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Structure Preserving Algorithms for Differential Equations - Applications, Computing, Education

Awarded: NOK 10.0 mill.

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 structu re 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 mo re 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 time 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 nationa lly and internationally, these research activities have evolved partly disjoint. For application areas, there is a huge potential in strengthening the interaction and exchange of ideas amongst these groups as well as 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 com bination 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 (Schroedinger, Yang-Mills, Einstein Field Equations ), will enable this group to pursue challenging and novel computational problems in the application areas, and advance research and applications of Structure Preserving Algorithms into new territories.

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