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Welcome to the Division of Computational Mathematics

 

 

Ariane45
Flows with Shocks

San Andreas Fault Aerial View

Wave propagation and Earthquakes

Tacoma50
Fluid Structure Interaction

Heatcond49
Conjugate Heat Transfer

Computational mathematics is the branch of applied mathematics that develops and analyses numerical methods and algorithms for the solution of mathematical problems mainly from science and engineering. Important topics are well-posedness of the governing partial differential equations and convergence of the related numerical approximation. Topics such as accuracay, stability and efficiency of the numerical approximations, software aspects and computer implementation are important. The research is directed towards the solution of time-dependent partial differential equations. A short summary of present activities is given below.

We have developed high order accurate and stable finite difference methods and improved the boundary treatment of finite volume methods. Another line of work deals with the development and implementation of boundary conditions for the Euler and Navier-Stokes equations. Future applications will include more coupled multi-physics problem. We are interested in well posedness for multiple equations sets as well as stable numerical coupling procedures. 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.

The research discussed above is done in collaboration with NASA Langley Research Center, Stanford University, San Diego State University and Southern Methodist University in USA, the Council for Scientific and Industrial Research (CSIR) in South Africa, the Swedish Defence Research Agency (FOI) and the Swedish Meteorological and Hydrological Institute (SMHI) in Sweden.

The base funding is from Linköping University while the external research is funded by Swedish Research Council, SMHI and the European Union FP7 projects IDIHOM and UMRIDA.

We teach at a number of programs at the Institute of Technology and the Faculty of Educational Sciences.

The division has five professors (three of them are emeritus and one adjunct), one senior lecturer, one assistant lecturer and 8 graduate students.

Read more about our research on the Research page and

http://www.liu.se/forskning/forskningsnyheter/1.456133?l=en

http://www.liu.se/forskning/forskningsnyheter/1.492990?l=en

 

NEWS

  • (17-09-20) Jan Nordström gave the talk “Energy Stable Boundary Conditions for the Nonlinear Incompressible Navier-Stokes Equations” at Naval Postgraduate School in Monterey, USA on August 29 and at Stanford University in Palo Alto, USA on September 1.
  • (17-07-04) Fatemeh Ghasemi and Jan Nordström visited the ECCOMAS conferences COUPLED PROBLEMS 2017  and UNCECOMP 2017 during  12-17 June in Rhodos Greece. Fatemeh  gave the talk "On coupling of the compressible and incompressible Navier-Stokes equations”  and Jan gave the talk “STOCHASTIC GALERKIN PROJECTION AND NUMERICAL INTEGRATION FOR STOCHASTIC SYSTEMS OF EQUATIONS”.
  • (17-04-02) Jan Nordström visited the conference HONOM 17 March 27-31 in Stuttgart. He gave the talk "Energy Bounded and Stable Boundary Conditions for the Nonlinear Incompressible Navier-Stokes Equations”.
  • (17-03-06) Jan Nordström visited  Rensselaer Polytechnic Institute March 07-09. He gave the talk "A Roadmap to Well Posed and Stable Problems in Computational Physics”
  • (17-03-06) Jan Nordström visited SIAM CSE 2017 in Atlanta Georgia USA February 27-March 03. He gave the talks  "Improved Numerical Performance Using the SBP-SAT Technique as the Main Building Block" and "Coupling Requirements for Multi-Physics Problems"
  • (16-12-18) Fatemeh Ghasemi Zinatabadi visited the conference 29th Nordic Seminar on Computational Mechanics on Chalmers 26-28 October and gave the talk WELL POSED, STABLE AND ACCURATE FORMULATIONS FOR THE COUPLING OF AN INCOMPLETELY PARABOLIC SYSTEM WITH A HYPERBOLIC SYSTEM
  • (16-11-08) Jan Nordström visited ICME, Stanford University October 31-November 04, 2016 and gave the seminar  A Roadmap to Well Posed and Stable Problems in Computational Physics in the course CME500.
  • (16-10-21) Oskar Ålund visited the workshop Scientific Computing in Sweden 2016 in Uppsala 19-20 October and participated in the poster session with the poster Summation-by-Part Approximations and Domain Decomposition
  • (16-10-21) Jan Nordström visited the conference EASN 2016 in Porto 17-21 October  and gave the talk New Developments for Initial Boundary Value Problems involving Multi-physics at Linköping University
  • (16-10-21) Jan Nordström visited UMRIDA - Uncertainty Management for Robust Industrial Design in Aeronautics workshop 20-22 September 2016 in Bryssel
  • (16-10-21) Jan Nordström visited Center for Turbulence Research, Stanford University June 26-July 22, 2016 and participated in the 2016 Summer Research Program
  • (16-10-21) Andrea Ruggiu visited the conference ECCOMAS 2016 on Crete 5-10 June and gave the talk A MULTIGRID FORMULATION FOR FINITE DIFFERENCE METHODS ON SUMMATION-BY-PARTS FORM
  • (16-10-21) Jan Nordström visited the conference ECCOMAS 2016 on Crete 5-10 June and gave the talk IMPROVED DUAL TIME–STEPPING BY USING SECOND DERIVATIVES
  • (16-04-06) Markus Wahlsten and Jan Nordström visited the conference SIAM UQ 2016 in Lausanne  5-8 April.
    Markus gave the talk "Robust Boundary Conditions for Stochastic Incompletely Parabolic and Hyperbolic Systems of Equations".
    Jan gave the talk "An Investigation of Uncertainty Effects in Mixed Hyperbolic- Parabolic Problems Due to Stochastically Varying Geometry".
  • (16-01-07) Viktor Linders and Jan Nordström visited the conference AIAA Scitech 2016 in San Diego 4-8 January. Viktor gave the lecture "Summation-by-Parts Operators with Minimal Dispersion Error for Accurate and Efficient Flow Calculations".


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Last updated: Wed Sep 20 17:28:13 CEST 2017