Reduced basis methods for parametrized partial differential equations

The applicant is invited to spend two years as a post-doctoral research fellow at Massachusetts Institute of Technology (MIT), Cambridge, USA, starting from September 2011. The applicant will be affiliated with Professor Anthony T. Patera in the Departmen t of Mechanical Engineering at MIT throughout the project period of two years. This application is for Magne S. Espedal's post-doctoral research fellowship and an overseas research grant. Professor Patera's group is one of the leading research groups in the world in the field of reduced basis methods for parameter-dependent partial differential equations. The group has worked on the development, implementation, and utilization of reduced basis methods for more than a decade, and has published a large num ber of scientific papers on this subject. The proposed project will focus on incorporation of reduced basis methods in higher-lever algorithms for applications that are relevant for engineering and industry, such as optimization, real-time control, desig n, parameter estimation, or multiscale simulation. This work will require both the development of new theory --- for example incorporation and interpretation of the reduced basis error bounds in these higher level algorithms --- and more practical develop ment and implementation of algorithms. The proposed project will conduct basic scientific research in theoretical mathematics and computational science, and at the same time maintain a strict focus on relevance and applications for engineering and indust ry. The applicant is a young researcher, and a post-doctoral research position at MIT would certainly provide a boost to both knowledge and skills within this rapidly developing research area.