\nPoincar 'e-Hopf theorem focusing on internal singularities.\n