A Parallel-in-Time Multigrid Approach to Constrained Optimization

Abstract

Valuable computer simulations such as weather prediction, traffic flow, and resource allocation are time dependent problems. One such example is the viscous Burgers’ equation which can model various systems such as fluids and traffic flow. Further, many of these models require optimization routines to meet the needs of many businesses. Unfortunately, traditional sequential-in-time algorithms have become bottlenecks in solution model generation. This is because computer architectures have begun to rely more and more on concurrency (parallel processing) as opposed to processor power to provide greater performance. To avoid this bottleneck, many researchers use parallelization methods to take advantage of the increasing number of processors in computers. This approach allows for variables in a problem to be solved for simultaneously. As such, parallelization is a crucial requirement to achieve high-performance computing.