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Traditionally, supercomputers and high performance systems have been used for large scale scientific computations. This talk will survey the key issues, propose solutions to critical problems and show scalable and portable implementations for several such applications in radar and sonar systems. Two key problems that arise in parallelizing such applications are data remapping between computational stages and task mapping to meet desired latency and throughput requirements. We show new conflict-free indirect schedules for the classic cyclic redistribution problem to minimize the communication cost. This provides tradeoffs between the start-up cost and the transfer time to minimize the overall communication time.