Tim Kelley

The PI will continue his research program in the design, implementation, analysis, and application of novel numerical methods for nonlinear equations and applications to multiphysics coupling, computational chemistry, and computational physics. The primary focus of the project is Anderson acceleration. This method is ubiquitous in quantum electronic structure codes. The PI will work on understanding CROP and CDIIS, two important variations of the method. The PI will also investigate open theoretical questions.

Quantifying the effects of input variations on computed outputs is critical in scientific computing; it is generally referred to as sensitivity analysis (SA). SA plays a key role in the verification, the understanding and, central to this proposal, the simplification of models. Indeed, models are often "simplified" by constructing mathematical surrogates whose properties approximate some–but not all–of the properties of the original model with the goal of enabling computational study. We propose to develop computational methods to (i) identify of the ‘"important parts" of a model and (ii) quantify the effects of ignoring the "less important parts." In other words, our work will contribute to dimension reduction and sensitivity analysis. The research is organized around three complementary thrusts in numerical linear algebra, nonlinear solvers and global sensitivity analysis. The RTG participants will not just "be trained," they will play an essential role in our research activities. Group dynamic and esprit de corps will be generated through working groups. Every year, we will organize three working groups consisting of undergraduates, graduate trainees, postdocs and faculty. Each group will be active for one semester and be led by a member of the senior personnel, possibly jointly with one of the postdoctoral fellows. The working groups will concentrate on specific aspects of randomized numerical analysis through hands-on exploratory activities of either computational or analytical nature. Advanced graduate students will be in charge of introducing the undergraduates to basic concepts through short presentations. The project will support 5 undergraduates per year as well as, over the duration of the award, 9 graduate students and 2 postdocs. The project will have a lasting impact on curriculum and departmental activities. It also has significant outreach components to (i) industry and national labs, (ii) to high school (North Carolina School of Science and Mathematics) and (iii) to the public as well as through the development on graduate distance education courses. Our public outreach efforts will take place in collaboration with the NC State Office of Public Science.

The project will perform fundamental research in developing computational methods and tools for dynamic Monte Carlo (MC) neutron transport simulations on exascale class computer architectures. The NC State research team will perform studies on hybrid deterministic-MC and multi-level computational methods. The expected results of this research will form the background for development of efficient numerical methods and tools for time-dependent neutron transport problems and will be used to determine the next step in this direction. The results will be delivered as technical reports and papers published in technical journals and proceedings of major technical conferences. The project will educate two Ph.D. students

We plan to develop open-source software for quantum simulations of materials for future NSF supercomputing platforms.

The Consortium for Advanced Simulation of Light Water Reactors, CASL, supports the broad national missions of enabling energy independence; supporting economic growth through the offering of superior technology ; and being good stewards of the environment, buy enabling predictive simulation of nuclear power plants. Such capability will make possible power uprates, lifetime extension and higher fuel burnups for currently operating and new Generation III+ nuclear power plants.

The PI will continue his long-term collaboration with the US Army Engineer Research and Development Center (ERDC) on problems in inverse bathemetry. The objective is to determine the bottom profile of the near-shore from remote sensing data such as wave speed, wave frequency, and reflectivity. The PI and a graduate student will compare combinations of models with different levels of resolution and inverse problem methods with different costs. The PI will address problems in both implementation and analysis.

The Consortium for Advanced Simulation of Light Water Reactors, CASL, supports the broad national missions of enabling energy independence; supporting economic growth through the offering of superior technology ; and being good stewards of the environment, buy enabling predictive simulation of nuclear power plants. Such capability will make possible power uprates, lifetime extension and higher fuel burnups for currently operating and new Generation III+ nuclear power plants. This proposal is for work that ORNL will pay TN state takes on.

This proposal is for a very large amount of supercomputer time at NSF's Blue Waters supercomputer. This time will be used for advanced simulations and design of nanoscale materials and devices. The proposal also contains a request for travel funds to Blue Waters symposia and training events.

The PI will design, analyze, and implement algorithms for the solution of nonlinear equations and optimization problems. The research will focus on problems in which the functions and constraints are the outcomes of experiments or Monte Carlo simulations.

This proposal requests funds to continue development of massively parallel quantum simulations software, to adapt it for usage on multitude of computer architectures, including current and future petascale supercomputers, and to distribute it to user community.