With teraflops-scale computational modeling expected to be routine shortly, according to the roadmap of the Accelerated Strategic Computing Initiative (ASCI) of the U.S. Department of Energy, and with teraflops-capable platforms already becoming available to a small group of users, attention naturally focuses on the next symbolically important milestone, computing at rates of 10**15 floating point operations per second, or ``petaflop/s''. For architectural designs that are in any sense extrapolations of today's, petaflops-scale computing will require at least one-million-fold instruction-level concurrency, and memory hierarchies will be deep. Given that cost-effective one-thousand-fold process-level concurrency is challenging in practical implicit PDE-based simulations today (some examples from the speaker's research group will be reviewed to crystallize the issues), algorithms are among the several possible hurdles for PDE-based simulations on petaflops systems. Nevertheless, the prospects are compelling.

The one-hour presentation requires an overhead slide projector.