Advances and Perspectives on Numerical Methods for Saddle Point Problems (09w5101)

Objectives

The primary objective of this workshop is to address and discuss the most recent advances in saddle point research and identify emerging new directions and applications. For example, saddle point problems in optimal flow control present new issues and have received much attention over the last few years: the contraints (forward problems) are partial differential equations whose numerical solution is a challenge by itself. Another example are multiphysics problems (e.g. multiphase flow or magnetohydrodynamics applications) in which several physical models of a different scale and different properties are coupled. Important numerical challenges are how to efficiently solve these problems, to what level of accuracy, and how to exploit the properties of the underlying continuous problems. More specifically, longstanding issues are: design and numerical analysis of new and robust discretization techniques, singularity detection and resolution, treatment of ill-posed inverse problems, development of preconditioners and fast iterative solvers, and implementation on parallel computing platforms for simulating large scale engineering applications.

In the proposed workshop we will bring together various experts on saddle point problems. We will invite researchers whose main areas of expertise
are mixed finite element methods, constrained optimization, and numerical linear algebra, along with practitioners from national labs who work on large scale applications. We plan to have 25 to 30 talks over the course of five days, with the goal of having enough time for informal discussions and exchange of ideas. We will aim at creating an international and diverse group of participants mainly from Europe and North America, including senior and junior researchers, students and postdoctoral fellows.