This program seeks to develop innovative mathematical methods and fast, reliable algorithms aimed at making radical advances in modeling and computational science in areas crucial to the Air Force of the future. Research successes in this program enable the analysis, understanding, and prediction of complex physical phenomena, as well as the design and control of vital Air Force systems and processes. Proposals to this program should focus on fundamental scientific and mathematical innovations as well as demonstrate strong connections to applications of interest to the Air Force. Application areas of current interest are wide ranging and support the Air Force’s future mission in air, space, and cyberspace. They include but are not limited to unsteady aerodynamics, plasma dynamics, propulsion, directed energy, information science, and biological materials, processes and systems. Research in this program also supports the national program in high performance computing.
Typically, the computational models in this program rely on numerical schemes that discretize a complex set of continuum mechanics equations – generally partial differential equations – that represent the physics of the particular problem. However, alternative computational models may be appropriate for some problems. To meet the computational challenges in simulating nonlinear, discontinuous, multi-physics and multi-scale problems of interest to the Air Force, we are examining numerical algorithms which include multi-scale and multi-physics approaches with particular emphasis on convergence, error analysis and adaptivity. Additionally, developing rigorous algorithms for efficient and robust multidisciplinary design and optimization as well as understanding and quantifying the effects of uncertainties in computational models are of increasing interest.
This program develops and improves a variety of numerical methods in these areas, including high-order spatial and temporal algorithms, mesh-free, particle methods, high-order moving interface algorithms, stochastic and hybrid methods.
This program also has an increasing interest in some emerging, challenging and cross-disciplinary mathematical modeling and computational problems in biology and information science where enabling mathematical and computational innovations are urgently needed. For example, in biology these include extracting fundamental engineering design principles from a deeper understanding of successful biological systems and processes. Such problems arise in the investigation of new methods for harvesting energy, the design of new materials and sensors, as well as information fusion, to name just a few. In information science, the real-time analysis of massive amounts of streaming data from heterogeneous, distributed sources remains a challenging problem. New ultrafast reliable algorithms for exploratory data analysis are required as well as finding the right blend of analog, digital, and distributed computation. In this connection recent advances in computational harmonic analysis provide some hope. Progress in this arena will also be useful in scientific informatics and computational forensics and in the verification and validation process for many complex computational models of physical processes or systems.