Date & Time:
Wednesday, November 7, 2012; 12:00 PM
We discuss the following problem: Given a target function on a domain, what is the Neumann data on the boundary so that its harmonic extension into the domain is the closest function to the target function in the L2 norm? For convex polygonal domains, we show that regularization is not needed in case the space for the Neumann data is chosen properly. In the second part of the talk we discuss solvers for the associated discrete Hessian which are robust with respect to regularization parameters and mesh sizes.
Prof. Marcus Sarkis
Worcester Polytechnic Institute
Marcus Sarkis is a professor of the Department of Mathematical Sciences at the Worcester Polytechnic Institute (WPI) and of the Instituto de Matematica Pura e Aplicada (IMPA-Brazil). Prof. Sarkis conducts research on the design, analysis, and implementation of fast parallel algorithms for the numerical solution of large systems of equations. In 1995 he received a National Science Foundation CAREER Award. He has over 60 peer-reviewed publications and conference papers and more than 70 invited presentations. He holds an MS in mathematics from Pontificia Universidade Catolica do Rio de Janeiro, Brazil and a PhD in mathematics from the Courant Institute of Mathematical Sciences at New York University.