Final Report Summary - CRISP (Collaborative Research in Structure Preservation)
The goal of this project was to reinforce an existing collaboration between three European research groups and two Third country groups in the field of structure preserving numerical methods and highly oscillatory problems. The Third country partners are La Trobe University, Melbourne, Australia and Massey University, Palmerston North, New Zealand. The European beneficiaries are two Norwegian universities (NTNU, Trondheim and University of Bergen) and the University of Cambridge, UK.
The main objective of our research is to develop numerical methods which exactly preserve some important geometric structure in the physical model under consideration. Typically this could mean the preservation of symplecticity in Hamiltonian systems, or the preservation of volume in divergence free systems. Geometric properties are very important in the modeling of physical and engineering systems and the potential impact of these structure preserving methods on applied fields is significant. To facilitate this impact, we are currently working together with non-academic partners to enable the use of the produced mathematical results in the innovation of software tools.
The research teams involved in this exchange programme have gained considerable expertise in complementary subfields of geometric numerical integration in the last two decades, and in particular Lie group methods (UiB, Cambridge, NTNU), structure preserving splitting methods (Massey, LaTrobe) and methods for highly oscillatory problems (Cambridge).
The exchange enabled a transfer of knowledge between the groups including training of early stage researchers. This led to the solution of challenging theoretical and practical problems in the structure preserving numerical solution of differential equations. Ideas for new research endeavors emerged form this project, which have led to planning of new joint research.
The main objective of our research is to develop numerical methods which exactly preserve some important geometric structure in the physical model under consideration. Typically this could mean the preservation of symplecticity in Hamiltonian systems, or the preservation of volume in divergence free systems. Geometric properties are very important in the modeling of physical and engineering systems and the potential impact of these structure preserving methods on applied fields is significant. To facilitate this impact, we are currently working together with non-academic partners to enable the use of the produced mathematical results in the innovation of software tools.
The research teams involved in this exchange programme have gained considerable expertise in complementary subfields of geometric numerical integration in the last two decades, and in particular Lie group methods (UiB, Cambridge, NTNU), structure preserving splitting methods (Massey, LaTrobe) and methods for highly oscillatory problems (Cambridge).
The exchange enabled a transfer of knowledge between the groups including training of early stage researchers. This led to the solution of challenging theoretical and practical problems in the structure preserving numerical solution of differential equations. Ideas for new research endeavors emerged form this project, which have led to planning of new joint research.