Christian Döding: Resolving Vortex Lattices in Type-II Superconductors with Multiscale Techniques скачать в хорошем качестве

Christian Döding: Resolving Vortex Lattices in Type-II Superconductors with Multiscale Techniques

Superconducting states can be modeled as minimizers of the Ginzburg–Landau energy functional. This functional predicts remarkable macroscopic phenomena, such as the formation of Abrikosov vortex lattices in the presence of an external magnetic field. Accurately computing these states is computationally demanding because classical discretizations require a very fine mesh resolution to capture these characteristics. These requirements can be quantified through error estimates linking the mesh size to the material parameters of the Ginzburg–Landau model. In this talk, I present recent progress toward overcoming these limitations. I propose approximation spaces based on the Localized Orthogonal Decomposition (LOD) method, a multiscale framework that incorporates problem information into computational spaces, substantially relaxing the constraints of classical mesh resolution. Consequently, vortex lattice configurations can be approximated with greater accuracy using fewer degrees of freedom. These advances pave the way for more manageable and reliable computational studies of complex pattern formation in superconductors governed by the Ginzburg–Landau theory.