Differential equations and numerical analysis (DNA)

Differential equations and numerical analysis (DNA)

Simulation of Kelvin-Helmholtz instability. Figure.
Simulation of Kelvin-Helmholtz instability

The DNA group works in the following areas:

Partial differential equations can be used to model phenomena such as gas flow through a pipeline or in porous media, water waves over an ocean or stock prices. Since Isaac Newton's initial studies, this field has witnessed an enormous development, and today practically all laws of nature are expressed in terms of differential equations. Central questions include whether there exists a solution of the equation; whether it is unique; and whether it is stable with respect to initial or boundary data.

Numerical methods of differential equations approximate the solution of a differential equation in a way suitable for implementation on computers. Thanks to advances in the field of numerical methods the past few decades, we have gotten better weather forecasts, safer cars and air planes, and we can predict the impact of tsunamis before they hit the shore.

Optimization theory covers problems where the main interest lies in finding the smallest or largest possible values of a function, given certain conditions. Such problems appear in a large number of physical models (such as minimal energy or entropy principles); medical or geophysical measurements (such as parameter identification or inverse problems); and improvements in the performance of technical or other systems (such as shape optimization).

We also teach a number of courses and offer project and master theses in the above areas.

Contact

Contact

Espen Robstad JakobsenProfessor Espen Jakobsen, head of the DNA group.

 

Recent publications

Recent publications

Current projects

Current projects

Current DNA Projects (alternative)

Joint Training on Numerical Modelling of Highly Flexible Structures for Industrial Applications is a European Training Network project funded by EU's Horizon 2020 programme. The project period is 2019–2023 and the contact at NTNU is Elena Celledoni.

Wave Phenomena and Stability – a Shocking Combination is funded through a FRIPRO Young Research Talent grant, featuring Katrin Grunert as the principal investigator.

Challenges in Preservation of Structure (CHiPS) is a EU Horizon 2020 project that will address challenges in preservation of structure for the numerical solution of evolutionary problems. The scientific innovations of the project will be incorporated into usable software tools in cooperation with our non-academic partner MathWorks.

The main goal of Waves and Nonlinear Phenomena (WaNP) is to analyze the interplay of singularities and nonlocal effects in the solutions of partial differential equations that model wave phenomena.

Funded by FRIPRO Toppforsk, 2015–2021.

The main purpose of Structure Preserving Integrators, Discrete Integrable Systems and Algebraic Combinatorics (SPIRIT) is to develop and analyse specially tailored numerical methods for approximating the solution to differential equations.

The work is focused on numerical methods which retain selected qualitative properties of the exact solution. The SPIRIT project runs from 2013 to 2020.

Completed Projects