Mathematician Dr. Martin Stoll awarded with Richard von Mises Prize
Models based on partial differential equations (PDE) play an important role throughout mathematics, engineering, and life sciences. The solution of forward models has been a core problem in numerical analysis for the past decades. With mathematical and algorithmic advances more challenging tasks could be tackled and much research has been devoted to compute 'optimal setups' of the governing equations. In many applications it is of paramount importance to compute the parameters, forcing terms, etc. of the PDE that best match measured data or describe a desired behaviour. Such problems are often formulated as optimization problems with PDE-constraints.
This field has seen much progress over the last years in terms of a better understanding of the mathematical structures and correspondingly the development of efficient numerical techniques to solve these problems. Martin Stolls field of interest is the solution of the linear systems that are often the computational bottleneck of the optimization procedure. This can be either representing the first order conditions or as part of a nonlinear outer solver such as Newton's method. The approach of the group follows a strategy where they solve the system in a monolithic manner, i.e., discretizing in space and time and then solving a large space-time linear system. It is in many cases possible to derive efficient preconditioners for these systems in saddle point form.
Nevertheless, the problems suffer from the curse of dimensionality, which means that refining spatial or temporal dimensions will result in an exponential increase of the matrix dimensions and thus the computational effort. To break this curse Martin Stolls group introduces a low-rank in time approach that utilizes the structure of the linear system and allows the solution of a parabolic problem at only a small multiple of the cost of the steady state problem. With recent progress made in the field of tensor solvers, Martin Stoll further shows how this approach extends to tasks with an even higher dimensionality such as problems with uncertain coefficients.
Martin Stoll received his diploma in mathematics from Technical University Chemnitz in 2005. From 2005 to 2008 he obtained his PhD degree in the Numerical Analysis Group of Prof. Andrew Wathen at the University of Oxford. In 2008 he joined the OCCAM Centre for Applied Mathematics at the University of Oxford as a postdoctoral researcher. In 2010 he joined the Max Planck Institute Magdeburg as a postdoctoral research fellow at the CSC group of Prof. Peter Benner. The Max Planck research group Numerical Linear Algebra for Dynamical Systems (W2 MPG research group), headed by Dr. Martin Stoll, was established in August 2013 at MPI Magdeburg. Furthermore, Martin Stoll committs himself as a member of three GAMM Activity Groups and as a Faculty Advisor of the SIAM Student Chapter (Society for Industrial and Applied Mathematics SIAM).
Since 1989, the Richard von Mises Prize is awarded every year by GAMM to a scientist for exceptional scientific achievements in the field of Applied Mathematics and Mechanics. In 2016 the prize will be awarded to Dr. Martin Stoll (MPI Magdeburg) and Jun.-Prof. Dr.-Ing. Josef Kiendl (TU Braunschweig).
Richard von Mises was an Austrian-American mathematician who worked among others on numerical mathematics, solid mechanics, fluid mechanics, statistics and probability theory.