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| Multiphysics problems Engineering applications that involves different kinds of physics (multi-physics) are very computationally challenging. As computers get more and more powerful, complicated coupled systems of non-linear partial differential equations can be solved on parallel machines. As a result of this development much more complex physical phenomena can be analyzed by computational means. Reliability and efficiency becomes crucial when solving these problems. Reliability comes down to a need for bounds of the error between the computed approximation and the exact solution, and efficiency is achieved by designing adaptive algorithms that distributes the computational effort where it is most needed. This work is done in collaboration with Prof. Michael Holst University of California at San Diego, Prof. Mats G. Larson and Dr. Robert Söderlund Umeå University, and Dr. Max Jensen Durham University. This project is supported by the Swedish Research Council and the Göran Gustafsson foundation. |
| Multiscale problems Multiscale problems are some of the greatest challenges in computational mathematics today. In all branches of the engineering sciences we encounter problems with features on several different scales. A typical example is simulations in a heterogenous media where material data such as module of elasticity, conductivity or permeability, varies in space over several different scales. In order to solve these problems efficiently we propose an adaptive multiscale method where the critical parameters of the method are chosen automatically through an adaptive algorithm. This work is done in collaboration with Prof. Mats G. Larson at Umeå University and Dr. Robert Söderlund at Umeå University, Dr. Daniel Peterseim Humboldt University, Reader Emmanuil Georgoulis at University of Leicester, and Ph.D. candidate Daniel Elfverson at Uppsala University. This project is supported by the Swedish Research Council and the Göran Gustafsson foundation. |
| A posteriori error analysis for finite element methods Error estimation in numerical simulation is a very important field of research since it shows how reliable the computation is. In a posteriori error analysis the approximate solution is used in order to compute a sharp bound of the true error of the simulation. An additional advantage of a posteriori error estimation is that the estimates can be used to improve the solution in an automated way using an adaptive algorithm. The solution is typically improved by refining the computational mesh or decreasing the time steps, but it can also be improved by improving the representation of the geometry, the data, or the numerical quadrature used in the finite element method. This work is done in collaboration with Prof. Mats G. Larson at Umeå University and Dr. Klas Pettersson at Narvik University College. |
| Uncertainty quantification In engineering applications it is very common that the data is given by experimental measurements. It is therefore associated with measurement errors. It is natural to model these errors using a probabilistic representation of the data. We develop efficient methods for forward sensitvity analysis of partial differential equations with uncertainty in the data. We present error estimates taking into account both the numerical and the statistical error e.g. when approximating the cumulative distribution function of a quantity of interest using numerical techniques. This work is done in collaboration with Prof. Donald Estep, Prof. Simon Tavener, and Dr. Michael Presho Colorado State University, and Ass. Prof. Victor Ginting University of Wyoming. This project is supported by the Swedish Research Council. |
Supervision
Ph.D. candidates
Sven-Erik Ekström, Uppsala University, 2011- (advisor)
Daniel Elfverson, Uppsala University, 2011- (principal advisor)
Robert Söderlund, Umeå University, (pdf), 2007-2011 (advisor)
M.Sc. candidates
Daniel Elfverson, Uppsala University, (pdf), 2010 (principal advisor)
Klas Pettersson, Uppsala University, (pdf), 2010 (principal advisor)
Yang Zeng, Uppsala University, (pdf), 2009 (principal advisor)
Grants/awards
Principal (and single) investigator for the VR grant "Computational methods and uncertainty quantification for porous media flow problems", 2012-2015
Investigator (PI: Mats G. Larson) for the VR grant "Adaptive finite element methods for multiphysics-multiscale problems", 2011-2013
Principal (and single) investigator for the Göran Gustafsson prize for young researchers, 2008-2011
Investigator (PI: Mats G. Larson) for the VR grant "Adaptive finite element methods for multiphysics-multiscale problems", 2008-2010
Co-authors
Donald Estep, Colorado State University, USA
Victor Ginting, University of Wyoming, USA
Michael Holst, University of California at San Diego, USA
Mats G. Larson, Umeå University, Sweden
Michael Presho, Colorado State University, USA
Robert Söderlund, Umeå University, Sweden
Simon Tavener, Colorado State University, USA
Erdös number: 4, e.g. through: Erdös - Faber - Manteuffel - Holst - Målqvist
Links
Department of Mathematics at Chalmers
My place in the global academic tree
Department of Mathematics at UCSD
Department of Mathematics at CSU
ENUMATH 2009 conference