Modeling Superconductor SFN-Structures Using the Finite Element Method

Abstract We consider the problem of mathematical modeling of the current distribution in Josephson structures based on semiclassical equations of the microscopic theory of superconductivity (the Usadel equations). These equations are a system of quasilinear elliptic equations for Green’s functions $$\Phi _\omega (r)$$ and $$G_\omega (r) $$ and the pairing potential $$\Delta (r) $$ , which is determined from the equation of self-consistency by summation of the functions $$\Phi _\omega (r)$$ over the frequencies $$\omega $$ . To solve the quasilinear equations, we propose a special mixed finite element method, and to solve the self-consistency equations, we apply the successive approximation method and Anderson’s convergence acceleration algorithm. Results of calculations are provided for a structure with a wedge-shaped ferromagnetic layer.