An Excursion in High-Level Mathematical Modeling through Convection-Diffusion Model Problems

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Computer Sciences | Mathematics | Physical Sciences and Mathematics


Michael Heroux, Computer Science and Mathematics


Convection-diffusion model problems require solving a partial differential equation (PDE). One will generally use a computer to solve this PDE. A software package called Sundance [3] provides a high-level interface for solving PDEs. One goal of this project is to explore mathematical modeling with Sundance. For large problems, a single processor may not have sufficient power to compute an answer in a reasonable amount of time. To overcome this obstacle, one uses a parallel computer to split up the work among multiple processors. The problem then becomes one of partitioning the work across the set of processors. Parameters including problem size and convection speed affect the efficiency of a given partitioning method. Another goal is to find efficient partitioning methods for various problem sizes and convection speeds.