This award will support an NSF/CMBS regional conference to be held at the Institute for Computational and Experimental Research in Mathematics in Providence, Rhode Island in the summer of 2012 on the topic of finite element exterior calculus. The principal speaker will be Douglas Arnold, McKnight Presidential Professor of Mathematics at the University of Minnesota. This award will support 25 participants at different stages of their careers.
Finite element exterior caluculs (FEEC) is a recently developed theory that provides a framework for understanding and constructing numerical methods that are used for solving partial differential equations. It touches on many different fields of mathematics, including differential geometry, algebraic topology, and homological algebra. This conference will demonstrate how these areas of mathematics can be linked together to better understand the structure of underlying problems and develop computational methods.
The topic of the conference was finite element exterior calculus. Finite element methods are widely used to solve important equations arising in engineering and the sciences. Finite element exterior calculus is an exciting approach that unifies in some sense finite element methods for different problems. The CBMS workshop was held in Providence in June 11-June 15, 2012. The principal lecturer was Douglas Arnold who is a McKnight Presidential Professor of Mathematics at the University of Minnesota and past SIAM president. He presented ten lectures (two per day). In addition, we had two one hour lectures given by Richard Falk (Rutgers University) and Anil Hirani (University of Illinois). Finally, we had a small poster session with four posters. There were fifty seven participants. The participants were highly engaged and there was much interaction between participants and with speakers. Many times during breaks you could find groups of participants interacting in the whiteboard or asking questions to the main lecturer. The participants seemed to be very happy with the conference. There was a survey giving at the end of conference and we had 29 out of 57 participants complete the survey. When the asked "Rate the importance of knowledge gained that will advance your current research", 14 said that it was extremely important and 11 others said that it was very important. Also when asked "Overall, how satisfied were you with the opportunities to collaborate", 17 (59%) said they were extremely satisfied.
