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Integral Curves in Adaptive Mesh Re nement Vector Fields

Eduard Deines, and Ken Joy


Abstract

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In certain application areas, such as astrophysics, the simulation must accommodate many different spatial scales. For example, in simulations of the solar system, the computational domain may span thousands of astronomical units (AU), whereas some physical structures that need to be resolved occupy significantly shorter length scales. As a consequence, it is not possible to use regular grids, which in many cases are a primary choice due to their conceptual simplicity, to discretize such simulation domains. The uniform resolution required to represent the smallest phenomena in a simulation would result in infeasible overall storage requirements. Unstructured grids, on the other hand, adapt well to differences in length scales, but they also introduce significant overhead by requiring an explicit representation of grid connectivity. Adaptive mesh refinement (AMR) techniques are a hybrid solution that discretizes the simulation domain as set of overlapping, nested grids. These grids are arranged in levels of increasing resolution, and information for a specific point of the domain is stored at the finest grid overlapping this point. Thus, AMR combines the adaptivity of unstructured grids with the implicit connectivity of regular grids, adding only little overhead in form of a layout description. This arrangement makes it possible to discretize adaptively simulations with comparatively little overhead.

Integral curves, such as streamlines, streaklines, pathlines, and timelines, are an essential tool in the analysis of vector field structures, o ffering straightforward and intuitive interpretation of visualization results. While such curves have a long-standing tradition in vector field visualization, their application to Adaptive Mesh Refinement (AMR) simulation results poses unique problems. First, portions of the coarse grid that spans the simulation domain are replaced with higher-accuracy information provided by grids at levels of higher resolution. Thus, it is necessary to detect this overlap and always consider data at the finest resolution available. Second, for methods that are built on the existence of a continuous interpolant over the entire data set, special care must be taken to reconcile coarse and fine information resolution at resolution boundaries to yield continuous interpolation. AMR simulations often specify cell-centered values, which further complicates interpolation. In this project, we conduct research to alleviate these problems.

Contact

Eduard Deines edeines@ucdavis.edu