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A second-order distributed memory parallel fast sweeping method for the Eikonal equation

The Eikonal equation is used to calculate wave propagation and distance fields, and due to its complexity requires numerical treatment for its solution. In this work, we present a second-order distributed memory parallel fast sweeping method. The second-order solution switches on a two-point stencil when two upwind points are available, and reverts to first-order otherwise. In all examples, the second-order method improves the solution over the first-order, allowing for significant savings in memory while achieving the same accuracy. Parallelization over distributed memory saw good weak scaling with optimal convergence. The computational time for second-order was approximately 2.5 times slower than first-order, where the largest amount of mesh points ran on 144 cores (512 GB) was ≈20 billion. The savings in memory from the second-order method combined with the distributed memory algorithm result in the ability to solve problems much larger than are possible with the serial first-order method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Exact signed distance fields using parallel Fast Sweeping Method

Signed distance fields are often used in multiphysics simulations to track material interfaces. We present a simple methodology based on the fast sweeping method to generate the exact signed distance from triangular meshes and linear paths on Cartesian grids. The methodology propagates the closest primitive to the boundary to the rest of the domain following the characteristics. A local upwind criterion is used to decide between the new and existing closest primitive at each grid point while capturing the correct sign of the global function. The methodology has optimal computational complexity and runs efficiently in distributed-memory architectures. We include 2D and 3D test cases along with a resolution study up to 0.512 trillion zones and 1,000 computer cores. The solution strategy can also be applied to other types of meshes or collections of primitives.

97 MATHEMATICS AND COMPUTING↗

Medial axis and local thickness computation using the Fast Sweeping Method

This report describes an efficient and robust voxel-based methodology for computing the medial axis, local thickness, and distance-to-skeleton of arbitrary three-dimensional geometries. It is assumed that the object can be represented by an exact or approximate signed distance function on a discrete grid. The gradient of such function is used to formulate a hyperbolic partial differential equation (PDE) that models the collapse of the position vector in space. By exploiting the causality property of the PDE, the Fast Sweeping Method is able to obtain the solution in a finite number of sweeps independent of the mesh resolution. The intersection of characteristic lines leads to the formation of shocks and a discrete bisector function is used to identify the medial axis. The same PDE approach is used to compute the local thickness inside the object and obtain the distance-to-skeleton field. Multiple examples are given in two and three dimensions along with a resolution study. The methodology has optimal complexity and yields subsecond computational times for geometries with over a million zones on a single core. The methodology is also capable of parallelization across shared and distributed memory architectures.

97 MATHEMATICS AND COMPUTING↗

Low-Field EMR Studies of Permalloy Films and Gratings

Flat and profile-modulated permalloy films have been studied by the electron magnetic resonance (EMR) method. In addition to ferromagnetic and spin-wave resonances, the structures demonstrate low-field EMR signals of an unusual shape, which form a hysteresis loop in sweeping fields. The low-field signals are attributed to a fast reorientation of magnetic domains. The low-field EMR behavior is comparable to the behavior in magneto-dependent photovoltage previously observed in the optical experiments. The shapes of the loops and typical values of the switching fields depend on the profile modulation parameters confirming the possibility of controlling magnetic properties and the coupling of magnetic and optical effects with nanoscale geometry.

36 MATERIALS SCIENCE↗

Cell dark current–voltage from non-calibrated module electroluminescence image analysis

Here, we present a fast, accurate, and reliable method of obtaining cell dark current–voltage (I–V) curves from module electroluminescence (EL) images without requiring calibration or correction. For a pristine module, EL-derived dark I–V are compared to directly probed data for a variety of changing imaging parameters: camera sensor, lens, filter, aperture width, exposure time (level of sensor saturation), number of images used, and various combinations of these. Pristine modules and those experiencing different modes and degrees of degradation are examined. A recent study of modules using five different cell technologies demonstrates the practicality of our “EL sweep” technique for performance and degradation studies.

14 SOLAR ENERGY↗