Abstract
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,
offering 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