Structure preserving algorithms for differential equations are discrete computational methods coined at exactly preserving important geometric or analytic properties of the continuous physical system. Over the last decade, the importance of exact structure preservation has been understood in a variety of application areas.

There are a number of computational problems where such algorithms are essential to a successful solution, and still a larger number where structure preserving algorithms outperform more classical methods due to better accuracy under long term simulations.

In Norway, three research groups have been in the international forefront in these developments. The groups at NTNU (Trondheim) and UiB (Bergen) have developed novel geometric integration schemes based on Lie Group techniques, while the UiO (Oslo) group together with international co-workers, has developed compatible space discretization (finite element) methods based on exterior differential calculus.

However, both internationally and nationally, these research activities have evolved partly disjoint. For application areas there is a huge potential in strengthening the bonds to physicists and mathematicians working on large scale simulations from physics and engineering. Through this project a strong international group consisting of the three Norwegian groups and a selected group of international participants is formed.

The unique combination of expertise in time- and space discretization together with strong connections to various application areas, such as fluid mechanics, elasticity and important equations of mathematical physics (Schrödinger, Yang-Mills, Einstein Field Equations), will enable this group to pursue challenging computational problems in the application areas, and advance research and application of structure preserving algorithms into new territories.