Engineering design drives economic prosperity and the quality of life. The world is comprised of complex dynamical systems from weather and natural disasters to financial systems and human health. Engineering design enables the development of products, systems and networks that allow us to thrive and to meet emerging challenges and opportunities. Since design involves trade-offs among many variables, an effective design must resolve conflicts at multiple scales and understand how the compromises affect the dynamical systems performance. A tool like topology optimization can guide the development of key design concepts but may have high computational costs. This project advances fundamental research to create efficient solvers that allow large-scale simulations at significantly reduced cost, thereby enabling the discovery of advanced systems with novel properties in areas such as energy, health care, and aerospace and with broad applicability across science and engineering. The project will train graduate, undergraduate, and high school students and design new graduate curriculum. The knowledge gained from the research will be broadly disseminated through social media and by organizing conference symposia.
This project will create new efficient and scalable solvers for linear and nonlinear systems of equations that enable the solution of systems of unprecedented size. Specifically, the systems of equations will be reformulated as fixed-point problems, which will be accelerated using the novel, efficient, and accurate extrapolation algorithms designed in this project. Parallel implementations of these approaches will be developed that can efficiently use large-scale distributed memory computer architectures. The researchers will also formulate linear-scaling approaches and scalable parallel implementations for Density Functional Theory (DFT) and topology optimization, which will be integrated to form a novel multiscale method for the design of new structures with tailored properties. In this process, laws for material behavior will be obtained from the first principles of quantum mechanics, with no ad-hoc approximations. Overall, the linear scaling DFT method will enable the accurate study of condensed matter systems at unparalleled length and time scales. The ability to perform large-scale ab-initio informed topology optimization will enhance the capacity to achieve high-resolution, accurate designs that can be realized in practical engineering applications.
