Alexis Macq
PhD student

Main project: Ginzburg-Landau and cross fields
Funding: UCL Grant
Supervisor(s): Jean-François Remacle

Minimizers of so-called Ginzburg-Landau functionals are functions that minimize both their variations and the passage of their norms to values ​​different from 1. The arbitration between the importance of these two elements is done via a parameter epsilon. When epsilon is set to 0, the norm of the minimizers is 1 unless, if necessary, in a finite number of points. The presence of those points (called singular points) depends on the surface considered. The study of Ginzburg-Landau functionals is fashionable. In the context of mesh applications, these functionals are notably used for the construction of the most regular possible cross fields intended to be supports for the construction of quadrangular meshes as regular as possible. In this context, the singular points of minimizers of Ginzburg-Landau functionals can be mapped to singular nodes in the meshes we are trying to construct. Indeed, these meshes pursue the same two objectives as those involved in the Ginzburg-Landau functionals, namely, be as regular as possible and placing singular nodes in an optimized manner if singular nodes are necessary. In the case of non-constant curvature surfaces, the introduction of a covariant gradient can potentially make it possible to construct Ginzburg-Laudau functionals that are more suitable for these surfaces.
-Study of a Ginzburg-Landau fonctional containing a co-variant -gradient.
-Implementation of mathematical curvature for numerical applications.
-Mathematical study of cross fields.

IMMC main research direction(s):
Computational science

eulerian-lagrangian method
finite elements
mesh generation

Research group(s): MEMA
Collaborations: Supervisor outside iMMC : Jean Van Schaftingen