Stable large-scale solver for Ginzburg-Landau equations for superconductors
Stable large-scale solver for Ginzburg-Landau equations for superconductors
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DOI：
10.1016/j.jcp.2015.04.002
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发表时间：
2015-08-01
影响因子：
4.1
通讯作者：
Glatz, A.
中科院分区：
文献类型：
--
作者：
Sadovskyy, I. A.;Koshelev, A. E.;Glatz, A.
理解第二类超导体中涡旋与夹杂物的相互作用是基础科学和能源应用的一个重大挑战。在与应用相关的尺度上，稠密涡旋配置之间的长程相互作用及其行为对外部参数（例如温度和外加磁场）的依赖性，对于超导体的净响应都很重要。捕捉这些功能，一般来说，排除了分析描述的旋涡动力学，也使得数值模拟昂贵得令人望而却步。在这里，我们报告了一个高度优化的迭代隐式求解器的时间相关的金-朗道方程适合调查的II型超导体的大规模并行架构。它的主要目的是研究无序或几何约束的介观系统中的涡旋动力学。在这项工作中，我们提出了离散和时间积分方案的详细两种类型的边界条件。我们描述了一个稳定的和物理上准确的集成的运动方程的必要条件。使用包含图案发生器，我们可以模拟复杂的钉扎景观和几何约束的影响。我们表明，我们的算法，在GPU上实现，可以提供静态和动态的解决方案的Ginzburg-Landau方程的介观大系统在数千个时间步长在几个小时内。使用我们的公式，研究科学相关的问题是一个计算合理的任务。(C)2015 Elsevier Inc. All rights reserved.
Understanding the interaction of vortices with inclusions in type-II superconductors is a major outstanding challenge both for fundamental science and energy applications. At application-relevant scales, the long-range interactions between a dense configuration of vortices and the dependence of their behavior on external parameters, such as temperature and an applied magnetic field, are all important to the net response of the superconductor. Capturing these features, in general, precludes analytical description of vortex dynamics and has also made numerical simulation prohibitively expensive. Here we report on a highly optimized iterative implicit solver for the time-dependent Ginzburg-Landau equations suitable for investigations of type-II superconductors on massively parallel architectures. Its main purpose is to study vortex dynamics in disordered or geometrically confined mesoscopic systems. In this work, we present the discretization and time integration scheme in detail for two types of boundary conditions. We describe the necessary conditions for a stable and physically accurate integration of the equations of motion. Using an inclusion pattern generator, we can simulate complex pinning landscapes and the effect of geometric confinement. We show that our algorithm, implemented on a GPU, can provide static and dynamic solutions of the Ginzburg-Landau equations for mesoscopically large systems over thousands of time steps in a matter of hours. Using our formulation, studying scientifically-relevant problems is a computationally reasonable task. (C) 2015 Elsevier Inc. All rights reserved.