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<p>Adaptive mesh refinement, developed by Marsha Berger and colleagues in the 1980s for gas dynamical simulations, is a type of multiscale algorithm that achieves high spatial resolution in localized regions of dynamic, multidimensional numerical simulations. Greg Bryan's excellent article in the March/April 1999 issue of Computing in Science & Engineering describes our cosmological AMR algorithm and how we have applied it to star, galaxy, and galaxy cluster formation. Basically, the algorithm allows us to place very high resolution grids precisely where we need them-where stars and galaxies condense out of diffuse gas. In our applications, AMR allows us to achieve a local mesh refinement relative to the global coarse grid of more than a factor of 106. Such resolution would be totally impossible to achieve with a global, uniform fine grid. Thus, AMR allows us to simulate multiscale phenomena that are out of reach with fixed grid methods.</p> <p>The AMR algorithm accomplishes this by producing a deep, dynamic hierarchy of increasingly refined grid patches. The data structures for storing AMR data are complex, hierarchical, dynamic, and in general quite large. </p> <p>Existing visualization, animation, and data-management tools developed for simple mesh data structures cannot handle AMR data sets. Consequently, in the past several years we have been working at the National Center for Supercomputing Applications to overcome this deficit. Here we describe our progress in four main areas: portable file formats, desktop visualization tools, virtual-reality navigation and animation techniques, and Web-based workbenches for handling and exploring AMR data. Although we have applied our work specifically to cosmology, we believe our solutions have broader applicability.</p>

G. Daues, J. Shalf, M. L. Norman and S. Levy, "Diving Deep: Data-Management and Visualization Strategies for Adaptive Mesh Refinement Simulations," in Computing in Science & Engineering, vol. 1, no. , pp. 36-47, 1999.
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