Optimization

Modern engineering designs require fast and high credible scientific computations which usually run in a parallel way. The proposed research focuses on the development of the parallel preconditioning technology used in large scale scientific computations. A multi-level recursive strategy is developed to improve the parallel computing performance when a large number of processors (up to at least 5000) are used. An existing Newton-Krylov flow solver will be improved by coupling with this multi-level preconditioner.

This research develops a comprehensive methodology for the integrated optimization and control of human-friendly robotic technology that will be applied for the advanced healthcare and biomedical manipulation. Some original ideas, methods and algorithms are proposed in this research based on several novel mathematical models, which will benefit the development of general robotics in the direction of safety with high performance to human beings.

Due to the explosive growth in the technology for manufacturing integrated circuits, modern chips contain millions of transistors. Using sophisticated optimization algorithms, it is possible to achieve notable increases in the performance of the chips, reduce the manufacturing costs, and produce faster, cheaper computing for society. Thus, the objective of this project is to enhance the solution of large-scale optimization problems arising in these applications.

This project aims to develop state-of-the-art mathematical tools for the aerospace industry to aid in the design of more efficient aircraft. Such tools have the potential to greatly reduce the time and cost associated with the design of new aircraft, thus providing a competitive advantage to the industry. In the past year, the team made considerable progress in the development of a three-dimensional aerodynamic shape optimization algorithm. Important improvements were made to the algorithms under development, leading to improved accuracy, efficiency, and applicability.