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Spacetime Spinoffs

Though the Einstein equations are very complex, they share the following common features with important equations embedded in other science and engineering problems:

• The equations are very general hyperbolic and elliptical systems.
• They deal with wave propagation.

For example, some of the algorithms that rapidly solve the equations to high accuracy on parallel machines could also find applications in the oil industry. Industry seismologists need to understand how sound waves propagate through the Earth's crust.

Tackling this Grand Challenge requires that relativity scientists work closely with computer scientists and computer manufacturers to advance the state-of-the-art in the following areas:

• Efficient numerical algorithms for parallel computers
• New methods for solving hyperbolic equations
• New methods for solving the mathematics of giant linear systems and elliptic equations
• Improved techniques for solving constrained systems
• Better methods for writing and processing huge (several gigabyte) files produced on parallel computers.
• For supercomputers, more efficient compilers, the software needed to translate computer code into machine-executable operations
• More advanced ways of visualizing complex scientific data, including
• Virtual reality
• Superior approaches to heterogeneous computing, the linking of diverse types of networked computers at different locations in order to solve problems in an optimal fashion.

Progress in numerical relativity will benefit other areas of astrophysics. Ultimately, researchers will develop codes that solve the complete, coupled spacetime-fluid equations that govern the evolution of all astrophysical systems, such as supernovae, neutron stars, accretion disks, quasars, and the universe itself.

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