Multithreaded model for dynamic load balancing parallel adaptive PDE computations

We present a multithreaded model for the dynamic load-balancing of numerical, adaptive computations required for the solution of Partial Di erential Equations (PDEs) on multiprocessors. Multithreading is used as a means of exploring concurrency at the processor level in order to tolerate synchronization costs inherent to traditional (non-threaded) parallel adaptive PDE solvers. Our preliminary analysis for parallel, adaptive PDE solvers indicates that multithreading can be used as a mechanism to mask overheads required for the dynamic balancing of processor workloads with computations required for the actual numerical solution of the PDEs. Also, multithreading can simplify the implementation of dynamic load-balancing algorithms, a task that is very di cult for traditional data parallel adaptive PDE computations. Unfortunately, multithreading does not always simplify program complexity, often makes code re-usability di cult, and increases software complexity. This work was supported by an Alex Nason Prize Award, by NSF ASC 93 18152/ PHY 93 18152 (ARPA supplemented), by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480, while the author was in residence at the Institute for Computer Applications in Science and Engineering, (ICASE), NASA Langley Research Center, Hampton, VA 23681 and in part by the Cornell Theory Center.