Traineeships will fund 5 graduate students at North Carolina State University to pursue doctoral research in the interdisciplinary area of high performance computing within the context of a specific application. Their training will equip them to perform research in area of national need that specifically incorporate high performance computing. Trainees and the faculty directing their research will be affiliated with the newly revitalized Center for Research in Scientific Computation (CRSC). Students' training will utilize two recently developed curricula at NCSU: the Concentration in Computational mathematics (CMA), which is an option for graduate students in applied mathematics, and the Computational Engineering and Sciences (CES) program, an interdisciplinary program in the colleges of Engineering and Physical and Mathematical Sciences administered by one of the Principal Investigators (PIs) of this proposal. Trainees' academic programs will include interdisciplinary research seminars focusing on application of high performance computing; participation in regional and national research conferences; opportunities to collaborate with researchers in industrial and international settings; and instruction in teaching. In addition to the technical PIs (Banks and Turinsky) and an administrative PI(King), the Traineeship program will involve several highly active research mathematician, scientist, and engineers. Traineeships will substantially boost our recent progress in designing programs for outstanding students in scientific computation.