A daptive mesh refinement, developed by Marsha Berger and her colleagues in the 1980s for gas dynamical simu- lations, 1 is a type of multiscale algo- rithm that achieves high spatial resolution in lo- calized regions of dynamic, multidimensional numerical simulations. Greg Bryan’s excellent ar- ticle 2 in the March/April 1999 issue of Computing in Science & Engineering describes our cosmolog- ical AMR algorithm and how we have applied it to star, galaxy, and galaxy cluster formation. Basi- cally, 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 10 6 . Such res- olution would be totally impossible to achieve with a global, uniform fine grid. Thus, AMR al- lows us to simulate multiscale phenomena that are out of reach with fixed grid methods. The AMR algorithm accomplishes this by producing a deep, dynamic hierarchy of increas- ingly refined grid patches. The data structures for storing AMR data are complex, hierarchical, dynamic, and in general quite large. For exam- ple, the simulation of an X-ray galaxy cluster shown in Figure 1 used a grid hierarchy seven levels deep containing over 300 grid patches. 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 Super- computing Applications to overcome this deficit. Here we describe our progress in four main ar- eas: portable file formats, desktop visualization tools, virtual-reality navigation and animation techniques, and Web-based workbenches for han- dling and exploring AMR data. Although we have applied our work specifically to cosmology, we be- lieve our solutions have broader applicability. AMR data structures Within an evolving AMR simulation, the data is organized in a grid hierarchy data structure— think of a tree of arbitrary structure and depth (see Figure 2). The AMR algorithm generates this tree recursively and adaptively. Every node and leaf of the tree is associated with a 3D grid patch (hereafter, simply a grid); these have vari- ous sizes, shapes, and spatial resolutions. DIVING DEEP : DATA -MANAGEMENT AND V ISUALIZATION S TRATEGIES FOR A DAPTIVE MESH R EFINEMENT S IMULATIONS The authors’ cosmological applications illustrate problems and solutions in storing, handling, visualizing, virtually navigating, and remote-serving data produced by large- scale adaptive mesh refinement simulations. MICHAEL L. NORMAN, JOHN SHALF , STUART LEVY, AND GREG DAUES National Center for Supercomputing Applications 1521-9615/99/$10.00 © 1999 IEEE M ASSIVE D ATA V ISUALIZATION 36 COMPUTING IN S CIENCE & E NGINEERING