Global collaboration boosts research in preserving structures
The field of geometric numerical integration can benefit significantly from international partnerships and knowledge exchange. In-depth knowledge of geometric properties is crucial for modelling physical and engineering systems, and could be furthered through better structure preserving methods. To this end, the EU-funded CRISP (Collaborative research in structure preservation) project strengthened collaboration among three European research groups in the field and two other groups outside Europe. Specifically, two Norwegian universities in Trondheim and Bergen, along with the University of Cambridge in the United Kingdom, collaborated with La Trobe University in Australia and Massey University in New Zealand on the project. Together, the consortium worked on developing numerical methods to preserve some important geometric structures in the physical model under consideration. Topics examined include preserving the symplecticity in Hamiltonian systems and preserving volume in divergence-free systems. To achieve its aims, the project team conducted staff exchanges to advance the use of its mathematical results in innovating software tools. It gained in-depth know-how in complementary subfields of geometric numerical integration, particularly with respect to Lie group methods, structure preserving splitting methods and methods for highly oscillatory problems. The resulting knowledge transfer among the project partners and affiliated researchers in training helped overcome challenging theoretical and practical problems in the structure preserving numerical solution of differential equations. This has led to new joint research initiatives, paving the way to a better understanding of structure preservation. The success of the project and its emerging results will undoubtedly contribute to reinforcing science fields that depend on structure preservation, not only within the European Research Area (ERA) but abroad as well.
Keywords
Physics, engineering, geometric numerical integration, structure preservation, symplecticity, Hamiltonian systems
