Solution to Ginzburg-Landau equations for inhomogeneous superconductors by nonlinear optimization

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Abstract
A modified steepest-descents optimization method is applied to solve the Ginzburg-Landau equations for inhomogeneous superconductors. The method is based on an approximate analytical solution to (fictitious) time-dependent Ginzburg-Landau equations. Calculations are performed of the condensation energy as a function of temperature for a Pb-Sn multilayer system in the absence of a magnetic field and the critical field as a function of temperature for a Nb-Ta multilayer system with parallel magnetic field. Rapid convergence of the residuals is achieved in both cases. Comparison is made with experimental results. These calculations are viewed as a step towards building a capability to study more complex systems, such as the mixed state in a layered material.