Stable large-scale solver for Ginzburg-Landau equations for superconductors

Abstract

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.

arXiv comment15 pages, 6 figures; minor corrections

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Cited by in corpus (28)

• Imaging of super-fast dynamics and flow instabilities of superconducting vortices
• Toward superconducting critical current by design
• Perspective: Challenges and Transformative Opportunities in Superconductor Vortex Physics
• Optimization of vortex pinning by nanoparticles using simulations of time-dependent Ginzburg-Landau model
• Strong-pinning regimes by spherical inclusions in anisotropic type-II superconductors
• Simulation of the vortex dynamics in a real pinning landscape of YBa${}_2$Cu${}_3$O${}_{7-\delta }$ coated conductors
• Time-dependent Ginzburg-Landau treatment of RF Magnetic Vortices in Superconductors: Vortex-Semiloops in a Spatially Nonuniform Magnetic Field
• Effect of hexagonal patterned arrays and defect geometry on the critical current of superconducting films
• Role of surface defects and material inhomogeneities for vortex nucleation in superconductors within time-dependent Ginzburg-Landau theory in 2 and 3 dimensions
• Decoupling and tuning competing effects of different types of defects on flux creep in irradiated YBa${}_2$Cu${}_3$O${}_{7-\delta }$ coated conductors
• Targeted evolution of pinning landscapes for large superconducting critical currents
• Probing the pinning landscape in type-II superconductors via Campbell penetration depth
• pyTDGL: Time-dependent Ginzburg-Landau in Python
• Parallel magnetic field suppresses dissipation in superconducting nanostrips
• The quest for high critical current in applied high-temperature superconductors
• Peak effect due to competing vortex ground states in superconductors with large inclusions
• Edge effect pinning in mesoscopic superconducting strips with non-uniform distribution of defects
• FTK: A Simplicial Spacetime Meshing Framework for Robust and Scalable Feature Tracking
• In silico optimization of critical currents in superconductors
• Phase Slips in Superconducting Weak Links
• SuperConga: an open-source framework for mesoscopic superconductivity
• Vortex dynamics induced by scanning SQUID susceptometry
• A Time-Dependent Ginzburg-Landau Framework for Sample-Specific Simulation of Superconductors for SRF Applications
• Vortex structure and intervortex interaction in superconducting structures with intrinsic diode effect
• Fractional vortex array realized at twin boundary in a nematic superconductor
• Vortex-driven superconducting diode effect in asymmetric multilayer heterostructures
• Disorder-induced trapping and anti-trapping of vortices in type-II superconductors
• Vortices in a Ginzburg Landau Theory of Superconductors with Nematic Order