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Research Multiscale problems 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. Reliable numerical simulation of these problems are a great challenge in scientific computing because of the computational complexity. We have developed the Localized Orthogonal Decomposition (LOD) method for solving multiscale problems. The method comes with a rigorous error analysis without assumptions on scale separation or periodicity. It has been applied to a great variety of problems including eigenvalue problems, evolution problems, network models and systems of partial differential equations. Fibre network models Numerical simulation of fibre networks modelling paper is important in the paper making industry. We develop multiscale methods for efficient simulation mechanical properties of paper using a network model. The aim is to perform large scale simulations on realistic fibre network models of paper and to consider non-linear effects such as breaking of fibres. This project is done in collaboration with Fraunhofer Chalmers Centre. Multiphysics problems Engineering applications that involves different kinds of physics (multi-physics) are computationally challenging. Reliability and efficiency is 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. Uncertainty quantification In engineering applications it is common that the data is given by experimental measurements or even that data is missing in some regions. It is natural to model this lack of exact information using a probabilistic representation of the data. We develop efficient methods for forward sensitvity analysis of partial differential equations with uncertainty in the data. Past and present members of the group Associated senior researchers Gustav Kettil, FCC, 2019- (part time) Fredrik Hellman, University of Gothenburg, 2018-2022 (part time) Postdocs Johan Wärnegård, Chalmers, 2025- Moritz Hauck, University of Gothenburg, 2023-2024, now at University of Karlsruhe Roland Maier, University of Gothenburg, 2020-2021, now at University of Karlsruhe Siyang Wang, Chalmers, 2017-2019, now at Umeå University Efthimios Karatzas, University of Gothenburg, 2016-2017, now at University of Thessaloniki Tony Stillfjord, University of Gothenburg, 2015-2017, now at Lund University Patrick Henning, Uppsala University, 2013-2014, now at Ruhr University of Bochum Ph.D. students (main supervisor) Lucia Swoboda, University of Gothenburg, 2024- Malin Mosquera, University of Gothenburg, (lic), 2019- Morgan Görtz, Chalmers/FCC, (lic,phd), 2019-2024, now at FCC Per Ljung, Chalmers, (lic,phd), 2018-2023, now at Saab Gustav Kettil, Chalmers/FCC, (lic,phd), 2014-2019, now at FCC Anna Persson, Chalmers, (lic,phd), 2013-2018, now at Uppsala University Fredrik Hellman, Uppsala University, (lic,phd), 2012-2017, now at Elekta Daniel Elfverson, Uppsala University, (lic,phd), 2011-2015, now at FOI M.Sc. students Luigi Romano, University of Gothenburg, (msc), 2023 now at NTNU Trondheim Eric Lindström, University of Gothenburg, (msc), 2021 now at University of Gothenburg Andrea Bertl, University of Gothenburg, (msc), 2021, now at GP Joule Oskar Eklund, Chalmers, (msc), 2020, now at Evolution gaming Per Ljung, Chalmers, (msc), 2018, now at Saab Tim Keil, University of Gothenburg, (msc), 2017, now at TNG Munich Robert Forslund, Chalmers, (msc), 2015, now at Silex Daniel Elfverson, Uppsala University, (msc), 2010, now at FOI Klas Pettersson, Uppsala University, (msc), 2010, now at Ericsson Yang Zeng, Uppsala University, (msc), 2009, now at Huawei External funding sources Co-authors Fredrik Edelvik, Fraunhofer Chalmers Centre, Sweden Daniel Elfverson, FOI, Sweden Donald Estep, Simon Fraser University, Canada Fritjof Fagerlund, Uppsala University, Sweden Emmanuil Georgoulis, NTU Athens, Greece/Heriot-Watt University, UK Victor Ginting, University of Wyoming, USA Morgan Görtz, Fraunhofer Chalmers Centre, Sweden Moritz Hauck, University of Karlsruhe, Germany Fredrik Hellman, Elekta, Sweden Patrick Henning, University of Bochum, Germany Michael Holst, University of California at San Diego, USA Max Jensen, University College London, UK Tim Keil, TNG Technology Consulting, Germany Gustav Kettil, Fraunhofer Chalmers Centre, Sweden Annika Lang, Chalmers, Sweden Mats G. Larson, Umeå University, Sweden Stig Larsson, Chalmers, Sweden Per Ljung, Saab, Sweden Anders Logg, Chalmers, Sweden Roland Maier, University of Karlsruhe, Germany Andreas Mark, Fraunhofer Chalmers Centre, Sweden Malin Mosquera, University of Gothenburg, Sweden Auli Niemi, Uppsala University, Sweden Anna Persson, Uppsala University, Sweden Daniel Peterseim, University of Augsburg, Germany Michael Presho, Southeast Missouri State University, USA Luigi Romano, NTNU, Norway/Linkökping, Sweden Tony Stillfjord, Lund University, Sweden Simon Tavener, Colorado State University, USA Barbara Verfürth, University of Bonn, Germany Siang Wang, Umeå University, Sweden Erdös number: 4, e.g. through: Erdös - Faber - Manteuffel - Holst - Målqvist Research related assignments Associate Editor BIT Numerical Mathematics Links Mathematisches Forschungsinstitut Oberwolfach Department of Information Technology at UU Hausdorff research institute for mathematics Swedish Foundation for Strategic Research Knut and Alice Wallenberg Foundation Department of Mathematics at UCSD My place in the global academic tree Department of Mathematics at CSU Göran Gustafsson Foundation BIT Numerical Mathematics Fraunhofer Chalmers Centre Swedish Research Council