Scientific Computing Research Environments for the Mathematical Sciences

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Scientific Computing Research Environmentsfor the Mathematical Sciences (DMS-0532160)Co-PIs: M. Holmes, D. Schwendeman, J. Mitchell and E. GiladiDepartment of Mathematical Sciences, Rensselaer Polytechnic InstituteThis project involves the purchase and use of a high-speed multiprocessor computing cluster to:1. Enable computationally intensive research projects to address complex mathematical modelingand optimization issues, including, in particular, multi-scale problems arising in thestudy of chemically reacting flows, mathematical biology, numerical optimization, and wavescattering.2. Significantly enhance graduate computational courses in the Mathematical Sciences at Rensselaerand expand our continuing efforts to attract women and other under-represented groupsinto our research programs.The proposed equipment will benefit our research projects in several ways. The equipment will (i)enable us to proceed with our research efforts directed towards the development and testing of newnumerical methods using parallel computing, (ii) open up new areas for research for our graduatestudents, and (iii) be essential for running production codes already working on our smaller fourprocessor system. These new avenues of research will strengthen our graduate student educationand career development in computational mathematics, and will become the basis for outreachactivities such as REUs (Research Experiences for Undergraduates).The specific projects for which the cluster will have immediate impact involve: the developmentof adaptive mesh refinement methods on composite overlapping grids for multiscale simulations ofchemically reacting flows in exploding and detonating media; the computational modeling of thenonlinear, three-dimensional, electromechanical processes responsible for transduction of soundin the cochlea; the development of parallel algorithms based on polyhedral and non-polyhedralcutting plane methods for solving large-scale semidefinite and integer programming problems; andthe development of hybrid asymptotic-numeric algorithms for solving scattering problems fromcomplex realistic three-dimensional objects, in the mid frequency regime. On a broader level, thecomputing cluster will provide us with the ability to develop scalable algorithms that are essential foranalyzing certain complex mathematical problems that arise in science and engineering applications,and it will provide us with a computational laboratory that will serve as an invaluable resourcefor the preparation and computational experience of our students and post-docs. As a result, thebroader impact of the computing cluster will be as a tool used in the career development of ourstudents and post-docs, the dissemination of the new results of our computational research throughpublications and talks, and the development of new interdisciplinary collaborations.