Abstract
Internationally, scientists and policy makers are making an effort to come up with strategies to combat climate change and mitigate its effects. To this end, many climate studies are using numerical simulation to explore future climate trajectories. Climate models are complex systems governed by non-linear, coupled partial differential equations (PDEs). Due to the non-linearity, changes in parameter values can drastically alter the climate. Bifurcation analysis maps all possible solutions of non-linear equations in function of their parameters. It can be used to identify tipping points: critical thresholds that, when crossed, lead to large (and often irreversible) qualitative changes in the climate. Identifying tipping points is highly relevant in today's rapidly changing climate. Until recently, the climate models considered in the study of tipping points assumed that the dynamical systems driving the climate are smooth, i.e., the right-hand sides have continuous first and second derivatives. However, this assumption is only partially valid. In the area of numerical bifurcation analysis of large-scale non-smooth systems, there are still many open questions. No numerical methods are currently available. This project aims to develop novel numerical subspace methods to solve the complementarity and similar systems of equations that describe non-smooth dynamics. This will allow the generation of numerical bifurcation diagrams of complex systems of PDEs with non-smooth behaviour.
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