Simulation
has long played an important role in the design of particle accelerators.
Used in concert with theory and experiment, simulation is essential
to improving the performance of existing accelerators, designing future
accelerators, and exploring advanced accelerator concepts. In this talk
I will focus on computational challenges associated with advancing the
high intensity, high brightness frontier. Examples include using simulation
to explore the fundamental limits on brightness in photoinjectors and
accurately modeling the effects of coherent sychrotron radiation. The
computational challenges posed by these and other problems are being
met by projects worldwide that are developing a new generation of parallel
beam dynamics codes. Adding to the challenge is the rapid growth in
computational capabilities -- it is now widely accepted that, by 2010,
computer systems will be available that have more than 100,000 processors
and that have a peak performance in excess of a petaflop. In this talk
I will describe progress and future challenges in developing algorithms
and accelerator design codes for today's terascale and tomorrow's petascale
platforms.