Solution of the Ginzburg-Landau equations with different interfaces extended to multiply connected domains

The thermodynamical properties of a thin superconducting film with a central square hole are found theoretically. It is assumed that two opposite outer edges of the sample are in contact with a thin layer of metallic material while the other two edges are in contact with a thin layer of superconducting material, its configuration allows to control the vortex entry in the sample. In this work, we solve numerically the Ginzburg Landau equations with general boundary conditions using the Link variable method extended to multiply connected domains. It is shown that the value of the magnetization, the first vortex entry field, and the free energy are sensitive to the material in contact with the inner edge of the hollow.