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.

中文翻译：

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使用有限元方法模拟超导体 SFN 结构

摘要 我们考虑了基于超导微观理论的半经典方程（Usadel 方程）的约瑟夫森结构中电流分布的数学建模问题。这些方程是格林函数 $$\Phi _\omega (r)$$ 和 $$G_\omega (r) $$ 以及配对势 $$\Delta (r) $$ 的拟线性椭圆方程组，其中通过在频率 $$\omega $$ 上对函数 $$\Phi _\omega (r)$$ 求和，由自洽方程确定。针对拟线性方程组，我们提出了一种特殊的混合有限元方法，对于自洽方程组，我们采用逐次逼近法和安德森收敛加速算法。提供了具有楔形铁磁层的结构的计算结果。