Geometric formulation of Ginzburg-Landau Theory

I’m now trying to integrate the Maxwell equation and the Ginzburg-Landau Theory in the geometric form because it can be suitable for FEM based simulation.

Wikipedia tells me the form of the equation but there is no information about its derivation.

https://en.wikipedia.org/wiki/Ginzburg%E2%80%93Landau_theory#Geometric_formulation

"Riemannian Geometry and Geometric Analysis", the book cited in the page, describes mathematical properties of the equation but nothing about physical properties like correspondence between the geometric formulation and the conventional (non-geometric) formulation or matching with experimental results.

https://archive.org/details/riemanniangeomet00jost_070

Are there any papers, books, webpages, etc. which describes details about the geometric formulation of Ginzburg-Landau Theory?