Adaptive Methods for Optimal Design (FY 97 AASERT)

摘要

This final technical report contains a summary and highlights of the research funded by AFOSR under Grant F49620O-97 1 0356, titled 'Adaptive Methods for Optimal Design (FY 97 AASERT)', for the period I May 1997 to 30 April 1999. This AASERT grant supported two graduate students to work on mathematical and computational methods for sensitivity analysis with application to shape optimization and optimal control of systems governed by partial differential equations. The focus of the project was the development of fast and accurate algorithms for sensitivity calculations and direct methods for computing functional gains for feedback control of thermal processes. We discovered that projection methods can greatly improved sensitivity accuracy in high Reynolds flows. We also observed fasier and more robust convergence when projected gradients were employed In addition, new numerical methods based on the method of mappings were constructed so that mesh gradients% could be avoided. Our effort on feedback control generated new finite element schemes to numerically solve the Riccati partial differential equations that define feedback functional gains. In addition, chandrasekhar partial differential equations were derived and used to construct new fast methods. These methods were applied to 2D problems. This report contains a summary of these results and a list of papers produced during this period.