Numerical approximations of time-dependent partial differential equation (PDE) problems in three spatial dimensions often require very fine grid resolutions, and parallel computing can be employed to speed up the computations by subdividing the spatial domain over the available parallel processors. However, parallelization in space alone becomes inefficient on new generations of parallel computers where the number of parallel processors (or cores) is very large. In order to increase the concurrency and parallel efficiency, one can consider to carry out computations that iteratively improve the approximation at different time levels in a concurrent fashion. This approach is very attractive conceptually. In particular, the topic of this project is to develop multigrid methods for parallel computing in time applied to model problem PDEs. Recent work has developed this type of methods for parabolic PDEs (see the link below), but there are exciting opportunities to extend this approach, for example, to PDEs of hyperbolic type. Relevant links: -http://computation.llnl.gov/project/parallel-time-integration/pubs/mgritPaper-2013-3.pdf -"A multigrid tutorial" Required: -you should have taken courses on numerical computing and on PDEs -experience with programming (any of Matlab, Python, C, Java, C++, MPI, ...) and interest in parallel computing Please email me if you are interested in this project or have questions about it. |

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