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To the Fourth Power and Back

Historically, numerical cosmologists targeted a single scale and resolved all of the physics possible within that scale. If they were studying the formation of a galaxy, about 100,000 light years in diameter, they'd divide the space into 10 zones, for a grid resolution of 10,000 light years across. That in itself is quite feasible. But there's a problem with the single-scale approach.

Gravity interacts with matter across all scales, and what happens at the supercluster scale--typically 100 million light years from end to end--affects the behavior of the galaxy cluster, which in turn influences individual galaxies, each about 100,000 light years in diameter. So, to really understand the physics and dynamics of galaxy formation, numerical cosmologists must include larger-scale structures in their simulations as well.

Now, it's conceivable that one could simply use the brute force method and multiply those 10,000 light-year zones--10 in each galaxy--by 10,000 for a supercluster simulation. In two dimensions, that would require 100 million (10^8) zones, which is still possible using current supercomputers.

But three-dimensional simulations are, of course, the goal of numerical cosmologists, and they would require a trillion (10^12) zones. And that's just out of the question with current technology.

A much more intelligent approach to the problem is to adopt a multiscale algorithm. In this case, the algorithmic employed is called AMR--Adaptive Mesh Refinement.The simulation begins with a coarse grid--64^3 or 128^3 zones at the most (in other words, 64 or 128 zones per dimension). If structures begin to form, the simulation zooms in on those areas and imposes upon them successively finer sub-grids.

Michael Norman, NCSA/Univ. of Illinois, on-camera
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The hierarchical system of grids spawns whole groups of calculations that are interdependent. The grids adapt hierarchically to resolve new structures, and track the motion of the structures within each grid. The approach conserves computer memory, focusing processing power only on those zones in which structures are forming.

Michael Norman, NCSA/Univ. of Illinois, on-camera
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Members of the Grand Challenge Cosmology Consortium are currently developing a general purpose AMR, called Hierarchical Adaptive Mesh Refinenment (HAMR) to computations using each of the three major approaches of cosmology code development.

To make HAMR specific to the application, numerical cosmologists must specify the physics, or mathematical applications, to be solved within each grid.

They're also developing parallel multiscale visualization tools to analyze the numerical output in a similarly hierarchically-adaptive manner.

Bringing these two key elements into new codes that can be run on different computer architectures alone or in combination is a major goal of the Cosmology Grand Challenge.

The beauty of HAMR is that it is physics-independent, applicable to a number of other scientific problems, including the simulation of the behavior of exotic objects like black holes.

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NCSA. Last modified 10/9/95.