Department of Information Technology

I am a PhD student in numerical analysis at the Centre for Interdisciplinary Mathematics (CIM) and Division of Scientific Computing. I am working on a research project on computer simulation of geologic carbon dioxide sequestration processes. My focus is on a few aspects of such a simulation. First, methods for uncertainty quantification of quantities achieved from such a simulation, e.g., capacity of a reservoir. Second, methods for multi-scale treatment of the multi-phase flow problem that arises when modeling the sequestration process.

My principal supervisor is Docent Axel Målqvist at Department of Mathematical Sciences, University of Gothenburg, and my two co-supervisors Prof. Auli Niemi and Docent Fritjof Fagerlund are at the Program for Air, Water and Landscape Sciences, Uppsala University.

Research

Publications

  • F. Hellman and A. Målqvist, Contrast independent localization of multiscale problems, submitted, arXiv
  • F. Hellman, P. Henning, and A. Målqvist, Multiscale mixed finite elements, Discrete and Continuous Dynamical Systems - Series S (DCDS-S), 9(5), 2016, pp. 1269-1298, doi
  • F. Fagerlund, F. Hellman, A. Målqvist, and A. Niemi, Multilevel Monte Carlo methods for computing failure probability of porous media flow systems, Advances in Water Resources, 94, 2016, pp. 498-509.
  • D. Elfverson, F. Hellman, and A. Målqvist, A multilevel Monte Carlo method for computing failure probabilities, SIAM/ASA J. Uncertainty Quantification, 4(1), 2016, pp. 312-330, doi
  • D. Elfverson, D. J. Estep, F. Hellman, and A. Målqvist, Uncertainty quantification for approximate p-quantiles for physical models with stochastic inputs, SIAM/ASA J. Uncertainty Quantification, 2(1), 2014, pp. 826-850, doi
  • H. Bar-Gera, F. Hellman, and M. Patriksson, Computational precision of traffic equilibria sensitivities in automatic network design and road pricing, Transportation Research Part B: Methodological, 57, 2013, pp. 485-500, doi

Presentations

  • European Finite Element Fair 2016, Bonn, Germany, 2016-05-20, Fast decay of corrected basis functions
  • SIAM UQ 16 conference, Lausanne, Switzerland, 2016-04-06, Multilevel Monte Carlo methods for computing failure probability
  • Chemnitz FEM Symposium, Burgstädt, Germany, 2015-09-29, Mixed multiscale finite elements
  • Licentiate seminar, Uppsala, Sweden, 2015-09-25, Multiscale and Multilevel Methods for Porous Media Flow Problems
  • SIAM GS 15 conference, Stanford University, CA, US, 2015-07-01, Monte Carlo methods for failure probabilities - Using error bounds to reduce costs
  • Seminar, INS, University of Bonn, Bonn, Germany, 2015-05-07, A multilevel Monte Carlo method for failure probabilities
  • Numerical Analysis Seminar, Kungliga Tekniska högskolan (KTH), Sweden, 2014-10-30, A multilevel Monte Carlo method for failure probabilities
  • Seminar, Centre for Interdisciplinary Mathematics, Uppsala University, Sweden, 2014-10-21, A mixed finite element multiscale method for Poisson's equation
  • Oberseminar Angewandte Mathematik, University of Münster, Münster, Germany, 2014-09-04, A multilevel Monte Carlo method for failure probabilities
  • SIAM UQ 14 conference, Savannah, GA, USA, 2014-03-31, Quantile bounds for numerical models with data uncertainty
  • Seminar, Centre for Interdisciplinary Mathematics, Uppsala University, Sweden, 2013-05-14, Quantile estimation for numerical solution of stochastic PDEs

Visits

  • Attending SIAM UQ 16 conference, Lausanne, Switzerland, 5th Apr - 8th Apr 2016, presentation 2016-06-04 (see above)
  • Attending Chemnitz FEM Symposium, Burgstädt, Germany, 28th Sep - 30th Sep 2015
  • Attending SIAM GS 15 conference, Stanford University, CA, USA, 29th Jun - 2nd Jul 2015
  • Visiting INS, University of Bonn, Bonn, Germany, 4th May - 8th May 2015
  • Visiting SINTEF, Oslo, Norway, 8th Dec - 12th Dec 2014
  • Attending International Conference on Numerical and Mathematical Modeling of Flow and Transport in Porous Media, Dubrovnik, Croatia, 29th Sep - 3rd Oct 2014, poster presentation 2014-09-30 (pdf)
  • Visiting University of Münster, Münster, Germany, 3rd Sep - 5th Sep 2014, presentation 2014-09-04 (see above)
  • Attending SIAM UQ 14 conference, Savannah, GA, USA, 31st Mar - 3rd Apr 2014, presentation 2014-03-31 (see above)
  • Attending SIAM GS 13 conference, Padova, Italy, 17th Jun - 20th Jun 2013
  • Visiting Colorado State University, Fort Collins, CO, USA, 1st Oct - 10th Oct 2012

Co-authors and collaborators

Daniel Elfverson, Donald Estep, Fritjof Fagerlund, Patrick Henning, Axel Målqvist, Auli Niemi

Teaching

  • Scientific Computing I (W1B), Uppsala University, P4 2016
  • Scientific Computing I (K1B), Uppsala University, P3 2016
  • Scientific Computing I (K1A, X1A), Uppsala University, P3 2015
  • Scientific Computing I (K1A), Uppsala University, P3 2014
  • Scientific Computing I (F1AB), Uppsala University, P2 2013
  • Scientific Computing I (F1AB), Uppsala University, P2 2012
Updated  2017-01-05 22:50:53 by Fredrik Hellman.