Scientific Computing Research Environments for the Mathematical Sciences (DMS-0532160)
Co-PIs: M. Holmes, D. Schwendeman, J. Mitchell and E. Giladi Department of Mathematical Sciences, Rensselaer Polytechnic Institute
This project involves the purchase and use of a high-speed multiprocessor computing cluster to: 1. Enable computationally intensive research projects to address complex mathematical modeling and optimization issues, including, in particular, multi-scale problems arising in the study of chemically reacting flows, mathematical biology, numerical optimization, and wave scattering. 2. Significantly enhance graduate computational courses in the Mathematical Sciences at Rensselaer and expand our continuing efforts to attract women and other under-represented groups into 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 new numerical methods using parallel computing, (ii) open up new areas for research for our graduate students, and (iii) be essential for running production codes already working on our smaller four processor system. These new avenues of research will strengthen our graduate student education and career development in computational mathematics, and will become the basis for outreach activities such as REUs (Research Experiences for Undergraduates). The specific projects for which the cluster will have immediate impact involve: the development of adaptive mesh refinement methods on composite overlapping grids for multiscale simulations of chemically reacting flows in exploding and detonating media; the computational modeling of the nonlinear, three-dimensional, electromechanical processes responsible for transduction of sound in the cochlea; the development of parallel algorithms based on polyhedral and non-polyhedral cutting plane methods for solving large-scale semidefinite and integer programming problems; and the development of hybrid asymptotic-numeric algorithms for solving scattering problems from complex realistic three-dimensional objects, in the mid frequency regime. On a broader level, the computing cluster will provide us with the ability to develop scalable algorithms that are essential for analyzing 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 resource for the preparation and computational experience of our students and post-docs. As a result, the broader impact of the computing cluster will be as a tool used in the career development of our students and post-docs, the dissemination of the new results of our computational research through publications and talks, and the development of new interdisciplinary collaborations.
