Time-dependent partial differential equations

In my research at Linköping University, we develop numerical methods for multi-physics applications governed by partial differential equations. We consider various kinds of uncertainties in the data or parameters of the problem and aim for a computational methodology that delivers an answer with error bars.

Professional activities

Professional activities

  • Head of Computational Mathematics at the Department of Mathematics
  • Member of the board of Linköping Institute of Technology (LiTH)
  • Member of the board of the National Supercomputer Centre in Sweden (NSC)
  • Associate editor of Journal of Computational Physics (JCP), Elsevier
  • Associate editor of BIT Numerical Mathematics, Springer Verlag

Affiliations

  • Senior Research Fellow, Center for Turbulence Research, Stanford University, USA, 2009 -
  • Honorary Professor, School of Computational and Applied Mathematics, University of the Witwatersrand, South Africa, 2010 -

Research networks

  • Partner in the FP7 project UMRIDA (the European Union's Seventh Framework Programme, Uncertainty Management for Robust Industrial Design in Aeronautics)
  • Partner in the VINNOVA (Sweden's innovation agency) project MIAU
  • Member in SIAM (Society for Industrial and Applied Mathematics) and AIAA (The American Institute of Aeronautics and Astronautics)

Teaching

  • Numerical Solution of Initial Boundary Value Problems (MAI0122), 3 hp, autumn 2017, Linköping University
  • Stochastic Galerkin Methods for Partial Differential Equations (MAI0129), 5 hp, spring 2016, Linköping University
  • Selected articles on well posed problems and numerical approximation, 5 hp, autumn 2014, Linköping University
  • Numerical Solution of Initial Boundary Value Problems (MAI0122), 3 hp, autumn 2013, Linköping University
  • Short course: Numerical Methods for Initial Boundary Value Problems, spring 2013, Council for Scientific and Industrial Research (CSIR) in South Africa
  • Numerical Methods for Initial Boundary Value Problems (MAI0106), autumn 2011, Linköping University
  • Numerical Methods for Initial Boundary Value Problems (CME 326), spring 2011, Stanford University
  • Numerical Methods for Initial Boundary Value Problems (CME 326), winter 2009, Stanford University 

Related documents

Research

News items

PhD students

Former PhD students

  • Cristina La Cognata. Thesis title: High order summation-by-parts based approximations for discontinuous and nonlinear problems, 2012 - 2017. Link to thesis.
  • Hannes Frenander. Thesis title: High-order finite difference approximations for hyperbolic problems: multiple penalties and non-reflecting boundary conditions, 2012 - 2017. Link to thesis.
  • Ossian O'Reilly. Thesis title: Numerical methods for wave propagation in solids containing faults and fluid-filled fractures, (jointly with Eric Dunham Stanford University), 2011 - 2016. Link to thesis.
  • Samira Nikkar. Thesis title: Stable High Order Finite Difference Methods for Wave Propagation and Flow Problems on Deforming Domains, 2011-2016. Link to thesis.
  • Tomas Lundquist. Thesis title: High order summation-by-parts methods in time and space, 2011-2016. Link to thesis.
  • Per Pettersson. Thesis title: Uncertainty Quantification and Numerical Methods for Conservation Laws, (jointly with Gianluca Iaccarino, Stanford University), 2008-2013. Link to thesis at Uppsala University och Link to thesis at Stanford University.
  • Jens Berg. Thesis title: Stable and High-Order Finite Difference Methods for Multiphysics Flow Problems, 2008-2013. Link to thesis.
  • Kenneth Duru. Thesis title: Perfectly Matched Layers and High Order Difference Methods for Wave Equations, (Gunilla Kreiss, Uppsala University, 1st advisor), 2007-2012. Link to thesis.
  • Sofia Eriksson. Thesis title: Stable Numerical Methods with Boundary and Interface Treatment for Applications in Aerodynamics, 2007-2012. Link to thesis.
  • Sven-Erik Ekström. Thesis title (Lic): A Vertex-Centered Discontinuous Galerkin Method for Flow Problems, (Martin Berggren, Umeå University, 1st advisor), 2006-2016. Link to thesis.
  • Qaiser Abbas. Thesis title: Weak Boundary and Interface Procedures for Wave and Flow Problems, 2006-2011. Link to thesis.
  • Jing Gong. Thesis title: Hybrid Methods for Unsteady Fluid Flow Problems in Complex Geometries, 2003-2007. Link to thesis.
  • Magnus Svärd. Thesis title: Stable High Order Finite Difference Methods for Aerodynamics, 1999-2004. Link to thesis.
  • Ken Mattsson. Thesis title: Summation-by-Parts Operators for High Order Finite Difference Methods, 1997-2003. Link to thesis.

Former postdoc

Marco Kupiainen. Project: IDIHOM, InDustrIalisation of Higher Order Methods, 2011-2014. 

Publications

2017

Ossian O'Reilly, Eric M Dunham, Jan Nordström

Simulation of Wave Propagation Along Fluid-Filled Cracks Using High-Order Summation-by-Parts Operators and Implicit-Explicit Time Stepping

In SIAM Journal on Scientific Computing

Article in journal

Samira Nikkar, Jan Nordström

A fully discrete, stable and conservative summation-by-parts formulation for deforming interfaces

In Journal of Computational Physics

Article in journal

Magnus Svärd, Jan Nordström

Response to “Convergence of Summation-by-Parts Finite Difference Methods for the Wave Equation”

In Journal of Scientific Computing

Article in journal

Ken Mattsson, Jan Nordström

Corrigendum to “Summation by parts operators for finite difference approximations of second derivatives” [J.Comput.Phys.199 (2004) 503–540]

In Journal of Computational Physics

Article in journal

Sofia Eriksson, Jan Nordström

Exact Non-reflecting Boundary Conditions Revisited: Well-Posedness and Stability

In Foundations of Computational Mathematics

Article in journal

Jan Nordström, Fatemeh Ghasemi

On the relation between conservation and dual consistency for summation-by-parts schemes

In Journal of Computational Physics

Article in journal

Jan Nordström

A Roadmap to Well Posed and Stable Problems in Computational Physics

In Journal of Scientific Computing

Article in journal

Markus Wahlsten, Jan Nordström

The effect of uncertain geometries on advection–diffusion of scalar quantities

In BIT Numerical Mathematics

Article in journal

Ossian O'Reilly, Tomas Lundquist, Eric M. Dunham, Jan Nordström

Energy stable and high-order-accurate finite difference methods on staggered grids

In Journal of Computational Physics

Article in journal

Hannes Frenander, Jan Nordström

A stable and accurate relaxation technique using multiple penalty terms in space and time

In Dynamics of atmospheres and oceans (Print)

Article in journal

Mark H Carpenter, Jan Nordström, David Gottlieb

Corrigendum to “A stable and conservative interface treatment of arbitrary spatial accuracy” [J.Comput.Phys.148(1999)341–365]

In Journal of Computational Physics

Article in journal

David A. Kopriva, Jan Nordström, Gregor J. Gassner

Error Boundedness of Discontinuous Galerkin Spectral Element Approximations of Hyperbolic Problems

In Journal of Scientific Computing

Article in journal

Yann T. Delorme, Kunal Puri, Jan Nordström, Viktor Linders, Suchuan Dong, Steven H. Frankel

A simple and efficient incompressible Navier-Stokes solver for unsteady complex geometry flows on truncated domains

In Computers & Fluids

Article in journal

Viktor Linders, Marco Kupiainen, Jan Nordström

Summation-by-Parts Operators with Minimal Dispersion Error for Coarse Grid Flow Calculations

In Journal of Computational Physics

Article in journal

Jan Nordström, Andrea Alessandro Ruggiu

On conservation and stability properties for summation-by-parts schemes

In Journal of Computational Physics

Article in journal

Hannes Frenander, Jan Nordström

Spurious solutions for the advection-diffusion equation using wide stencils for approximating the second derivative

In Numerical Methods for Partial Differential Equations

Article in journal

Hannes Frenander, Jan Nordström

Constructing non-reflecting boundary conditions using summation-by-parts in time

In Journal of Computational Physics

Article in journal

2016

Per Pettersson, Jan Nordström, Alireza Doostan

A Well-posed and Stable Stochastic Galerkin Formulation of the Incompressible Navier-Stokes Equations with Random Data

In Journal of Computational Physics

Article in journal

Hannes Frenander, Jan Nordström

A Stable and Accurate Davies-like Relaxation Procedure using Multiple Penalty Terms for Lateral Boundary Conditions

In Dynamics of atmospheres and oceans (Print)

Article in journal

Jan Nordström, Tomas Lundquist

Summation-By-Parts in Time: The Second Derivative

In SIAM Journal on Scientific Computing

Article in journal

Jan Nordström, Samira Nikkar

Hyperbolic systems of equations posed on erroneous curved domains

In Journal of Computational Physics

Article in journal

Cristina La Cognata, Jan Nordström

Well-posedness, stability and conservation for a discontinuous interface problem

In BIT Numerical Mathematics

Article in journal

Irvy M.A. Gledhill, Hamed Roohani, Karl Forsberg, Peter Eliasson, Beric M. Skews, Jan Nordström

Theoretical treatment of fluid flow for accelerating bodies

In Theoretical and Computational Fluid Dynamics

Article in journal

Tomas Lundquist, Jan Nordström

Efficient fully discrete summation-by-parts schemes for unsteady flow problems

In BIT Numerical Mathematics

Article in journal

David Amsallem, Jan Nordström

Energy Stable Model Reduction of Neurons by Non-negative Discrete Empirical Interpolation

In SIAM Journal on Scientific Computing

Article in journal

2015

Ossian O’Reilly, Jan Nordström, Jeremy E. Kozdon, Eric M. Dunham

Simulation of Earthquake Rupture Dynamics in Complex Geometries Using Coupled Finite Difference and Finite Volume Methods

In Communications in Computational Physics

Article in journal

Jan Nordström, Peter Eliasson

New developments for increased performance of the SBP-SAT finite difference technique

In IDIHOM: Industrialization of High-Order Methods - A Top-Down Approach

Chapter in book

Viktor Linders, Jan Nordström

Uniformly Best Wavenumber Approximations by Spatial Central Difference Operators

In Journal of Computational Physics

Article in journal

Viktor Linders, Jan Nordström

Uniformly Best Wavenumber Approximations by Spatial Central Difference Operators: An Initial Investigation

In Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014

Chapter in book

Jan Nordström, Markus Wahlsten

Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations

In Journal of Computational Physics

Article in journal