Elisabeth Ullmann

Elisabeth Ullmann (b. 1979) conducts research on mathematical methods of uncertainty quantification using tools from numerical analysis, data science and computational science and engineering. The goal of her work is the design and analysis of efficient algorithms and estimators for partial differential equations with random coefficients. The current focus is on multilevel estimators, Bayesian inverse problems, and rare events.

Education

• 2002–2008 Doctorate in Mathematics (Dr. rer. nat.) at TU Bergakademie Freiberg, Germany Dissertation: Solution Strategies for Stochastic Finite Element Discretizations Rating: summa cum laude, Supervisor: Oliver G. Ernst

• 1997–2002 Diploma in Applied Mathematics (Dipl.-Math.) at TU Bergakademie Freiberg Thesis: Adaptive Finite Element Methods for Groundwater Flow Calculations (in German), Supervisor: Oliver G. Ernst

Research Interests

• Uncertainty quantification for PDE-based simulations in science and engineering • Discretizations, solvers and estimators for partial differential equations with random data – Multilevel Monte Carlo estimators – Stochastic Galerkin methods • Finite element methods, in particular mixed elements • Numerical Linear Algebra: Iterative solvers, Krylov subspace methods, Preconditioning • Estimation of rare events

Professional Experience

• July 2014 – present Research Associate at Universit¨at Hamburg
• July 2011 – June 2014 Research Associate at University of Bath
• August 2008 – June 2011 Postdoctoral Research Associate in the German Research Foundation (DFG) Priority Program 1324 “Extraction of quantifiable information from complex systems” at TU Bergakademie Freiberg
• April – September 2009 Visiting Research Associate at University of Maryland, College Park, USA
• June 2002 – July 2008 Research Associate and Teaching Assistant at the Department of Mathematics and Computer Science, TU Bergakademie Freiberg

Publications

Wagner F, Latz J, Papaioannou I, Ullmann E: “Error analysis for probabilities of rare events with approximate models”. SIAM Journal on Numerical Analysis. 2021; 59(4): 1948-1975.

Latz J, Papaioannou I, Ullmann E: “Multilevel Sequential^2 Monte Carlo for Bayesian Inverse Problems”. Journal of Computational Physics. 2018; 368: 154-178.

Ahmad Ali A, Ullmann E, Hinze M: “Multilevel Monte Carlo analysis for optimal control of elliptic PDEs with random coefficients”. SIAM/ASA Journal on Uncertainty Quantification. 2017; 5(1): 466-492

Ullmann E, Papaioannou I: „Multilevel estimation of rare events“. SIAM/ASA Journal on Uncertainty Quantification. 2015; 3(1): 922-953.

Ullmann E: “A Kronecker product preconditioner for stochastic Galerkin finite element discretizations”. SIAM Journal on Scientific Computing. 2010; 32(2): 923-946