The network is focused on the synergetic interplay of modelling, analysis and large-scale computer simulations based on advanced mathematical methods towards understanding and solving real life problems.
The innovative training network (ITN) entitled Modelling and Computation of Shocks and Interfaces will focus on the training of young researchers (ESRs) in the general area of nonlinear hyperbolic and convection dominated PDEs (HCD-PDEs), with emphasis on innovative modelling and computational methods. Computational and Applied Mathematics is a driving force in the current development of multiple fields of science from physics and engineering to biology and medicine. In the future, we are poised to also experience an increasing relevance of related concepts even to modelling and simulation of social and economic behaviour patterns.
The synergetic interplay of modelling, analysis and large-scale computer simulations based on advanced mathematical methods plays a prominent role in this effort.
The research program of the network is centered on an important field (in terms of both history and scope), that is placed at the forefront of modern Computational and Applied Mathematics.
In fact, the field of HCD-PDEs has the following characteristics:
• models originate from the need to describe important physical phenomena of technological relevance;
• a plethora of highly influential analytical methods has been developed to study these models;
• pioneering and advanced computational methods were designed to approximate HCD-PDEs, with regard to singular solutions such as shocks, phase transitions, propagating interfaces.
Physical modelling, analytical approaches, and advanced computational methods are interlinked in the field of hyperbolic and convection dominated PDEs.
This has rendered this field eminently suitable for training young researchers.
It has always been very quick to adopt and explore new ideas in analysis, or novel numerical methods, and of course requires very good understanding of modelling.
The ERS's will be trained in a wide inter-disciplinary area and can become research leaders as well as impact both industry and non-academic scientific institutions.