Over the past decade, advanced simulation has shown to be increasingly essential to the design and analysis of modern accelerators as they continually strive for higher energy and increased intensity. Designed to run on the latest, most powerful computers new simulation codes enable the large-scale simulations that lead to scientific discovery and better engineering design. The development of advanced simulation codes for accelerator and other scientific/engineering applications is being pursued in the areas of parallel electromagnetic modeling and parallel beams simulations. Developing these advanced tools requires research not only in the application area but also in computer and computational science, applied mathematics and computing technologies. We have assembled a multi-disciplinary team drawn from a wide range of fields to work together on solving some of the most challenging problems facing the applications through advanced simulation. The current efforts range from analyzing the beam heating in the PEP-II interaction region to designing the accelerating cavities for and calculating the dipole wakefields in the Linear Collider (LC) linac, and from studying dark current and RF breakdown in high-gradient structures to finding spurious oscillations in high-power klystrons.