SLAC’s Advanced Computations Department (ACD) has developed the parallel 3D electromagnetic time-domain code T3P for simulations of wakefields and transients in complex accelerator structures. T3P is based on state-of-the-art Finite Element methods on unstructured grids and features unconditional stability, quadratic surface approximation and up to 6th-order vector basis functions for unprecedented simulation accuracy. Optimized for large-scale parallel processing on leadership supercomputing facilities, T3P allows simulations of realistic 3D structures with fast turn-around times, aiding the design of the next generation of accelerator facilities. Applications include simulations of the proposed two-beam accelerator structures for the Compact Linear Collider (CLIC) - wakefield damping in the Power Extraction and Transfer Structure (PETS) and power transfer to the main beam accelerating structures are investigated. Show Partial Abstract