Hybrid Schr?dinger-Ginzburg-Landau (Sch-GL) approach to study of superconducting integrated structures

Hybrid Schrodinger-Ginzburg-Landau approach is based on the fact of the mathematical similarity of Ginzburg-Landau (GL) and Schrodinger formalisms. Starting from Schrodinger approach by replacing the term V (x)-E with the term alpha(x)+beta(x)|psi(x)|2 we get the Ginzburg-Landau equation. In the proposed relaxation algorithm, we use one- and two-dimensional ground energy solutions of the Schrodinger equation and apply them as a starting trial solution for the GL relaxation method. The obtained numerical results and used methodology form the basis of the simulation platform for studying superconducting integrated structures and modeling various superconducting devices, including their time-dependent geometry.