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## More Numerical Tricks

The quest to probe the complexity of Nature with richer, more computationally-intensive models drives the development of yet more sophisticated tools and techniques for simulation. Some of these devise ingenious tricks to get around otherwise intractable bottlenecks.

Numerical relativists and other computational scientists are developing new techniques collectively called hierarchical adaptive mesh refinement
or HAMR. Acting as a kind of "digital zoom lens," the algorithms enable researchers to zero in on fine details very near an object
such as a black hole, then zoom out to faraway, large-scale phenomena, all within the same simulation.
These same scaling techniques are being applied to other Grand Challenge problems, including a major effort
to model cosmic evolution since the Big Bang.

One of the greatest difficulties posed by the Einstein equations is their non-linearity. What this means is that the values of the terms change rapidy and, in turn, are changed by the results. Beyond the event horizon that surrounds a spacetime singularity, quantities quickly approach infinity as they near the singularity within. A computer abhors infinity and will crash when the numbers get close to it. To get around this problem, numerical relativists are developing new tricks to avoid infinity, such as solving the equations only outside the black hole's boundary (the event horizon), while ignoring the troublesome region inside.

**Ed Seidel, NCSA/Univ. of Illinois, on-camera**

QuickTime Movie (1.4 MB);
Sound File (900K);
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By working in tandem with researchers from many distinct areas, scientists in a given discipline, such
as numerical relativity, can avoid having to re-invent the wheel. Also, innovative computational
techniques developed by one discipline may yield spinoffs applicable to another.

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*NCSA. Last modified 11/9/95.*