Outcome of Carnegie/Caledonian PhD Scholarships round 2020
Project Title: Efficient numerical algorithms for the Schrödinger-Poisson system with applications in cosmology
The Schrödinger-Poisson system (SPS) is a nonlinear model used in Cosmology to model the aggregation of mass in the Universe during the formation of galaxies. It is known to have solutions with sharply localised features, corresponding to sheets, filaments and clusters of high mass concentration. From a computational point of view, approximating these features is extremely demanding, especially in two and three spatial dimensions. This project will lead to a new generation of numerical solvers for the SPS, making two- and three-dimensional computations practical. These advances are expected to drive the construction of adaptive algorithms, i.e., numerical solvers using nonuniform meshes, which automatically become finer in the regions of mass concentration. Thus, they will be able to resolve the localised features without performing unnecessarily detailed computations over empty space.
This procedure will make possible the practical simulation of the SPS in higher spatial dimensions for the first time, opening the way for realistic cosmological applications in particular. Our algorithms and simulations will provide powerful new tools to cosmologists for their study of galaxy formation.
Awarded: Research Incentive Grant
Field: Applied Mathematics & Theoretical Physics
University: University of Dundee